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A sharp form of an inequality by N. Trudinger

1971-01-01
J. Moser

A nanomechanical mass sensor with yoctogram resolution

2012-04-01
Julien Chaste , Alexander Eichler , J. Moser +3 more
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Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene

2011-05-15
Alexander Eichler , J. Moser , Julien Chaste +3 more
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Rational and elliptic solutions of the korteweg‐de vries equation and a related many‐body problem

1977-01-01
Hélène Airault , H. P. McKean , J. Moser

Current-induced cleaning of graphene

2007-10-15
J. Moser , Amelia Barreiro , Adrian Bachtold
A simple yet highly reproducible method to suppress contamination of graphene at low temperature inside the cryostat is presented. The method consists of applying a current of several mA through … A simple yet highly reproducible method to suppress contamination of graphene at low temperature inside the cryostat is presented. The method consists of applying a current of several mA through the graphene device, which is here typically a few $μ$m wide. This ultra-high current density is shown to remove contamination adsorbed on the surface. This method is well suited for quantum electron transport studies of undoped graphene devices, and its utility is demonstrated here by measuring the anomalous quantum Hall effect.
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The rotation number for almost periodic potentials

1983-06-01
Randal Johnson , J. Moser
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Ultrasensitive force detection with a nanotube mechanical resonator

2013-06-09
J. Moser , J. Güttinger , Alexander Eichler +4 more
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The rotation number for almost periodic potentials

1982-09-01
Randal Johnson , J. Moser
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Geometry of Quadrics and Spectral Theory

1980-01-01
J. Moser

Various Aspects of Integrable Hamiltonian Systems

2010-01-01
J. Moser
(a) In these informal lecture notes we discuss a number of integrable Hamiltonian systems which have surfaced recently in very different connections. It is our goal to discuss various aspects … (a) In these informal lecture notes we discuss a number of integrable Hamiltonian systems which have surfaced recently in very different connections. It is our goal to discuss various aspects underlying the integrability of a system like that of group representation, isospectral deformation and geometrical considerations. Since this subject is still far from being understood or being systematic we discuss a number of examples which are seemingly disconnected. In fact, there are some rather unexpected connections like between the inverse square potential of Calogero (Section 4) and the Korteweg de Vries equation. Here we show a surprising new connection between the geodesics on an ellipsoid and Hill's equation with finite gap potential. (b) The differential equations of mechanics can be written in Hamiltonian form 1 $${{\dot x}}_{\text{k}} = \frac{{\partial {\text{H}}}}{{\partial {\text{y}}_{\text{k}} }},\,\,\,\,\,\,\,{{\dot y}}_{\text{k}} = - \frac{{\partial {\text{H}}}}{{\partial {\text{x}}_{\text{k}} }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{k = 1,2,}}...{\text{n}}} \right)$$

Nanotube mechanical resonators with quality factors of up to 5 million

2014-10-26
J. Moser , Alexander Eichler , J. Güttinger +2 more
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Transport Properties of Graphene in the High-Current Limit

2009-08-12
Amelia Barreiro , Michele Lazzeri , J. Moser +2 more
We present a detailed study of the high-current transport properties of graphene devices patterned in a four-point configuration. The current tends to saturate as the voltage across graphene is increased … We present a detailed study of the high-current transport properties of graphene devices patterned in a four-point configuration. The current tends to saturate as the voltage across graphene is increased but never reaches the complete saturation as in metallic nanotubes. Measurements are compared to a model based on the Boltzmann equation, which includes electron-scattering processes due to charged and neutral impurities, and graphene optical phonons. The saturation is incomplete because of the competition between disorder and optical phonon scattering.
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On a pointwise estimate for parabolic differential equations

1971-09-01
J. Moser

Tunneling Anisotropic Magnetoresistance and Spin-Orbit Coupling in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Fe</mml:mi><mml:mo>/</mml:mo><mml:mi>GaAs</mml:mi><mml:mo>/</mml:mo><mml:mi>Au</mml:mi></mml:math>Tunnel Junctions

2007-08-02
J. Moser , Alex Matos-Abiague , D. Schuh +3 more
We report the observation of tunneling anisotropic magnetoresistance effect (TAMR) in the epitaxial metal-semiconductor system Fe/GaAs/Au. The observed two-fold anisotropy of the resistance can be switched by reversing the bias … We report the observation of tunneling anisotropic magnetoresistance effect (TAMR) in the epitaxial metal-semiconductor system Fe/GaAs/Au. The observed two-fold anisotropy of the resistance can be switched by reversing the bias voltage, suggesting that the effect originates from the interference of the spin-orbit coupling at the interfaces. Corresponding model calculations reproduce the experimental findings very well.
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Magnetotransport in disordered graphene exposed to ozone: From weak to strong localization

2010-05-28
J. Moser , Haihua Tao , Stephan Roche +3 more
We present a magneto-transport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples … We present a magneto-transport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples exposed to ozone becomes very sensitive to temperature: it decreases by more than 3 orders of magnitude between 100K and 1K. By varying either an external gate voltage or temperature, we continuously tune the transport properties from the weak to the strong localization regime. We show that the transition occurs as the phase coherence length becomes comparable to the localization length. We also highlight the important role of disorder-enhanced electron-electron interaction on the resistivity.
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The environment of graphene probed by electrostatic force microscopy

2008-03-24
J. Moser , Albert Verdaguer , David Jiménez +2 more
We employ electrostatic force microscopy to study the electrostatic environment of graphene sheets prepared with the micromechanical exfoliation technique. We detect the electric dipole of residues left from the adhesive … We employ electrostatic force microscopy to study the electrostatic environment of graphene sheets prepared with the micromechanical exfoliation technique. We detect the electric dipole of residues left from the adhesive tape during graphene preparation, as well as the dipole of water molecules adsorbed on top of graphene. Water molecules form a dipole layer that can generate an electric field as large as ∼109Vm−1. We expect that water molecules can significantly modify the electrical properties of graphene devices.
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On a Nonlinear Problem in Differential Geometry††AMS (MOS) 1970 SUBJECT CLASSIFICATION: 53C99, 35T50.‡‡Results obtained at the Courant Institute of Mathematical Sciences, New York University, under National Science Foundation Grant NSF-GP-27719.

1973-01-01
J. Moser

On the Theory of Quasiperiodic Motions

1966-04-01
J. Moser
Next article On the Theory of Quasiperiodic MotionsJ. MoserJ. Moserhttps://doi.org/10.1137/1008035PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. I. Arnol'd, Small denominators. I. Mapping the circle onto itself, Izv. Akad. Nauk … Next article On the Theory of Quasiperiodic MotionsJ. MoserJ. Moserhttps://doi.org/10.1137/1008035PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. I. Arnol'd, Small denominators. I. Mapping the circle onto itself, Izv. Akad. Nauk SSSR Ser. Mat., 25 (1961), 21–86 MR0140699 Google Scholar[2] V. I. Arnol'd, Small denominators and problems of stability of motion in classical and celestial mechanics, Uspehi Mat. Nauk, 18 (1963), 91–192 MR0170705 Google Scholar[3] V. I. Arnol'd, Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, Uspehi Mat. Nauk, 18 (1963), 13–40 MR0163025 Google Scholar[4] N. Bogolioùboff, Sur quelques propriétés arithmétiques des presque-périodes, Ann. Chaire Phys. Math. Kiev, 4 (1939), 185–205 MR0020164 0022.33201 Google Scholar[5] N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics, Izdat. Akad. Nauk Ukrain. SSR, Kiev, 1945 Google Scholar[6] N. N. Bogoliubov and , Yu. A. Mitropolsky, The method of integral manifolds in nonlinear mechanics, Contributions to Differential Equations, 2 (1963), 123–196 (1963) MR0149036 0137.28406 Google Scholar[7] N. N. Bogoliubov, On quasiperiodic solutions in nonlinear problems of mechanics, First Mathematical Summer School, Akad. Nauk Ukrain. SSR, Kanev, 1963, 1964 Google Scholar[8] P. Bohl, Über die Darstellung von Funktionen einer Variabeln durch trigonometrische Reihen mit mehreren einer Variabeln proportionalen Argumenten, Magisterdissertation, Dorpat, 1893 Google Scholar[9] P. Bohl, Über eine Differentialgleichung der Störungstheorie, J. Reine Angew. Math., 131 (1906), 286–321 Google Scholar[10] H. Bohr, Zur Theorie der fast-periodischen Funktionen, I, II, III, Acta Math., 45, 46, 47 (1924, 1925, 1926), 29–127, 101–214, 237–281 Google Scholar[11] H. Bohr and , O. Neugebauer, Über lineare Differentialgleichungen mit konstanten Koeffizienten und fast periodischen rechter Seite, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, (1926), 8–22 Google Scholar[12A] Stephen P. Diliberto, Perturbation theorems for periodic surfaces. I. Definitions and main theorems, Rend. Circ. Mat. Palermo (2), 9 (1960), 265–299 MR0142852 0099.29402 CrossrefGoogle Scholar[12B] Stephen P. Diliberto, Perturbation theorems for periodic surfaces. II, Rend. Circ. Mat. Palermo (2), 10 (1961), 111–161 MR0142853 0109.31401 Google Scholar[13] A. N. Kolmogorov, On conservation of conditionally periodic motions for a small change in Hamilton's function, Dokl. Akad. Nauk SSSR (N.S.), 98 (1954), 527–530 MR0068687 Google Scholar[14] A. N. Kolmogorov, General theory of dynamical systems and classical mechanics, Proceedings of International Congress of Mathematics, Vol. 1, Noordhoff, Amsterdam, 1957, 315–333 Google Scholar[15] Wilhelm Maak, Fastperiodische Funktionen, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXI, Springer-Verlag, Berlin, 1950, 25–27 MR0041961 0037.05701 CrossrefGoogle Scholar[16] I. G. Malkin, Some problems of the theory of nonlinear oscillations, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956, 492– MR0081402 Google Scholar[17] J. A. Mitropolski, On the construction of quasiperiodic solutions of nonlinear differential equations by a method ensuring "rapid" convergence, Ukrain. Mat. Ž., 16 (1964), 475–501 CrossrefGoogle Scholar[18] J. Moser, A rapidly convergent iteration method and nonlinear partial differential equations, 1964, International Mathematical Summer Center, Varenna, Italy, to be published Google Scholar[19] Jürgen Moser, A new technique for the construction of solutions of nonlinear differential equations, Proc. Nat. Acad. Sci. U.S.A., 47 (1961), 1824–1831 MR0132859 0104.30503 CrossrefISIGoogle Scholar[20] Jurgen Moser, Combination tones for Duffing's equation, Comm. Pure Appl. Math., 18 (1965), 167–181 MR0179430 0136.08303 CrossrefISIGoogle Scholar[21] Thomas G. Proctor and , Raimond A. Struble, Motion of two weakly coupled nonlinear oscillators, Arch. Rational Mech. Anal., 18 (1965), 293–303 10.1007/BF00251668 MR0171974 0125.41001 CrossrefGoogle Scholar[22] R. Sacker, On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations, Comm. Pure Appl. Math., to appear Google Scholar[23] Otto Staude, Ueber eine Gattung doppelt reell periodischer Functionen zweier Veränderlicher, Math. Ann., 29 (1887), 468–485 10.1007/BF01475496 MR1510426 CrossrefGoogle Scholar[24] J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950, 235–239 MR0034932 Google Scholar[25] L. S. Pontrjagin, Topologische Gruppen. 2, B. G. Teubner Verlagsgesellschaft, Leipzig, 1958, 308–, 2d ed. MR0097456 0085.01704 Google Scholar[26] V. K. Mel'nikov, On certain cases of conservation of almost periodic motions with a small change of the Hamiltonian function, Dokl. Akad. Nauk SSSR, 165 (1965), 1245–1248 MR0201753 0143.11801 Google Scholar Next article FiguresRelatedReferencesCited ByDetails Sensitivity analysis for periodic orbits and quasiperiodic invariant tori using the adjoint methodJournal of Computational Dynamics, Vol. 9, No. 3 | 1 Jan 2022 Cross Ref Spatially Quasi-Periodic Water Waves of Infinite DepthJournal of Nonlinear Science, Vol. 31, No. 3 | 20 April 2021 Cross Ref Invariant Sets in Quasiperiodically Forced Dynamical SystemsYoshihiko Susuki and Igor MezićSIAM Journal on Applied Dynamical Systems, Vol. 19, No. 1 | 30 January 2020AbstractPDF (2922 KB)Quasiperiodic behavior in the electrodeposition of Cu/Sn multilayers: extraction of activation energies and wavelet analysisPhysical Chemistry Chemical Physics, Vol. 21, No. 37 | 1 January 2019 Cross Ref Refined betatron tune measurements by mixing beam position dataPhysical Review Accelerators and Beams, Vol. 22, No. 7 | 8 July 2019 Cross Ref A-posteriori KAM theory with optimal estimates for partially integrable systemsJournal of Differential Equations, Vol. 266, No. 2-3 | 1 Jan 2019 Cross Ref Rigorous Computer-Assisted Application of KAM Theory: A Modern ApproachFoundations of Computational Mathematics, Vol. 17, No. 5 | 17 November 2016 Cross Ref Whitney smooth families of invariant tori within the reversible context 2 of KAM theoryRegular and Chaotic Dynamics, Vol. 21, No. 6 | 18 December 2016 Cross Ref Computing the Conjugacy of Invariant Tori for Volume-Preserving MapsAdam M. 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MeissSIAM Journal on Applied Dynamical Systems, Vol. 11, No. 1 | 8 March 2012AbstractPDF (1358 KB)Hamiltonian Perturbation Theory (and Transition to Chaos)Mathematics of Complexity and Dynamical Systems | 1 Jan 2012 Cross Ref A KAM theorem without action-angle variables for elliptic lower dimensional toriNonlinearity, Vol. 24, No. 4 | 17 February 2011 Cross Ref The reversible context 2 in KAM theory: the first stepsRegular and Chaotic Dynamics, Vol. 16, No. 1-2 | 13 October 2010 Cross Ref Invariant Sets of Impulsive Differential Equations with Particularities in ω -Limit SetAbstract and Applied Analysis, Vol. 2011 | 1 Jan 2011 Cross Ref Problems in Hamiltonian PDE'SVisions in Mathematics | 1 Jan 2010 Cross Ref KAM Theory: Quasi-periodicity in Dynamical SystemsHandbook of Dynamical Systems | 1 Jan 2010 Cross Ref Almost periodically forced circle flowsJournal of Functional Analysis, Vol. 257, No. 3 | 1 Aug 2009 Cross Ref Lectures on Mixing and Dynamical SystemsAnalysis and Control of Mixing with an Application to Micro and Macro Flow Processes | 1 Jan 2009 Cross Ref Hamiltonian Perturbation Theory (and Transition to Chaos)Encyclopedia of Complexity and Systems Science | 1 Jan 2009 Cross Ref KAM tori: persistence and smoothnessNonlinearity, Vol. 21, No. 10 | 15 July 2008 Cross Ref Partial preservation of frequencies and floquet exponents in KAM theoryProceedings of the Steklov Institute of Mathematics, Vol. 259, No. 1 | 1 Dec 2007 Cross Ref Bifurcation analysis of attitude control systems with switching-constrained actuatorsNonlinear Dynamics, Vol. 51, No. 1-2 | 31 January 2007 Cross Ref Degree Theory and Almost Periodic ProblemsDifferential Equations, Chaos and Variational Problems | 1 Jan 2007 Cross Ref The Foundations of Oceanic Dynamics and Climate ModelingHandbook of Mathematical Fluid Dynamics | 1 Jan 2007 Cross Ref Normal linear stability of quasi-periodic toriJournal of Differential Equations, Vol. 232, No. 2 | 1 Jan 2007 Cross Ref Partial preservation of frequencies in KAM theoryNonlinearity, Vol. 19, No. 5 | 10 April 2006 Cross Ref Persistence of elliptic invariant tori for Hamiltonian systemsNonlinear Analysis: Theory, Methods & Applications, Vol. 45, No. 2 | 1 Jul 2001 Cross Ref Persistence of Hyperbolic Invariant Tori for Hamiltonian SystemsJournal of Differential Equations, Vol. 164, No. 2 | 1 Jul 2000 Cross Ref Общий подход к интегрированию обратимых динамических систем, определяемых отображениями из группы Кремоны бирациональных преобразований $\operatorname{Cr}(P^n_k)$Математические заметки, Vol. 68, No. 5 | 1 Jan 2000 Cross Ref Transition Curves for the Quasi-Periodic Mathieu EquationRandolph S. Zounes and Richard H. RandSIAM Journal on Applied Mathematics, Vol. 58, No. 4 | 26 July 2006AbstractPDF (4717 KB)Nonalgebraic integrability of one reversible dynamical system of the Cremona typeJournal of Mathematical Physics, Vol. 39, No. 5 | 1 May 1998 Cross Ref Algebraic-geometry approach to integrability of birational plane mappings. Integrable birational quadratic reversible mappings. IJournal of Geometry and Physics, Vol. 24, No. 3 | 1 Feb 1998 Cross Ref Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case)Physica D: Nonlinear Phenomena, Vol. 82, No. 1-2 | 1 Apr 1995 Cross Ref Unfoldings of quasi-periodic tori in reversible systemsJournal of Dynamics and Differential Equations, Vol. 7, No. 1 | 1 Jan 1995 Cross Ref Normal forms of reversible dynamical systemsInternational Journal of Theoretical Physics, Vol. 33, No. 9 | 1 Sep 1994 Cross Ref Resonances in the system of the interacted sources of vibration: Formulation of problem and general resultsInternational Journal of Non-Linear Mechanics, Vol. 29, No. 1 | 1 Jan 1994 Cross Ref Classical and quantum proton vibration in a nonharmonic strongly coupled systemThe Journal of Chemical Physics, Vol. 99, No. 6 | 15 Sep 1993 Cross Ref Lower‐dimensional tori in reversible systemsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 1, No. 2 | 1 Aug 1991 Cross Ref On the bifurcations of subharmonics in reversible systemsSingularity Theory and its Applications | 1 October 2006 Cross Ref Invariant m-dimensional tori of reversible systems with phase space of dimension greater than 2mJournal of Soviet Mathematics, Vol. 51, No. 3 | 1 Sep 1990 Cross Ref A class of bifurcation solutions of almost-periodic parametric vibration systemsActa Mechanica Sinica, Vol. 6, No. 3 | 1 Aug 1990 Cross Ref Bifurcations in two-dimensional reversible mapsPhysica A: Statistical Mechanics and its Applications, Vol. 164, No. 3 | 1 Apr 1990 Cross Ref Local reversibility in dynamical systemsPhysics Letters A, Vol. 142, No. 2-3 | 1 Dec 1989 Cross Ref The bifurcation to homoclinic tori in the quasiperiodically forced duffing oscillatorPhysica D: Nonlinear Phenomena, Vol. 34, No. 1-2 | 1 Jan 1989 Cross Ref A stability theorem for minimal foliations on a torusErgodic Theory and Dynamical Systems, Vol. 8, No. 8 | 10 December 2009 Cross Ref The theory of quasi periodic motionsOrdinary and Partial Differential Equations | 15 September 2006 Cross Ref Bifurcations in distributed kinetic systems with aperiodic instabilityPhysica D: Nonlinear Phenomena, Vol. 14, No. 1 | 1 Dec 1984 Cross Ref Review of concepts of stabilityCelestial Mechanics, Vol. 34, No. 1-4 | 1 Sep 1984 Cross Ref Review of Concepts of StabilityThe Stability of Planetary Systems | 1 Jan 1984 Cross Ref On the three-dimensional lunar problem and other perturbation problems of the Kepler problemJournal of Mathematical Analysis and Applications, Vol. 93, No. 1 | 1 Apr 1983 Cross Ref Quasi Periodicity in Local Bifurcation TheoryBifurcation Theory, Mechanics and Physics | 1 Jan 1983 Cross Ref Semiclassical quantization of the shell modelNuclear Physics A, Vol. 391, No. 1 | 1 Dec 1982 Cross Ref Phase locking of biological clocksJournal of Mathematical Biology, Vol. 15, No. 3 | 1 Nov 1982 Cross Ref The floquet theory for quasi-periodic linear systemsApplied Mathematics and Mechanics, Vol. 3, No. 3 | 1 Jun 1982 Cross Ref A High Order Generalized Method of AveragingDavid E. GilsinnSIAM Journal on Applied Mathematics, Vol. 42, No. 1 | 12 July 2006AbstractPDF (1624 KB)PERIODIC AND NONPERIODIC SOLUTIONS OF REVERSIBLE SYSTEMSNonlinear Differential Equations | 1 Jan 1981 Cross Ref A universal instability of many-dimensional oscillator systemsPhysics Reports, Vol. 52, No. 5 | 1 May 1979 Cross Ref Non-linear dynamic systems, limit cycles, transformation groups, and perturbation techniquesJournal of Physics A: Mathematical and General, Vol. 10, No. 12 | 18 January 2001 Cross Ref Invariants and stability in classical mechanicsReports on Progress in Physics, Vol. 40, No. 9 | 9 February 2001 Cross Ref Planck distribution in a classical nonlinear coupled harmonic-oscillator systemIl Nuovo Cimento B Series 11, Vol. 22, No. 1 | 29 October 2007 Cross Ref Limit-cycles in enzyme-systems with nonlinear negative feedbackBiophysics of Structure and Mechanism, Vol. 1, No. 1 | 1 Jan 1974 Cross Ref On the conservation of hyperbolic invariant tori for Hamiltonian systemsJournal of Differential Equations, Vol. 15, No. 1 | 1 Jan 1974 Cross Ref Locally connected almost periodic minimal setsRecent Advances in Topological Dynamics | 24 August 2006 Cross Ref Periodic Families of Systems Possessing a First IntegralDaniel SweetSIAM Journal on Applied Mathematics, Vol. 22, No. 3 | 12 July 2006AbstractPDF (1424 KB)Perturbation Methods for Hamiltonian Systems. GeneralizationsPerturbation Methods in Non-Linear Systems | 1 Jan 1972 Cross Ref Perturbations of Integrable SystemsPerturbation Methods in Non-Linear Systems | 1 Jan 1972 Cross Ref Perturbations of Area Preserving MappingsPerturbation Methods in Non-Linear Systems | 1 Jan 1972 Cross Ref ResonancePerturbation Methods in Non-Linear Systems | 1 Jan 1972 Cross Ref The velocity autocorrelation function of a finite model systemJournal of Statistical Physics, Vol. 6, No. 2-3 | 1 Jan 1972 Cross Ref Quasi-periodic solutions of Hamiltonian systemsJournal of Differential Equations, Vol. 11, No. 1 | 1 Jan 1972 Cross Ref On the existence of quasiperiodic solutions of nonlinear hyperbolic partial differential equationsProceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 48, No. 5 | 1 Jan 1972 Cross Ref Populations of biochemical oscillators as circadian clocksJournal of Theoretical Biology, Vol. 33, No. 2 | 1 Nov 1971 Cross Ref How to avoid « secular » terms in classical and quantum mechanicsIl Nuovo Cimento B Series 11, Vol. 1, No. 2 | 26 January 2008 Cross Ref Class of Perturbation Theories of Ordinary Differential EquationsJournal of Mathematical Physics, Vol. 12, No. 1 | 1 Jan 1971 Cross Ref On an almost periodic Mathieu equationQuarterly of Applied Mathematics, Vol. 28, No. 2 | 1 January 1970 Cross Ref Higher Order Averaging and Related Methods for Perturbed Periodic and Quasi-Periodic SystemsLawrence M. PerkoSIAM Journal on Applied Mathematics, Vol. 17, No. 4 | 12 July 2006AbstractPDF (2092 KB)Populations of interacting oscillators and circadian rhythmsJournal of Theoretical Biology, Vol. 22, No. 3 | 1 Mar 1969 Cross Ref Thomas MacFarland cherryJournal of the Australian Mathematical Society, Vol. 9, No. 1-2 | 9 April 2009 Cross Ref BibliographyDifferential and Integral Inequalities - Theory and Applications: Ordinary Differential Equations | 1 Jan 1969 Cross Ref Convergent series expansions for quasi-periodic motionsMathematische Annalen, Vol. 169, No. 1 | 1 Mar 1967 Cross Ref Periodic OrbitsTheory of Orbit | 1 Jan 1967 Cross Ref Volume 8, Issue 2| 1966SIAM Review145-275 History Submitted:17 August 1965Published online:01 August 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1008035Article page range:pp. 145-172ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

On a theorem of Anosov

1969-05-01
J. Moser

Parametric Amplification and Self-Oscillation in a Nanotube Mechanical Resonator

2011-05-26
Alexander Eichler , Julien Chaste , J. Moser +1 more
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification … A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the line shape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultralow force sensing experiments.
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Mesoscopic physics of nanomechanical systems

2022-12-08
Adrian Bachtold , J. Moser , M. I. Dykman
Recent technological advances allow nanomechanical vibrational systems to be fabricated with small dimensions, large oscillation frequencies, and long vibrational lifetimes. Novel physical behavior occurs in the mesoscopic regime which applies … Recent technological advances allow nanomechanical vibrational systems to be fabricated with small dimensions, large oscillation frequencies, and long vibrational lifetimes. Novel physical behavior occurs in the mesoscopic regime which applies only to studying individual systems and not to solid-state ensemble systems probed with molecular or vibrational spectroscopies. This review addresses the experimental work on physical phenomena in vibrational systems, including fluctuations in the nonequilibrium regime, relaxations, nonlinearities, dynamics both conservative and dissipative, and mode couplings and their interplay.
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A fixed point theorem in symplectic geometry

1978-01-01
J. Moser
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Various Aspects of Integrable Hamiltonian Systems

1980-01-01
J. Moser

A stability theorem for minimal foliations on a torus

1988-12-01
J. Moser
Abstract This paper is concerned with minimal foliations; these are foliations whose leaves are extremals of a prescribed variational problem, as for example foliations consisting of minimal surfaces. Such a … Abstract This paper is concerned with minimal foliations; these are foliations whose leaves are extremals of a prescribed variational problem, as for example foliations consisting of minimal surfaces. Such a minimal foliation is called stable if for any small perturbation of the variational problem there exists a minimal foliation conjugate under a smooth diffeomorphism to the original foliation. In this paper the stability of special foliations of codimension 1 on a higher-dimensional torus is established. This result requires small divisor assumptions similar to those encountered in dynamical systems. This theorem can be viewed as a generalization of the perturbation theory of invariant tori for Hamiltonian systems to elliptic partial differential equations for which one obtains quasi-periodic solutions.
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Fabrication of large addition energy quantum dots in graphene

2009-10-26
J. Moser , Adrian Bachtold
We present a simple technique to fabricate graphene quantum dots in a cryostat. It relies upon the controlled rupture of a suspended graphene sheet subjected to the application of a … We present a simple technique to fabricate graphene quantum dots in a cryostat. It relies upon the controlled rupture of a suspended graphene sheet subjected to the application of a large electron current. This results in the in-situ formation of a clean and ultra-narrow constriction, which hosts one quantum dot, and occasionally a few quantum dots in series. Conductance spectroscopy indicates that individual quantum dots can possess an addition energy as large as 180 meV and a level spacing as large as 25 meV. Our technique has several assets: (i) the dot is suspended, thus the electrostatic influence of the substrate is reduced, and (ii) contamination is minimized, since the edges of the dot have only been exposed to the vacuum in the cryostat.
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Symmetry breaking in a mechanical resonator made from a carbon nanotube

2013-11-25
Alexander Eichler , J. Moser , M. I. Dykman +1 more
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Bias dependent inversion of tunneling magnetoresistance in Fe∕GaAs∕Fe tunnel junctions

2006-10-16
J. Moser , Marcus Zenger , C. Gerl +7 more
We investigated spin dependent transport through Fe/GaAs/Fe tunnel junctions. The tunneling magnetoresistance effect (TMR) was probed for different types of Fe/GaAs interfaces. For interfaces cleaned by hydrogen plasma the TMR … We investigated spin dependent transport through Fe/GaAs/Fe tunnel junctions. The tunneling magnetoresistance effect (TMR) was probed for different types of Fe/GaAs interfaces. For interfaces cleaned by hydrogen plasma the TMR effect is increased and observable at room temperature. If an epitaxial Fe/GaAs(001) interface is involved, the tunnel junction exhibits a bias dependent inversion of the TMR effect. This is a first experimental signature for band structure effects at a Fe/GaAs interface and relevant for spin injection experiments.
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From spin-Peierls to superconductivity: (TMTTF)<sub>2</sub>PF<sub>6</sub>under high pressure

2001-01-11
D. Jaccard , H. Wilhelm , D. Jérôme +3 more
The nature of the attractive electron-electron interaction, leading to the formation of Cooper-pairs in unconventional superconductors has still to be fully understood and is subject to intensive research. Here we … The nature of the attractive electron-electron interaction, leading to the formation of Cooper-pairs in unconventional superconductors has still to be fully understood and is subject to intensive research. Here we show that the sequence spin-Peierls, antiferromagnetism, superconductivity observed in (TMTTF)_2PF_6 under pressure makes the (TM)_2X phase diagram universal. We argue that the suppression of the spin-Peierls transition under pressure, the close vicinity of antiferromagnetic and superconducting phases at high pressure as well as the existence of critical antiferromagnetic fluctuations above T_c strongly support the intriguing possibility that the interchain exchange of antiferromagnetic fluctuations provides the pairing mechanism required for bound charge carriers.
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Proof of a generalized from of a fixed point theorem due to G. D. Birkhoff

1977-01-01
J. Moser

Interplay of Driving and Frequency Noise in the Spectra of Vibrational Systems

2014-12-16
Yaxing Zhang , J. Moser , J. Güttinger +2 more
We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically … We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically driven systems, the interplay of the driving and frequency fluctuations results in specific spectral features. We present measurements on a carbon nanotube resonator and show that our theory allows not only the characterization of the frequency fluctuations but also the quantification of the decay rate without ring-down measurements. The results bear on identifying the decoherence of mesoscopic oscillators and on the general problem of resonance fluorescence and light scattering by oscillators.
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High-frequency nanotube mechanical resonators

2011-11-21
Julien Chaste , Marianna Sledzinska , Mariusz Zdrojek +2 more
We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for … We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for higher order eigenmodes. The high-frequency resonances are achieved using short suspended nanotubes and by introducing tensile stress in the nanotube. These devices allow us to determine the coefficient of the thermal expansion of an individual nanotube, which is negative and is about -0.7E-5 1/K at room temperature. High-frequency resonators made of nanotubes hold promise for mass sensing and experiments in the quantum limit.
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Probing the electron-phonon coupling in ozone-doped graphene by Raman spectroscopy

2010-08-23
F. Alzina , Haihua Tao , J. Moser +3 more
We have investigated the effects of ozone treatment on graphene by Raman scattering. Sequential ozone short-exposure cycles resulted in increasing the $p$-doping levels as inferred from the blueshift of the … We have investigated the effects of ozone treatment on graphene by Raman scattering. Sequential ozone short-exposure cycles resulted in increasing the $p$-doping levels as inferred from the blueshift of the $2D$ and $G$ peak frequencies, without introducing significant disorder. The two-phonon $2D$ and $2{D}^{\ensuremath{'}}$ Raman peak intensities show a significant decrease while, on the contrary, the one-phonon $G$ Raman peak intensity remains constant for the whole exposure process. The former reflects the dynamics of the photoexcited electrons (holes) and, specifically, the increase in the electron-electron-scattering rate with doping. From the ratio of $2D$ to $2{D}^{\ensuremath{'}}$ intensities, which remains constant with doping, we could extract the ratio of electron-phonon coupling parameters. This ratio is found independent on the number of layers up to ten layers. Moreover, the rate of decrease in $2D$ and $2{D}^{\ensuremath{'}}$ intensities with doping was found to slowdown inversely proportional to the number of graphene layers, revealing the increase in the electron-electron collision probability.
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Orbital effects on tunneling anisotropic magnetoresistance in Fe/GaAs/Au junctions

2009-09-01
Michael Wimmer , M. Lobenhofer , J. Moser +6 more
We report experiments on epitaxially grown Fe/GaAs/Au tunnel junctions demonstrating that the magnitude of the tunneling anisotropic magnetoresistance (TAMR) effect can be controlled by magnetic field strength. Theoretical modeling shows … We report experiments on epitaxially grown Fe/GaAs/Au tunnel junctions demonstrating that the magnitude of the tunneling anisotropic magnetoresistance (TAMR) effect can be controlled by magnetic field strength. Theoretical modeling shows that the interplay of the orbital effects of a magnetic field and the Dresselhaus spin-orbit coupling in the GaAs barrier leads to an independent contribution to the TAMR effect with uniaxial symmetry, whereas the Bychkov-Rashba spin-orbit coupling does not play a role. The effect is intrinsic to barriers with bulk inversion asymmetry.
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Sliding nanomechanical resonators

2022-10-27
Yue Ying , Zhuo‐Zhi Zhang , J. Moser +3 more
The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant … The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the clamping points is modulated as the string vibrates. At the nanoscale, the simplest way to emulate this principle would be to controllably make nanoresonators slide across their clamping points, which would effectively modulate their vibrating length. Here, we report measurements of flexural vibrations in nanomechanical resonators that reveal such a sliding motion. Surprisingly, the resonant frequency of vibrations draws a loop as a tuning gate voltage is cycled. This behavior indicates that sliding is accompanied by a delayed frequency response of the resonators, making their dynamics richer than that of resonators with fixed clamping points. Our work elucidates the dynamics of nanomechanical resonators with unconventional boundary conditions, and offers opportunities for studying friction at the nanoscale from resonant frequency measurements.
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Aluminum arsenide cleaved-edge overgrown quantum wires

2005-07-25
J. Moser , T. Zibold , D. Schuh +6 more
We report conductance measurements in quantum wires made of aluminum arsenide, a heavy-mass, multi-valley one-dimensional (1D) system. Zero-bias conductance steps are observed as the electron density in the wire is … We report conductance measurements in quantum wires made of aluminum arsenide, a heavy-mass, multi-valley one-dimensional (1D) system. Zero-bias conductance steps are observed as the electron density in the wire is lowered, with additional steps observable upon applying a finite dc bias. We attribute these steps to depopulation of successive 1D subbands. The quantum conductance is substantially reduced with respect to the anticipated value for a spin- and valley-degenerate 1D system. This reduction is consistent with disorder-induced, intra-wire backscattering which suppresses the transmission of 1D modes. Calculations are presented to demonstrate the role of strain in the 1D states of this cleaved-edge structure.
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High-field magnetoresistance of Fe∕GaAs∕Fe tunnel junctions

2004-08-02
Marcus Zenger , J. Moser , W. Wegscheider +2 more
We investigate transport through 6–10nm thin epitaxial GaAs(001) barriers sandwiched between polycrystalline iron films. Apart from a pronounced tunneling magnetoresistance effect at low magnetic fields, we observe a distinct negative … We investigate transport through 6–10nm thin epitaxial GaAs(001) barriers sandwiched between polycrystalline iron films. Apart from a pronounced tunneling magnetoresistance effect at low magnetic fields, we observe a distinct negative magnetoresistance (MR) at low and a positive MR at higher temperatures. We show that the negative MR contribution is only observed for the ferromagnetic iron contacts but is absent if iron is replaced by copper or gold electrodes. Possible explanations of the negative MR involve suppression of spin-flip scattering or Zeeman splitting of the tunneling barrier, but neither of these explanations is fully consistent with the data.
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Inverse engineering of shortcut pulses for high fidelity initialization on qubits closely spaced in frequency

2019-03-07
Ying Yan , Yichao Li , Adam Kinos +6 more
High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is … High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where qubits are closely spaced in frequency. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in frequency detuning and Rabi frequency. Such protocol, relevant to frequency selectivity, is applied to rare-earth ions qubit system, where the excitation of frequency-neighboring qubits should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting qubits, and any other systems where qubits are addressed in frequency.
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Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

2007-12-06
J. Horas , A. Siddiki , J. Moser +2 more

Interaction-mediated asymmetries of the quantized Hall effect

2009-10-01
A. Siddiki , J. Horas , J. Moser +2 more
Experimental and theoretical investigations on the integer quantized Hall effect in gate-defined narrow Hall bars are presented. At low electron mobility the classical (high-temperature) Hall resistance line RH(B) cuts through … Experimental and theoretical investigations on the integer quantized Hall effect in gate-defined narrow Hall bars are presented. At low electron mobility the classical (high-temperature) Hall resistance line RH(B) cuts through the center of all Hall plateaus. In contrast, for our high-mobility samples the intersection point, at even filling factors ν=2, 4, ..., is clearly shifted towards larger magnetic fields B. This asymmetry is in good agreement with predictions of the screening theory, i.e. taking Coulomb interaction into account. The observed effect is directly related to the formation of incompressible strips in the Hall bar. The spin-split plateau at ν=1 is found to be almost symmetric regardless of the mobility. We explain this within the so-called effective g-model.
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Disordered AlAs wires: Temperature-dependent resonance areas within the Fermi-liquid paradigm

2006-11-10
J. Moser , Stefano Roddaro , D. Schuh +3 more
AlAs cleaved-edge overgrown quantum wires near pinch-off reveal conductance resonances with an unconventional dependence on temperature $T$. The resonance areas decrease with reduced $T$ consistent with classical Coulomb blockade (CB) … AlAs cleaved-edge overgrown quantum wires near pinch-off reveal conductance resonances with an unconventional dependence on temperature $T$. The resonance areas decrease with reduced $T$ consistent with classical Coulomb blockade (CB) in a single dot, but then become rapidly smaller below a crossover ${T}_{X}$. Though resembling Luttinger liquid behavior below the crossover, the anomalous $T$ dependence including the crossover fit quantitatively to a classical-to-stochastic CB transition, whereby stochastic multidot CB sets in at low temperatures. Conductance at finite bias resembles a depinned charge density wave as expected for a chain of disorder induced dots. These studies highlight the applicability of the Fermi liquid paradigm to the description of disordered heavy-mass quantum wires.
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Donor binding energy and thermally activated persistent photoconductivity in high mobility (001) AlAs quantum wells

2007-10-01
S. Dasgupta , C. Knaak , J. Moser +5 more
A doping series of AlAs (001) quantum wells with Si δ-modulation doping on both sides reveals different dark and postillumination saturation densities, as well as temperature dependent photoconductivity. The lower … A doping series of AlAs (001) quantum wells with Si δ-modulation doping on both sides reveals different dark and postillumination saturation densities, as well as temperature dependent photoconductivity. The lower dark two-dimensional electron density saturation is explained assuming deep binding energy of ΔDK=65.2meV for Si donors in the dark. Persistent photoconductivity (PPC) is observed upon illumination, with higher saturation density indicating shallow postillumination donor binding energy. The photoconductivity is thermally activated, with 4K illumination requiring postillumination annealing to T=30K to saturate the PPC. Dark and postillumination doping efficiencies are reported.
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Fast and robust creation of an arbitrary single qubit state by nonadiabatic shortcut pulses in a three-level system

2019-04-08
Ying Yan , Yi Chao Li , Adam Kinos +6 more
High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is … High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where qubits are closely spaced in frequency. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in frequency detuning and Rabi frequency. Such protocol, relevant to frequency selectivity, is applied to rare-earth ions qubit system, where the excitation of frequency-neighboring qubits should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting qubits, and any other systems where qubits are addressed in frequency.
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Dynamical systems — Past and present

2008-12-01
J. Moser

Image Analysis for Cosmology: Shape Measurement Challenge Review &amp; Results from the Mapping Dark Matter Challenge

2012-01-01
Thomas Kitching , Jason Rhodes , Catherine Heymans +7 more
In this paper we present results from the Mapping Dark Matter competition that expressed the weak lensing shape measurement task in its simplest form and as a result attracted over … In this paper we present results from the Mapping Dark Matter competition that expressed the weak lensing shape measurement task in its simplest form and as a result attracted over 700 submissions in 2 months and a factor of 3 improvement in shape measurement accuracy on high signal to noise galaxies, over previously published results, and a factor 10 improvement over methods tested on constant shear blind simulations. We also review weak lensing shape measurement challenges, including the Shear TEsting Programmes (STEP1 and STEP2) and the GRavitational lEnsing Accuracy Testing competitions (GREAT08 and GREAT10).
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Controlled assembly of graphene sheets and nanotubes: Fabrication of suspended multi-element all-carbon vibrational structures

2013-09-13
Ioannis Tsioutsios , J. Moser , J.A. Plaza +1 more
We report on the fabrication and operation of a multi-element vibrational structure consisting of two graphene mechanical resonators coupled by a nanotube beam. The whole structure is suspended. Each graphene … We report on the fabrication and operation of a multi-element vibrational structure consisting of two graphene mechanical resonators coupled by a nanotube beam. The whole structure is suspended. Each graphene resonator is clamped by two metal electrodes. The structure is fabricated using a combination of electron-beam lithography and atomic-force microscopy nano-manipulation. This layout allows us to detect the mechanical vibrations electrically. The measured eigenmodes are localized in either one of the graphene resonators. The coupling due to the nanotube is studied by measuring the shift of the resonance frequency of one graphene resonator as a function of the vibration amplitude of the other resonator. Coupled graphene resonators hold promise for the study of nonlinear dynamics, the manipulation of mechanical states, and quantum non-demolition measurements.
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Robust pulses for high fidelity non-adiabatic geometric gate operations in an off-resonant three-level system

2019-01-10
Ying Yan , Jie Lu , Lin Wan +1 more
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Parallel Measurements of Vibrational Modes in a Few-Layer Graphene Nanomechanical Resonator Using Software-Defined Radio Dongles

2022-01-01
Heng Lu , Chen Yang , Ye Tian +6 more
Software-defined radio dongles are small and inexpensive receivers well known to amateur radio enthusiasts. When connected to an antenna, they enable monitoring of a wide range of the radio spectrum … Software-defined radio dongles are small and inexpensive receivers well known to amateur radio enthusiasts. When connected to an antenna, they enable monitoring of a wide range of the radio spectrum by conditioning the input signal and transferring a downconverted version of it to a personal computer for software processing. Here, we employ a composite of two such dongles, interfaced with codes written in MATLAB and GNU Radio, as a measuring instrument to study the flexural vibrations of a few-layer graphene nanomechanical resonator. Instead of an antenna, we connect the dongles to the split output of a photodetector used to detect vibrations optically. We first perform a quantitative analysis of the dynamics of the first vibrational mode. We then measure the response of the first two vibrational modes in parallel. To illustrate our technique, we detect changes in the vibrational amplitude of both modes induced by periodic strain modulation with a delay of ≈1 ms between measurements. Last, we show that our software-based instrument can be employed to demodulate human voice encoded in the vibrations of our resonator. For parallel measurements of several frequency channels, and provided that the input signal is not too weak, our composite system may offer an alternative to the use of multiple lock-in amplifiers or multiple spectrum analyzers, with the distinct advantage of being cost-effective per frequency channel.
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Switching off energy decay channels in nanomechanical resonators

2016-01-01
J. Guettinger , Adrien Noury , P. Weber +7 more
Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a … Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a system leaking energy irreversibly into an environmental bath. Here, we report on energy decay measurements in nanomechanical systems based on multi-layer graphene that cannot be explained by the paradigm of a system directly coupled to a bath. As the energy of a vibrational mode freely decays, the rate of energy decay switches abruptly to a lower value. This finding can be explained by a model where the measured mode hybridizes with other modes of the resonator at high energy. Below a threshold energy, modes are decoupled, resulting in comparatively low decay rates and giant quality factors exceeding 1 million. Our work opens up new possibilities to manipulate vibrational states, engineer hybrid states with mechanical modes at completely different frequencies, and to study the collective motion of this highly tunable system.

Dissipative and conservative nonlinearity in carbon nanotube and graphene mechanical resonators

2012-07-26
J. Moser , Alexander Eichler , B. Lassagne +5 more
This chapter reviews several types of nonlinear behaviour in nanotubes and graphene resonators. It first discusses a scenario where damping is described by a nonlinear force. Several experimental facts support … This chapter reviews several types of nonlinear behaviour in nanotubes and graphene resonators. It first discusses a scenario where damping is described by a nonlinear force. Several experimental facts support this: the quality factor varies with the motional amplitude as a power law whose exponent coincides with the value predicted by the nonlinear damping model, hysteretic behaviour (of the motional amplitude vs. driving frequency) is absent in some resonators even for large driving forces, as expected when nonlinear damping forces are large, and the linear damping force extracted from parametric excitation measurements is significantly smaller than the nonlinear damping force. The chapter then reviews parametric excitation measurements, an alternative actuation method based on nonlinear dynamics. Finally, it discusses experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling is so strong that the associated force acting on the nanotube is highly nonlinear with displacement and velocity.
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Mesoscopic physics of nanomechanical systems

2022-01-01
Adrian Bachtold , J. Moser , M. I. Dykman
Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms … Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms of dissipation come into play. At the same time, the exquisite control of these systems makes them a platform for studying many problems of classical and quantum physics far from thermal equilibrium in a well-characterized setting. This review describes, at a conceptual level, basic theoretical ideas and explicative experiments pertaining to mesoscopic physics of nanomechanical systems. Major applications of nanomechanics in science and technology are also outlined. A broad range of phenomena related to the conservative as well as dissipative nonlinearity and fluctuations are discussed within a unifying framework. They include the linear response of single and coupled vibrational modes as well as nonlinear effects of periodic driving. Such driving breaks the continuous time-translation symmetry and the detailed balance, with conspicuous consequences for fluctuations, particularly in the presence of the driving-induced bi- and multistability. Mathematical techniques are described in the appendices to streamline the reading, but also to provide an introduction to the theory. The goal of the review is to show the richness of the physics at work. The continuous experimental and theoretical advances make nanomechanical systems a vibrant area of research, with many new phenomena to discover.
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Symmetry breaking of large-amplitude parametric oscillations in few-layer-graphene nanomechanical resonators

2025-05-13
Chen Yang , YuBin Zhang , Heng Lu +6 more

Tailoring the light-matter interaction for high-fidelity holonomic gate operations in multiple systems

2024-11-25
Zhihuang Kang , Shutong Wu , Kunji Han +4 more
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Tailoring the light-matter interaction for high-fidelity holonomic gate operations in multiple systems

2024-09-10
Zhihuang Kang , Shutong Wu , Kunji Han +4 more
Realization of quantum computing requires the development of high-fidelity quantum gates that are resilient to decoherence, control errors, and environmental noise. While non-adiabatic holonomic quantum computation (NHQC) offers a promising … Realization of quantum computing requires the development of high-fidelity quantum gates that are resilient to decoherence, control errors, and environmental noise. While non-adiabatic holonomic quantum computation (NHQC) offers a promising approach, it often necessitates system-specific adjustments. This work presents a versatile scheme for implementing NHQC gates across multiple qubit systems by optimizing multiple degrees of freedom using a genetic algorithm. The scheme is applied to three qubit systems: ensemble rare-earth ion (REI) qubits, single REI qubits, and superconducting transmon qubits. Numerical simulations demonstrate that the optimized gate operations are robust against frequency detuning and induce low off-resonant excitations, making the scheme effective for advancing fault-tolerant quantum computation across various platforms.
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Strong effects of thermally induced low-spin-to-high-spin crossover on transport properties of correlated metals

2024-08-07
J. Moser , Jernej Mravlje , Markus Aichhorn
We use dynamical mean-field theory to study how electronic transport in multi-orbital metals is influenced by correlated (nominally) empty orbitals that are in proximity to the Fermi level. Specifically, we … We use dynamical mean-field theory to study how electronic transport in multi-orbital metals is influenced by correlated (nominally) empty orbitals that are in proximity to the Fermi level. Specifically, we study 2 + 1 orbital and 3 + 2 orbital (i.e. t2g + eg ) models on a Bethe lattice with a crystal field that is set so that the higher lying orbitals are nearly empty at low temperatures but get a non-negligible occupancy at elevated temperature. The high temperature regime is characterized by thermal activation of carriers leading to higher magnetic response (i.e., thermally induced low-spin to high-spin transition) and substantial influence on resistivity, where one can distinguish two counteracting effects: increased scattering due to formation of high spin and increased scattering phase space on one hand, and additional parallel conduction channel on the other. The former effect is stronger and one may identify cases where resistivity increases by a factor of three at high temperatures even though the occupancy of the unoccupied band remains small (< 10%). We discuss implications of our findings for transport properties of correlated materials.
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Mesoscopic physics of nanomechanical systems

2022-12-08
Adrian Bachtold , J. Moser , M. I. Dykman
Recent technological advances allow nanomechanical vibrational systems to be fabricated with small dimensions, large oscillation frequencies, and long vibrational lifetimes. Novel physical behavior occurs in the mesoscopic regime which applies … Recent technological advances allow nanomechanical vibrational systems to be fabricated with small dimensions, large oscillation frequencies, and long vibrational lifetimes. Novel physical behavior occurs in the mesoscopic regime which applies only to studying individual systems and not to solid-state ensemble systems probed with molecular or vibrational spectroscopies. This review addresses the experimental work on physical phenomena in vibrational systems, including fluctuations in the nonequilibrium regime, relaxations, nonlinearities, dynamics both conservative and dissipative, and mode couplings and their interplay.
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Sliding nanomechanical resonators

2022-10-27
Yue Ying , Zhuo‐Zhi Zhang , J. Moser +3 more
The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant … The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the clamping points is modulated as the string vibrates. At the nanoscale, the simplest way to emulate this principle would be to controllably make nanoresonators slide across their clamping points, which would effectively modulate their vibrating length. Here, we report measurements of flexural vibrations in nanomechanical resonators that reveal such a sliding motion. Surprisingly, the resonant frequency of vibrations draws a loop as a tuning gate voltage is cycled. This behavior indicates that sliding is accompanied by a delayed frequency response of the resonators, making their dynamics richer than that of resonators with fixed clamping points. Our work elucidates the dynamics of nanomechanical resonators with unconventional boundary conditions, and offers opportunities for studying friction at the nanoscale from resonant frequency measurements.
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Mesoscopic physics of nanomechanical systems

2022-01-01
Adrian Bachtold , J. Moser , M. I. Dykman
Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms … Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms of dissipation come into play. At the same time, the exquisite control of these systems makes them a platform for studying many problems of classical and quantum physics far from thermal equilibrium in a well-characterized setting. This review describes, at a conceptual level, basic theoretical ideas and explicative experiments pertaining to mesoscopic physics of nanomechanical systems. Major applications of nanomechanics in science and technology are also outlined. A broad range of phenomena related to the conservative as well as dissipative nonlinearity and fluctuations are discussed within a unifying framework. They include the linear response of single and coupled vibrational modes as well as nonlinear effects of periodic driving. Such driving breaks the continuous time-translation symmetry and the detailed balance, with conspicuous consequences for fluctuations, particularly in the presence of the driving-induced bi- and multistability. Mathematical techniques are described in the appendices to streamline the reading, but also to provide an introduction to the theory. The goal of the review is to show the richness of the physics at work. The continuous experimental and theoretical advances make nanomechanical systems a vibrant area of research, with many new phenomena to discover.
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Parallel Measurements of Vibrational Modes in a Few-Layer Graphene Nanomechanical Resonator Using Software-Defined Radio Dongles

2022-01-01
Heng Lu , Chen Yang , Ye Tian +6 more
Software-defined radio dongles are small and inexpensive receivers well known to amateur radio enthusiasts. When connected to an antenna, they enable monitoring of a wide range of the radio spectrum … Software-defined radio dongles are small and inexpensive receivers well known to amateur radio enthusiasts. When connected to an antenna, they enable monitoring of a wide range of the radio spectrum by conditioning the input signal and transferring a downconverted version of it to a personal computer for software processing. Here, we employ a composite of two such dongles, interfaced with codes written in MATLAB and GNU Radio, as a measuring instrument to study the flexural vibrations of a few-layer graphene nanomechanical resonator. Instead of an antenna, we connect the dongles to the split output of a photodetector used to detect vibrations optically. We first perform a quantitative analysis of the dynamics of the first vibrational mode. We then measure the response of the first two vibrational modes in parallel. To illustrate our technique, we detect changes in the vibrational amplitude of both modes induced by periodic strain modulation with a delay of ≈1 ms between measurements. Last, we show that our software-based instrument can be employed to demodulate human voice encoded in the vibrations of our resonator. For parallel measurements of several frequency channels, and provided that the input signal is not too weak, our composite system may offer an alternative to the use of multiple lock-in amplifiers or multiple spectrum analyzers, with the distinct advantage of being cost-effective per frequency channel.
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Imaging vibrations of locally gated, electromechanical few layer graphene resonators with a moving vacuum enclosure

2021-01-01
Heng Lu , Chen Yang , Ye Tian +7 more
Imaging the vibrations of nanomechanical resonators means measuring their flexural mode shapes from the dependence of their frequency response on in-plane position. Applied to two-dimensional resonators, this technique provides a … Imaging the vibrations of nanomechanical resonators means measuring their flexural mode shapes from the dependence of their frequency response on in-plane position. Applied to two-dimensional resonators, this technique provides a wealth of information on the mechanical properties of atomically-thin membranes. We present a simple and robust system to image the vibrations of few layer graphene (FLG) resonators at room temperature and in vacuum with an in-plane displacement precision of $\approx0.20$ $\mu$m. It consists of a sturdy vacuum enclosure mounted on a three-axis micropositioning stage and designed for free space optical measurements of vibrations. The system is equipped with ultra-flexible radio frequency waveguides to electrically actuate resonators. With it we characterize the lowest frequency mode of a FLG resonator by measuring its frequency response as a function of position on the membrane. The resonator is suspended over a nanofabricated local gate electrode acting both as a mirror and as a capacitor plate to actuate vibrations at radio frequencies. From these measurements, we estimate the ratio of thermal expansion coefficient to thermal conductivity of the membrane, and we measure the effective mass of the lowest frequency mode. We complement our study with a globally gated resonator and image its first three vibration modes. There, we find that folds in the membrane locally suppress vibrations.
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Fast and robust creation of an arbitrary single qubit state by nonadiabatic shortcut pulses in a three-level system

2019-04-08
Ying Yan , Yi Chao Li , Adam Kinos +6 more
High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is … High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where qubits are closely spaced in frequency. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in frequency detuning and Rabi frequency. Such protocol, relevant to frequency selectivity, is applied to rare-earth ions qubit system, where the excitation of frequency-neighboring qubits should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting qubits, and any other systems where qubits are addressed in frequency.
View PDF Chat

Inverse engineering of shortcut pulses for high fidelity initialization on qubits closely spaced in frequency

2019-03-07
Ying Yan , Yichao Li , Adam Kinos +6 more
High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is … High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where qubits are closely spaced in frequency. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in frequency detuning and Rabi frequency. Such protocol, relevant to frequency selectivity, is applied to rare-earth ions qubit system, where the excitation of frequency-neighboring qubits should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting qubits, and any other systems where qubits are addressed in frequency.
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Robust pulses for high fidelity non-adiabatic geometric gate operations in an off-resonant three-level system

2019-01-10
Ying Yan , Jie Lu , Lin Wan +1 more
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Switching off energy decay channels in nanomechanical resonators

2016-01-01
J. Guettinger , Adrien Noury , P. Weber +7 more
Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a … Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a system leaking energy irreversibly into an environmental bath. Here, we report on energy decay measurements in nanomechanical systems based on multi-layer graphene that cannot be explained by the paradigm of a system directly coupled to a bath. As the energy of a vibrational mode freely decays, the rate of energy decay switches abruptly to a lower value. This finding can be explained by a model where the measured mode hybridizes with other modes of the resonator at high energy. Below a threshold energy, modes are decoupled, resulting in comparatively low decay rates and giant quality factors exceeding 1 million. Our work opens up new possibilities to manipulate vibrational states, engineer hybrid states with mechanical modes at completely different frequencies, and to study the collective motion of this highly tunable system.

Interplay of Driving and Frequency Noise in the Spectra of Vibrational Systems

2014-12-16
Yaxing Zhang , J. Moser , J. Güttinger +2 more
We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically … We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically driven systems, the interplay of the driving and frequency fluctuations results in specific spectral features. We present measurements on a carbon nanotube resonator and show that our theory allows not only the characterization of the frequency fluctuations but also the quantification of the decay rate without ring-down measurements. The results bear on identifying the decoherence of mesoscopic oscillators and on the general problem of resonance fluorescence and light scattering by oscillators.
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Nanotube mechanical resonators with quality factors of up to 5 million

2014-10-26
J. Moser , Alexander Eichler , J. Güttinger +2 more
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Symmetry breaking in a mechanical resonator made from a carbon nanotube

2013-11-25
Alexander Eichler , J. Moser , M. I. Dykman +1 more
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Controlled assembly of graphene sheets and nanotubes: Fabrication of suspended multi-element all-carbon vibrational structures

2013-09-13
Ioannis Tsioutsios , J. Moser , J.A. Plaza +1 more
We report on the fabrication and operation of a multi-element vibrational structure consisting of two graphene mechanical resonators coupled by a nanotube beam. The whole structure is suspended. Each graphene … We report on the fabrication and operation of a multi-element vibrational structure consisting of two graphene mechanical resonators coupled by a nanotube beam. The whole structure is suspended. Each graphene resonator is clamped by two metal electrodes. The structure is fabricated using a combination of electron-beam lithography and atomic-force microscopy nano-manipulation. This layout allows us to detect the mechanical vibrations electrically. The measured eigenmodes are localized in either one of the graphene resonators. The coupling due to the nanotube is studied by measuring the shift of the resonance frequency of one graphene resonator as a function of the vibration amplitude of the other resonator. Coupled graphene resonators hold promise for the study of nonlinear dynamics, the manipulation of mechanical states, and quantum non-demolition measurements.
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Ultrasensitive force detection with a nanotube mechanical resonator

2013-06-09
J. Moser , J. Güttinger , Alexander Eichler +4 more
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Dissipative and conservative nonlinearity in carbon nanotube and graphene mechanical resonators

2012-07-26
J. Moser , Alexander Eichler , B. Lassagne +5 more
This chapter reviews several types of nonlinear behaviour in nanotubes and graphene resonators. It first discusses a scenario where damping is described by a nonlinear force. Several experimental facts support … This chapter reviews several types of nonlinear behaviour in nanotubes and graphene resonators. It first discusses a scenario where damping is described by a nonlinear force. Several experimental facts support this: the quality factor varies with the motional amplitude as a power law whose exponent coincides with the value predicted by the nonlinear damping model, hysteretic behaviour (of the motional amplitude vs. driving frequency) is absent in some resonators even for large driving forces, as expected when nonlinear damping forces are large, and the linear damping force extracted from parametric excitation measurements is significantly smaller than the nonlinear damping force. The chapter then reviews parametric excitation measurements, an alternative actuation method based on nonlinear dynamics. Finally, it discusses experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling is so strong that the associated force acting on the nanotube is highly nonlinear with displacement and velocity.
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A nanomechanical mass sensor with yoctogram resolution

2012-04-01
Julien Chaste , Alexander Eichler , J. Moser +3 more
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Parametric amplification and self-oscillation in a nanotube mechanical resonator

2012-01-31
Alexander Eichler , Julien Chaste , J. Moser +1 more
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification … A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the lineshape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultra-low force sensing experiments.

Image Analysis for Cosmology: Shape Measurement Challenge Review &amp; Results from the Mapping Dark Matter Challenge

2012-01-01
Thomas Kitching , Jason Rhodes , Catherine Heymans +7 more
In this paper we present results from the Mapping Dark Matter competition that expressed the weak lensing shape measurement task in its simplest form and as a result attracted over … In this paper we present results from the Mapping Dark Matter competition that expressed the weak lensing shape measurement task in its simplest form and as a result attracted over 700 submissions in 2 months and a factor of 3 improvement in shape measurement accuracy on high signal to noise galaxies, over previously published results, and a factor 10 improvement over methods tested on constant shear blind simulations. We also review weak lensing shape measurement challenges, including the Shear TEsting Programmes (STEP1 and STEP2) and the GRavitational lEnsing Accuracy Testing competitions (GREAT08 and GREAT10).
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Parametric amplification and self-oscillation in a nanotube mechanical resonator

2012-01-01
Alexander Eichler , Julien Chaste , J. Moser +1 more
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification … A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the lineshape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultra-low force sensing experiments.
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High-frequency nanotube mechanical resonators

2011-11-21
Julien Chaste , Marianna Sledzinska , Mariusz Zdrojek +2 more
We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for … We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for higher order eigenmodes. The high-frequency resonances are achieved using short suspended nanotubes and by introducing tensile stress in the nanotube. These devices allow us to determine the coefficient of the thermal expansion of an individual nanotube, which is negative and is about -0.7E-5 1/K at room temperature. High-frequency resonators made of nanotubes hold promise for mass sensing and experiments in the quantum limit.
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Parametric Amplification and Self-Oscillation in a Nanotube Mechanical Resonator

2011-05-26
Alexander Eichler , Julien Chaste , J. Moser +1 more
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification … A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the line shape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultralow force sensing experiments.
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Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene

2011-05-15
Alexander Eichler , J. Moser , Julien Chaste +3 more
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Dissipative and conservative nonlinearity in carbon nanotube and graphene mechanical resonators

2011-01-01
J. Moser , Alexander Eichler , B. Lassagne +5 more
Graphene and carbon nanotubes represent the ultimate size limit of one and two-dimensional nanoelectromechanical resonators. Because of their reduced dimensionality, graphene and carbon nanotubes display unusual mechanical behavior; in particular, … Graphene and carbon nanotubes represent the ultimate size limit of one and two-dimensional nanoelectromechanical resonators. Because of their reduced dimensionality, graphene and carbon nanotubes display unusual mechanical behavior; in particular, their dynamics is highly nonlinear. Here, we review several types of nonlinear behavior in resonators made from nanotubes and graphene. We first discuss an unprecedented scenario where damping is described by a nonlinear force. This scenario is supported by several experimental facts: (i) the quality factor varies with the amplitude of the motion as a power law whose exponent coincides with the value predicted by the nonlinear damping model, (ii) hysteretic behavior (of the motional amplitude as a function of driving frequency) is absent in some of our resonators even for large driving forces, as expected when nonlinear damping forces are large, and (iii) when we quantify the linear damping force (by performing parametric excitation measurements) we find that it is significantly smaller than the nonlinear damping force. We then review parametric excitation measurements, an alternative actuation method which is based on nonlinear dynamics. Finally, we discuss experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling can be made so strong that the associated force acting on the nanotube becomes highly nonlinear with displacement and velocity. Overall, graphene and nanotube resonators hold promise for future studies on classical and quantum nonlinear dynamics.
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Probing the electron-phonon coupling in ozone-doped graphene by Raman spectroscopy

2010-08-23
F. Alzina , Haihua Tao , J. Moser +3 more
We have investigated the effects of ozone treatment on graphene by Raman scattering. Sequential ozone short-exposure cycles resulted in increasing the $p$-doping levels as inferred from the blueshift of the … We have investigated the effects of ozone treatment on graphene by Raman scattering. Sequential ozone short-exposure cycles resulted in increasing the $p$-doping levels as inferred from the blueshift of the $2D$ and $G$ peak frequencies, without introducing significant disorder. The two-phonon $2D$ and $2{D}^{\ensuremath{'}}$ Raman peak intensities show a significant decrease while, on the contrary, the one-phonon $G$ Raman peak intensity remains constant for the whole exposure process. The former reflects the dynamics of the photoexcited electrons (holes) and, specifically, the increase in the electron-electron-scattering rate with doping. From the ratio of $2D$ to $2{D}^{\ensuremath{'}}$ intensities, which remains constant with doping, we could extract the ratio of electron-phonon coupling parameters. This ratio is found independent on the number of layers up to ten layers. Moreover, the rate of decrease in $2D$ and $2{D}^{\ensuremath{'}}$ intensities with doping was found to slowdown inversely proportional to the number of graphene layers, revealing the increase in the electron-electron collision probability.
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Magnetotransport in disordered graphene exposed to ozone: From weak to strong localization

2010-05-28
J. Moser , Haihua Tao , Stephan Roche +3 more
We present a magneto-transport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples … We present a magneto-transport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples exposed to ozone becomes very sensitive to temperature: it decreases by more than 3 orders of magnitude between 100K and 1K. By varying either an external gate voltage or temperature, we continuously tune the transport properties from the weak to the strong localization regime. We show that the transition occurs as the phase coherence length becomes comparable to the localization length. We also highlight the important role of disorder-enhanced electron-electron interaction on the resistivity.
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Various Aspects of Integrable Hamiltonian Systems

2010-01-01
J. Moser
(a) In these informal lecture notes we discuss a number of integrable Hamiltonian systems which have surfaced recently in very different connections. It is our goal to discuss various aspects … (a) In these informal lecture notes we discuss a number of integrable Hamiltonian systems which have surfaced recently in very different connections. It is our goal to discuss various aspects underlying the integrability of a system like that of group representation, isospectral deformation and geometrical considerations. Since this subject is still far from being understood or being systematic we discuss a number of examples which are seemingly disconnected. In fact, there are some rather unexpected connections like between the inverse square potential of Calogero (Section 4) and the Korteweg de Vries equation. Here we show a surprising new connection between the geodesics on an ellipsoid and Hill's equation with finite gap potential. (b) The differential equations of mechanics can be written in Hamiltonian form 1 $${{\dot x}}_{\text{k}} = \frac{{\partial {\text{H}}}}{{\partial {\text{y}}_{\text{k}} }},\,\,\,\,\,\,\,{{\dot y}}_{\text{k}} = - \frac{{\partial {\text{H}}}}{{\partial {\text{x}}_{\text{k}} }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{k = 1,2,}}...{\text{n}}} \right)$$

Fabrication of large addition energy quantum dots in graphene

2009-10-26
J. Moser , Adrian Bachtold
We present a simple technique to fabricate graphene quantum dots in a cryostat. It relies upon the controlled rupture of a suspended graphene sheet subjected to the application of a … We present a simple technique to fabricate graphene quantum dots in a cryostat. It relies upon the controlled rupture of a suspended graphene sheet subjected to the application of a large electron current. This results in the in-situ formation of a clean and ultra-narrow constriction, which hosts one quantum dot, and occasionally a few quantum dots in series. Conductance spectroscopy indicates that individual quantum dots can possess an addition energy as large as 180 meV and a level spacing as large as 25 meV. Our technique has several assets: (i) the dot is suspended, thus the electrostatic influence of the substrate is reduced, and (ii) contamination is minimized, since the edges of the dot have only been exposed to the vacuum in the cryostat.
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Interaction-mediated asymmetries of the quantized Hall effect

2009-10-01
A. Siddiki , J. Horas , J. Moser +2 more
Experimental and theoretical investigations on the integer quantized Hall effect in gate-defined narrow Hall bars are presented. At low electron mobility the classical (high-temperature) Hall resistance line RH(B) cuts through … Experimental and theoretical investigations on the integer quantized Hall effect in gate-defined narrow Hall bars are presented. At low electron mobility the classical (high-temperature) Hall resistance line RH(B) cuts through the center of all Hall plateaus. In contrast, for our high-mobility samples the intersection point, at even filling factors ν=2, 4, ..., is clearly shifted towards larger magnetic fields B. This asymmetry is in good agreement with predictions of the screening theory, i.e. taking Coulomb interaction into account. The observed effect is directly related to the formation of incompressible strips in the Hall bar. The spin-split plateau at ν=1 is found to be almost symmetric regardless of the mobility. We explain this within the so-called effective g-model.
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Orbital effects on tunneling anisotropic magnetoresistance in Fe/GaAs/Au junctions

2009-09-01
Michael Wimmer , M. Lobenhofer , J. Moser +6 more
We report experiments on epitaxially grown Fe/GaAs/Au tunnel junctions demonstrating that the magnitude of the tunneling anisotropic magnetoresistance (TAMR) effect can be controlled by magnetic field strength. Theoretical modeling shows … We report experiments on epitaxially grown Fe/GaAs/Au tunnel junctions demonstrating that the magnitude of the tunneling anisotropic magnetoresistance (TAMR) effect can be controlled by magnetic field strength. Theoretical modeling shows that the interplay of the orbital effects of a magnetic field and the Dresselhaus spin-orbit coupling in the GaAs barrier leads to an independent contribution to the TAMR effect with uniaxial symmetry, whereas the Bychkov-Rashba spin-orbit coupling does not play a role. The effect is intrinsic to barriers with bulk inversion asymmetry.
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Transport Properties of Graphene in the High-Current Limit

2009-08-12
Amelia Barreiro , Michele Lazzeri , J. Moser +2 more
We present a detailed study of the high-current transport properties of graphene devices patterned in a four-point configuration. The current tends to saturate as the voltage across graphene is increased … We present a detailed study of the high-current transport properties of graphene devices patterned in a four-point configuration. The current tends to saturate as the voltage across graphene is increased but never reaches the complete saturation as in metallic nanotubes. Measurements are compared to a model based on the Boltzmann equation, which includes electron-scattering processes due to charged and neutral impurities, and graphene optical phonons. The saturation is incomplete because of the competition between disorder and optical phonon scattering.
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Dynamical systems — Past and present

2008-12-01
J. Moser

The environment of graphene probed by electrostatic force microscopy

2008-03-24
J. Moser , Albert Verdaguer , David Jiménez +2 more
We employ electrostatic force microscopy to study the electrostatic environment of graphene sheets prepared with the micromechanical exfoliation technique. We detect the electric dipole of residues left from the adhesive … We employ electrostatic force microscopy to study the electrostatic environment of graphene sheets prepared with the micromechanical exfoliation technique. We detect the electric dipole of residues left from the adhesive tape during graphene preparation, as well as the dipole of water molecules adsorbed on top of graphene. Water molecules form a dipole layer that can generate an electric field as large as ∼109Vm−1. We expect that water molecules can significantly modify the electrical properties of graphene devices.
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Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

2007-12-06
J. Horas , A. Siddiki , J. Moser +2 more

Current-induced cleaning of graphene

2007-10-15
J. Moser , Amelia Barreiro , Adrian Bachtold
A simple yet highly reproducible method to suppress contamination of graphene at low temperature inside the cryostat is presented. The method consists of applying a current of several mA through … A simple yet highly reproducible method to suppress contamination of graphene at low temperature inside the cryostat is presented. The method consists of applying a current of several mA through the graphene device, which is here typically a few $μ$m wide. This ultra-high current density is shown to remove contamination adsorbed on the surface. This method is well suited for quantum electron transport studies of undoped graphene devices, and its utility is demonstrated here by measuring the anomalous quantum Hall effect.
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Donor binding energy and thermally activated persistent photoconductivity in high mobility (001) AlAs quantum wells

2007-10-01
S. Dasgupta , C. Knaak , J. Moser +5 more
A doping series of AlAs (001) quantum wells with Si δ-modulation doping on both sides reveals different dark and postillumination saturation densities, as well as temperature dependent photoconductivity. The lower … A doping series of AlAs (001) quantum wells with Si δ-modulation doping on both sides reveals different dark and postillumination saturation densities, as well as temperature dependent photoconductivity. The lower dark two-dimensional electron density saturation is explained assuming deep binding energy of ΔDK=65.2meV for Si donors in the dark. Persistent photoconductivity (PPC) is observed upon illumination, with higher saturation density indicating shallow postillumination donor binding energy. The photoconductivity is thermally activated, with 4K illumination requiring postillumination annealing to T=30K to saturate the PPC. Dark and postillumination doping efficiencies are reported.
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Tunneling Anisotropic Magnetoresistance and Spin-Orbit Coupling in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Fe</mml:mi><mml:mo>/</mml:mo><mml:mi>GaAs</mml:mi><mml:mo>/</mml:mo><mml:mi>Au</mml:mi></mml:math>Tunnel Junctions

2007-08-02
J. Moser , Alex Matos-Abiague , D. Schuh +3 more
We report the observation of tunneling anisotropic magnetoresistance effect (TAMR) in the epitaxial metal-semiconductor system Fe/GaAs/Au. The observed two-fold anisotropy of the resistance can be switched by reversing the bias … We report the observation of tunneling anisotropic magnetoresistance effect (TAMR) in the epitaxial metal-semiconductor system Fe/GaAs/Au. The observed two-fold anisotropy of the resistance can be switched by reversing the bias voltage, suggesting that the effect originates from the interference of the spin-orbit coupling at the interfaces. Corresponding model calculations reproduce the experimental findings very well.
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Disordered AlAs wires: Temperature-dependent resonance areas within the Fermi-liquid paradigm

2006-11-10
J. Moser , Stefano Roddaro , D. Schuh +3 more
AlAs cleaved-edge overgrown quantum wires near pinch-off reveal conductance resonances with an unconventional dependence on temperature $T$. The resonance areas decrease with reduced $T$ consistent with classical Coulomb blockade (CB) … AlAs cleaved-edge overgrown quantum wires near pinch-off reveal conductance resonances with an unconventional dependence on temperature $T$. The resonance areas decrease with reduced $T$ consistent with classical Coulomb blockade (CB) in a single dot, but then become rapidly smaller below a crossover ${T}_{X}$. Though resembling Luttinger liquid behavior below the crossover, the anomalous $T$ dependence including the crossover fit quantitatively to a classical-to-stochastic CB transition, whereby stochastic multidot CB sets in at low temperatures. Conductance at finite bias resembles a depinned charge density wave as expected for a chain of disorder induced dots. These studies highlight the applicability of the Fermi liquid paradigm to the description of disordered heavy-mass quantum wires.
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Bias dependent inversion of tunneling magnetoresistance in Fe∕GaAs∕Fe tunnel junctions

2006-10-16
J. Moser , Marcus Zenger , C. Gerl +7 more
We investigated spin dependent transport through Fe/GaAs/Fe tunnel junctions. The tunneling magnetoresistance effect (TMR) was probed for different types of Fe/GaAs interfaces. For interfaces cleaned by hydrogen plasma the TMR … We investigated spin dependent transport through Fe/GaAs/Fe tunnel junctions. The tunneling magnetoresistance effect (TMR) was probed for different types of Fe/GaAs interfaces. For interfaces cleaned by hydrogen plasma the TMR effect is increased and observable at room temperature. If an epitaxial Fe/GaAs(001) interface is involved, the tunnel junction exhibits a bias dependent inversion of the TMR effect. This is a first experimental signature for band structure effects at a Fe/GaAs interface and relevant for spin injection experiments.
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Aluminum arsenide cleaved-edge overgrown quantum wires

2005-07-25
J. Moser , T. Zibold , D. Schuh +6 more
We report conductance measurements in quantum wires made of aluminum arsenide, a heavy-mass, multi-valley one-dimensional (1D) system. Zero-bias conductance steps are observed as the electron density in the wire is … We report conductance measurements in quantum wires made of aluminum arsenide, a heavy-mass, multi-valley one-dimensional (1D) system. Zero-bias conductance steps are observed as the electron density in the wire is lowered, with additional steps observable upon applying a finite dc bias. We attribute these steps to depopulation of successive 1D subbands. The quantum conductance is substantially reduced with respect to the anticipated value for a spin- and valley-degenerate 1D system. This reduction is consistent with disorder-induced, intra-wire backscattering which suppresses the transmission of 1D modes. Calculations are presented to demonstrate the role of strain in the 1D states of this cleaved-edge structure.
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High-field magnetoresistance of Fe∕GaAs∕Fe tunnel junctions

2004-08-02
Marcus Zenger , J. Moser , W. Wegscheider +2 more
We investigate transport through 6–10nm thin epitaxial GaAs(001) barriers sandwiched between polycrystalline iron films. Apart from a pronounced tunneling magnetoresistance effect at low magnetic fields, we observe a distinct negative … We investigate transport through 6–10nm thin epitaxial GaAs(001) barriers sandwiched between polycrystalline iron films. Apart from a pronounced tunneling magnetoresistance effect at low magnetic fields, we observe a distinct negative magnetoresistance (MR) at low and a positive MR at higher temperatures. We show that the negative MR contribution is only observed for the ferromagnetic iron contacts but is absent if iron is replaced by copper or gold electrodes. Possible explanations of the negative MR involve suppression of spin-flip scattering or Zeeman splitting of the tunneling barrier, but neither of these explanations is fully consistent with the data.
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From spin-Peierls to superconductivity: (TMTTF)<sub>2</sub>PF<sub>6</sub>under high pressure

2001-01-11
D. Jaccard , H. Wilhelm , D. Jérôme +3 more
The nature of the attractive electron-electron interaction, leading to the formation of Cooper-pairs in unconventional superconductors has still to be fully understood and is subject to intensive research. Here we … The nature of the attractive electron-electron interaction, leading to the formation of Cooper-pairs in unconventional superconductors has still to be fully understood and is subject to intensive research. Here we show that the sequence spin-Peierls, antiferromagnetism, superconductivity observed in (TMTTF)_2PF_6 under pressure makes the (TM)_2X phase diagram universal. We argue that the suppression of the spin-Peierls transition under pressure, the close vicinity of antiferromagnetic and superconducting phases at high pressure as well as the existence of critical antiferromagnetic fluctuations above T_c strongly support the intriguing possibility that the interchain exchange of antiferromagnetic fluctuations provides the pairing mechanism required for bound charge carriers.
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A stability theorem for minimal foliations on a torus

1988-12-01
J. Moser
Abstract This paper is concerned with minimal foliations; these are foliations whose leaves are extremals of a prescribed variational problem, as for example foliations consisting of minimal surfaces. Such a … Abstract This paper is concerned with minimal foliations; these are foliations whose leaves are extremals of a prescribed variational problem, as for example foliations consisting of minimal surfaces. Such a minimal foliation is called stable if for any small perturbation of the variational problem there exists a minimal foliation conjugate under a smooth diffeomorphism to the original foliation. In this paper the stability of special foliations of codimension 1 on a higher-dimensional torus is established. This result requires small divisor assumptions similar to those encountered in dynamical systems. This theorem can be viewed as a generalization of the perturbation theory of invariant tori for Hamiltonian systems to elliptic partial differential equations for which one obtains quasi-periodic solutions.
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The rotation number for almost periodic potentials

1983-06-01
Randal Johnson , J. Moser
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The rotation number for almost periodic potentials

1982-09-01
Randal Johnson , J. Moser
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Geometry of Quadrics and Spectral Theory

1980-01-01
J. Moser

Various Aspects of Integrable Hamiltonian Systems

1980-01-01
J. Moser
Coauthor Papers Together
Adrian Bachtold 22
Alexander Eichler 11
Ying Yan 8
Julien Chaste 8
W. Wegscheider 6
D. Schuh 5
M. I. Dykman 5
D. Weiß 4
M. Bichler 3
J. Güttinger 3
Jie Lu 3
M. Grayson 3
I. Wilson‐Rae 3
Amelia Barreiro 3
Randal Johnson 2
Marcus Zenger 2
Haihua Tao 2
Y. Tarakanov 2
G. Abstreiter 2
V. Pellegrini 2
Zhihuang Kang 2
Xi Chen 2
Lars Rippe 2
Stefano Roddaro 2
Ce Zhang 2
Chunyan Shi 2
J. Horas 2
Jiamin Qiu 2
C. M. Sotomayor Torres 2
Jaroslav Fabian 2
Heng Lu 2
FengNan Chen 2
Stefan Kröll 2
A. Siddiki 2
Adam Kinos 2
Stefan Ludwig 2
F. Alzina 2
Andreas Walther 2
Alex Matos-Abiague 2
Ye Tian 2
Jari M. Kinaret 2
Mariusz Zdrojek 2
B. Lassagne 2
G. Ceballos 1
Marianna Sledzinska 1
Michele Lazzeri 1
Andreas Wallraff 1
B. L. Cragin 1
M. T. O’Leary 1
Axel M. Eriksson 1

Strong Coupling Between Single-Electron Tunneling and Nanomechanical Motion

2009-07-24
Gary A. Steele , A. K. Hüttel , B. Witkamp +4 more
Nanoscale resonators that oscillate at high frequencies are useful in many measurement applications. We studied a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying … Nanoscale resonators that oscillate at high frequencies are useful in many measurement applications. We studied a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying a periodic radio frequency potential using a nearby antenna. Single-electron charge fluctuations created periodic modulations of the mechanical resonance frequency. A quality factor exceeding 10^5 allows the detection of a shift in resonance frequency caused by the addition of a single-electron charge on the nanotube. Additional evidence for the strong coupling of mechanical motion and electron tunneling is provided by an energy transfer to the electrons causing mechanical damping and unusual nonlinear behavior. We also discovered that a direct current through the nanotube spontaneously drives the mechanical resonator, exerting a force that is coherent with the high-frequency resonant mechanical motion.
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A tunable carbon nanotube electromechanical oscillator

2004-09-01
V. A. Sazonova , Yuval Yaish , Hande Üstünel +3 more
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Digital and FM Demodulation of a Doubly Clamped Single‐Walled Carbon‐Nanotube Oscillator: Towards a Nanotube Cell Phone

2010-04-14
V. Gouttenoire , Thomas Barois , S. Perisanu +4 more
Abstract Electromechanical resonators are a key element in radio‐frequency telecommunication devices and thus new resonator concepts from nanotechnology can readily find important industrial opportunities. Here, the successful experimental realization of … Abstract Electromechanical resonators are a key element in radio‐frequency telecommunication devices and thus new resonator concepts from nanotechnology can readily find important industrial opportunities. Here, the successful experimental realization of AM, FM, and digital demodulation with suspended single‐walled carbon‐nanotube resonators in a field‐effect transistor configuration is reported. The crucial role played by the electromechanical resonance in demodulation is clearly demonstrated. The FM technique is shown to lead to the suppression of unwanted background signals and the reduction of noise for a better detection of the mechanical motion of nanotubes. The digital data‐transfer rate of standard cell‐phone technology is within the reach of these devices.
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Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene

2011-05-15
Alexander Eichler , J. Moser , Julien Chaste +3 more
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Performance of monolayer graphene nanomechanical resonators with electrical readout

2009-09-20
Changyao Chen , Sami Rosenblatt , Kirill I. Bolotin +6 more
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Carbon Nanotubes as Ultrahigh Quality Factor Mechanical Resonators

2009-06-03
A. K. Hüttel , Gary A. Steele , B. Witkamp +3 more
We have observed the transversal vibration mode of suspended carbon nanotubes at millikelvin temperatures by measuring the single-electron tunneling current. The suspended nanotubes are actuated contact-free by the radio frequency … We have observed the transversal vibration mode of suspended carbon nanotubes at millikelvin temperatures by measuring the single-electron tunneling current. The suspended nanotubes are actuated contact-free by the radio frequency electric field of a nearby antenna; the mechanical resonance is detected in the time-averaged current through the nanotube. Sharp, gate-tunable resonances due to the bending mode of the nanotube are observed, combining resonance frequencies of up to ν0 = 350 MHz with quality factors above Q = 105, much higher than previously reported results on suspended carbon nanotube resonators. The measured magnitude and temperature dependence of the Q factor shows a remarkable agreement with the intrinsic damping predicted for a suspended carbon nanotube. By adjusting the radio frequency power on the antenna, we find that the nanotube resonator can easily be driven into the nonlinear regime.
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A nanomechanical mass sensor with yoctogram resolution

2012-04-01
Julien Chaste , Alexander Eichler , J. Moser +3 more
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Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators

2010-03-30
Vibhor Singh , Shamashis Sengupta , Hari S. Solanki +5 more
We use suspended graphene electromechanical resonators to study the variation of resonant frequency as a function of temperature. Measuring the change in frequency resulting from a change in tension, from … We use suspended graphene electromechanical resonators to study the variation of resonant frequency as a function of temperature. Measuring the change in frequency resulting from a change in tension, from 300 to 30 K, allows us to extract information about the thermal expansion of monolayer graphene as a function of temperature, which is critical for strain engineering applications. We find that thermal expansion of graphene is negative for all temperatures between 300 and 30 K. We also study the dispersion, the variation of resonant frequency with DC gate voltage, of the electromechanical modes and find considerable tunability of resonant frequency, desirable for applications like mass sensing and RF signal processing at room temperature. With a lowering of temperature, we find that the positively dispersing electromechanical modes evolve into negatively dispersing ones. We quantitatively explain this crossover and discuss optimal electromechanical properties that are desirable for temperature-compensated sensors.
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NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES

1976-02-28
Boris Dubrovin , V. B. Matveev , S. P. Novikov
The basic content of this survey is an exposition of a recently developed method of constructing a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics … The basic content of this survey is an exposition of a recently developed method of constructing a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable. These solutions are such that the spectrum of their associated linear differential operators has a finite-zone structure. The set of linear operators with a given finite-zone spectrum is the Jacobian variety of a Riemann surface, which is determined by the structure of the spectrum. We give an explicit solution of the corresponding non-linear equations in the language of the theory of Abelian functions.
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Electric Field Effect in Atomically Thin Carbon Films

2004-10-21
Kostya S. Novoselov , A. K. Geǐm , С. В. Морозов +5 more
We report a naturally-occurring two-dimensional material (graphene that can be viewed as a gigantic flat fullerene molecule, describe its electronic properties and demonstrate all-metallic field-effect transistor, which uniquely exhibits ballistic … We report a naturally-occurring two-dimensional material (graphene that can be viewed as a gigantic flat fullerene molecule, describe its electronic properties and demonstrate all-metallic field-effect transistor, which uniquely exhibits ballistic transport at submicron distances even at room temperature.
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Dynamical strong coupling and parametric amplification of mechanical modes of graphene drums

2016-06-13
John P. Mathew , Raj N. Patel , Abhinandan Borah +2 more
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Subkelvin Parametric Feedback Cooling of a Laser-Trapped Nanoparticle

2012-09-07
Jan Gieseler , Bradley Deutsch , Romain Quidant +1 more
Recent experiments have demonstrated the ability to optically cool a macroscopic mechanical oscillator to its quantum ground state by means of dynamic backaction. Such experiments allow quantum mechanics to be … Recent experiments have demonstrated the ability to optically cool a macroscopic mechanical oscillator to its quantum ground state by means of dynamic backaction. Such experiments allow quantum mechanics to be tested with mesoscopic objects, and represent an essential step toward quantum optical memories, transducers, and amplifiers. Most oscillators considered so far are rigidly connected to their thermal environment, fundamentally limiting their mechanical Q-factors and requiring cryogenic precooling to liquid helium temperatures. Here we demonstrate parametric feedback cooling of a laser-trapped nanoparticle which is entirely isolated from the thermal bath. The lack of a clamping mechanism provides robust decoupling from internal vibrations and makes it possible to cool the nanoparticle in all degrees of freedom by means of a single laser beam. Compared to laser-trapped microspheres, nanoparticles have the advantage of higher resonance frequencies and lower recoil heating, which are favorable conditions for quantum ground state cooling
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Dynamics and Dissipation Induced by Single-Electron Tunneling in Carbon Nanotube Nanoelectromechanical Systems

2012-04-24
Marc Ganzhorn , Wolfgang Wernsdorfer
We demonstrate the effect of single-electron tunneling (SET) through a carbon nanotube quantum dot on its nanomechanical motion. We find that the frequency response and the dissipation of the nanoelectromechanical … We demonstrate the effect of single-electron tunneling (SET) through a carbon nanotube quantum dot on its nanomechanical motion. We find that the frequency response and the dissipation of the nanoelectromechanical system (NEMS) to SET strongly depends on the electronic environment of the quantum dot, in particular on the total dot capacitance and the tunnel coupling to the metal contacts. Our findings suggest that one could achieve quality factors of 10$^{6}$ or higher by choosing appropriate gate dielectrics and/or by improving the tunnel coupling to the leads.
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The spectrum of Hill's equation

1975-10-01
H. P. McKean , Pierre van Moerbeke

Mechanical Detection of Carbon Nanotube Resonator Vibrations

2007-08-20
David García-Sánchez , Álvaro San Paulo , M.J. Esplandiu +4 more
Bending-mode vibrations of carbon nanotube resonator devices were mechanically detected in air at atmospheric pressure by means of a novel scanning force microscopy method. The fundamental and higher order bending … Bending-mode vibrations of carbon nanotube resonator devices were mechanically detected in air at atmospheric pressure by means of a novel scanning force microscopy method. The fundamental and higher order bending eigenmodes were imaged at up to 3.1GHz with sub-nanometer resolution in vibration amplitude. The resonance frequency and the eigenmode shape of multi-wall nanotubes are consistent with the elastic beam theory for a doubly clamped beam. For single-wall nanotubes, however, resonance frequencies are significantly shifted, which is attributed to fabrication generating, for example, slack. The effect of slack is studied by pulling down the tube with the tip, which drastically reduces the resonance frequency.
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Tunable phonon-cavity coupling in graphene membranes

2016-06-13
Roberto De Alba , Francesco Massel , Isaac R. Storch +5 more
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Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points

1976-03-01
H. P. McKean , Eugene Trubowitz

Coherent control of a classical nanomechanical two-level system

2013-06-28
Thomas B. Faust , Juliane Rieger , M. J. Seitner +2 more
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Real-space tailoring of the electron–phonon coupling in ultraclean nanotube mechanical resonators

2014-01-10
Avishai Benyamini , Assaf Hamo , Silvia Viola Kusminskiy +2 more
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A local optical probe for measuring motion and stress in a nanoelectromechanical system

2012-01-22
Antoine Reserbat‐Plantey , Laëtitia Marty , O. Arcizet +2 more
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Ultrasensitive force detection with a nanotube mechanical resonator

2013-06-09
J. Moser , J. Güttinger , Alexander Eichler +4 more
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Coherent phonon manipulation in coupled mechanical resonators

2013-06-28
Hajime Okamoto , Adrien Gourgout , Chia-Yuan Chang +4 more
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Nanomechanical motion measured with an imprecision below that at the standard quantum limit

2009-11-01
John Teufel , Tobias Donner , Manuel Castellanos-Beltran +2 more

Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity

2014-08-24
Vibhor Singh , Sal J. Bosman , Ben Schneider +3 more
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An atomic-resolution nanomechanical mass sensor

2008-07-20
K. Jensen , Kwanpyo Kim , Alex Zettl
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High-frequency nanotube mechanical resonators

2011-11-21
Julien Chaste , Marianna Sledzinska , Mariusz Zdrojek +2 more
We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for … We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for higher order eigenmodes. The high-frequency resonances are achieved using short suspended nanotubes and by introducing tensile stress in the nanotube. These devices allow us to determine the coefficient of the thermal expansion of an individual nanotube, which is negative and is about -0.7E-5 1/K at room temperature. High-frequency resonators made of nanotubes hold promise for mass sensing and experiments in the quantum limit.
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Single-crystal diamond nanomechanical resonators with quality factors exceeding one million

2014-04-08
Ye Tao , J. M. Boss , B. A. Moores +1 more
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Coherent phonon dynamics in spatially separated graphene mechanical resonators

2020-03-02
Zhuo‐Zhi Zhang , Xiang‐Xiang Song , Gang Luo +7 more
Vibrational modes in mechanical resonators provide a promising candidate to interface and manipulate classical and quantum information. The observation of coherent dynamics between distant mechanical resonators can be a key … Vibrational modes in mechanical resonators provide a promising candidate to interface and manipulate classical and quantum information. The observation of coherent dynamics between distant mechanical resonators can be a key step toward scalable phonon-based applications. Here we report tunable coherent phonon dynamics with an architecture comprising three graphene mechanical resonators coupled in series, where all resonators can be manipulated by electrical signals on control gates. We demonstrate coherent Rabi oscillations between spatially separated resonators indirectly coupled via an intermediate resonator serving as a phonon cavity. The Rabi frequency fits well with the microwave burst power on the control gate. We also observe Ramsey interference, where the oscillation frequency corresponds to the indirect coupling strength between these resonators. Such coherent processes indicate that information encoded in vibrational modes can be transferred and stored between spatially separated resonators, which can open the venue of on-demand phonon-based information processing.
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Fluctuation broadening in carbon nanotube resonators

2012-11-06
Arthur Barnard , V. A. Sazonova , Arend M. van der Zande +1 more
We simulated the behavior of suspended carbon-nanotube (CNT) resonators over a broad range of temperatures to address the unexplained spectral broadening and frequency shifts seen in experiments. We find that … We simulated the behavior of suspended carbon-nanotube (CNT) resonators over a broad range of temperatures to address the unexplained spectral broadening and frequency shifts seen in experiments. We find that thermal fluctuations induce strong coupling between resonance modes. This effect leads to spectral fluctuations which readily account for the experimentally observed quality factors $Q\sim100$ at $300\ K$. Using a mean field approach to describe entropic fluctuations we analytically calculate $Q$ and frequency shifts in tensioned and buckled CNTs and find excellent agreement with simulations.
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Parametric Amplification and Self-Oscillation in a Nanotube Mechanical Resonator

2011-05-26
Alexander Eichler , Julien Chaste , J. Moser +1 more
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification … A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the line shape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultralow force sensing experiments.
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Stamp Transferred Suspended Graphene Mechanical Resonators for Radio Frequency Electrical Readout

2011-12-05
Xuefeng Song , Mika Oksanen , Mika A. Sillanpää +3 more
We present a simple micromanipulation technique to transfer suspended graphene flakes onto any substrate and to assemble them with small localized gates into mechanical resonators. The mechanical motion of the … We present a simple micromanipulation technique to transfer suspended graphene flakes onto any substrate and to assemble them with small localized gates into mechanical resonators. The mechanical motion of the graphene is detected using an electrical, radio-frequency (RF) reflection readout scheme where the time-varying graphene capacitor reflects a RF carrier at f=5-6 GHz producing modulation sidebands at f +/- fm. A mechanical resonance frequency up to fm=178 MHz is demonstrated. We find both hardening/softening Duffing effects on different samples, and obtain a critical amplitude of ~40 pm for the onset of nonlinearity in graphene mechanical resonators. Measurements of the quality factor of the mechanical resonance as a function of DC bias voltage Vdc indicate that dissipation due to motion-induced displacement currents in graphene electrode is important at high frequencies and large Vdc.
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Strong Coupling between Mechanical Modes in a Nanotube Resonator

2012-07-11
Alexander Eichler , M. Ruiz , J.A. Plaza +1 more
We report on the nonlinear coupling between the mechanical modes of a nanotube resonator. The coupling is revealed in a pump-probe experiment where a mode driven by a pump force … We report on the nonlinear coupling between the mechanical modes of a nanotube resonator. The coupling is revealed in a pump-probe experiment where a mode driven by a pump force is shown to modify the motion of a second mode measured with a probe force. In a second series of experiments, we actuate the resonator with only one oscillating force. Mechanical resonances feature exotic line shapes with reproducible dips, peaks, and jumps when the measured mode is commensurate with another mode with a frequency ratio of either 2 or 3. Conventional line shapes are recovered by detuning the frequency ratio using the voltage on a nearby gate electrode. The exotic line shapes are attributed to strong coupling between the mechanical modes. The possibility to control the strength of the coupling with the gate voltage holds promise for various experiments, such as quantum manipulation, mechanical signal processing, and the study of the quantum-to-classical transition.
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Phase Transitions of Adsorbed Atoms on the Surface of a Carbon Nanotube

2010-01-28
Zenghui Wang , Wei Jiang , Peter K. Morse +3 more
A suspended carbon nanotube can act as a nanoscale resonator with remarkable electromechanical properties and the ability to detect adsorption on its surface at the level of single atoms. Understanding … A suspended carbon nanotube can act as a nanoscale resonator with remarkable electromechanical properties and the ability to detect adsorption on its surface at the level of single atoms. Understanding adsorption on nanotubes and other graphitic materials is key to many sensing and storage applications. Here we show that nanotube resonators offer a powerful new means of investigating fundamental aspects of adsorption on carbon, including the collective behaviour of adsorbed matter and its coupling to the substrate electrons. By monitoring the vibrational resonance frequency in the presence of noble gases, we observe the formation of monolayers on the cylindrical surface and phase transitions within these monolayers, and simultaneous modification of the electrical conductance. The monolayer observations also demonstrate the possibility of studying the fundamental behaviour of matter in cylindrical geometry.
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De problemate quodam mechanico, quod ad primam integralium ultraellipticorum classem revocatur.

1859-01-01
C. Neumann
Article De problemate quodam mechanico, quod ad primam integralium ultraellipticorum classem revocatur. was published on January 1, 1859 in the journal Journal für die reine und angewandte Mathematik (volume 1859, … Article De problemate quodam mechanico, quod ad primam integralium ultraellipticorum classem revocatur. was published on January 1, 1859 in the journal Journal für die reine und angewandte Mathematik (volume 1859, issue 56).
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Experimental quantum-state tomography of a solid-state qubit

2008-02-07
Lars Rippe , Brian Julsgaard , Andreas Walther +2 more
Quantum-state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in ${\mathrm{Pr}}^{3+}$ ions, doped into a ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ crystal. We experimentally verify that … Quantum-state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in ${\mathrm{Pr}}^{3+}$ ions, doped into a ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-M\o{}lmer dark-state scheme [Roos and M\o{}lmer, Phys. Rev. A 69, 022321 (2004)] Fidelities above $>90%$, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-M\o{}lmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.
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Frequency and phase noise of ultrahigh<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>silicon nitride nanomechanical resonators

2012-04-27
King Yan Fong , Wolfram H. P. Pernice , Hong X. Tang
We describe the measurement and modeling of amplitude noise and phase noise in ultrahigh $Q$ nanomechanical resonators made from stoichiometric silicon nitride. With quality factors exceeding 2 million, the resonators' … We describe the measurement and modeling of amplitude noise and phase noise in ultrahigh $Q$ nanomechanical resonators made from stoichiometric silicon nitride. With quality factors exceeding 2 million, the resonators' noise performance is studied with high precision. We find that the amplitude noise can be well described by the thermomechanical model, however, the resonators exhibit sizable extra phase noise due to their intrinsic frequency fluctuations. We develop a method to extract the resonator frequency fluctuation of a driven resonator and obtain a noise spectrum with ${k}_{B}T/f$ dependence, which could be attributed to defect motion with broadly distributed relaxation times.
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Symmetry breaking in a mechanical resonator made from a carbon nanotube

2013-11-25
Alexander Eichler , J. Moser , M. I. Dykman +1 more
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Intrinsic dissipation in nanomechanical resonators due to phonon tunneling

2008-06-13
I. Wilson‐Rae
State of the art nanomechanical resonators present quality factors $Q\ensuremath{\sim}{10}^{3}--{10}^{5}$, which are much lower than those that can be naively extrapolated from the behavior of micromechanical resonators. We analyze the … State of the art nanomechanical resonators present quality factors $Q\ensuremath{\sim}{10}^{3}--{10}^{5}$, which are much lower than those that can be naively extrapolated from the behavior of micromechanical resonators. We analyze the dissipation mechanism that arises in nanomechanical beam structures due to the tunneling of mesoscopic phonons between the beam and its supports (known as clamping losses). We derive the environmental force spectral density that determines the quantum Brownian motion of a given resonance. Our treatment is valid for low frequencies and provides the leading contribution in the aspect ratio. This yields fundamental limits for the $Q$ values, which are described by simple scaling laws and are relevant for state of the art experimental structures. In this context, for resonant frequencies in the $0.1--1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ range, while this dissipation mechanism can limit flexural resonators, it is found to be negligible for torsional ones. In the case of structureless three-dimensional supports, the corresponding environmental spectral densities are Ohmic for flexural resonators and super-Ohmic for torsional ones, while for two-dimensional slab supports, they yield $1∕f$ noise. Furthermore, analogous results are established for the case of suspended semiconducting single-walled carbon nanotubes. Finally, we provide a general expression for the spectral density that allows us to extend our treatment to other geometries and illustrate its use by applying it to a microtoroid. Our analysis is relevant for applications in high precision measurements and for the prospects of probing quantum effects in a macroscopic mechanical degree of freedom.
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Nanotube mechanical resonators with quality factors of up to 5 million

2014-10-26
J. Moser , Alexander Eichler , J. Güttinger +2 more
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Stabilization of a linear nanomechanical oscillator to its thermodynamic limit

2013-12-11
E. Gavartin , P. Verlot , Tobias J. Kippenberg
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Quantum computing with an inhomogeneously broadened ensemble of ions: Suppression of errors from detuning variations by specially adapted pulses and coherent population trapping

2004-02-26
Ingela Roos , Klaus Mølmer
The proposal for quantum computing with rare-earth-metal-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding … The proposal for quantum computing with rare-earth-metal-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected frequency channels. We show that a class of Gaussian composite pulses and complex sech pulses provide accurate qubit $\ensuremath{\pi}$ rotations, which are at the same time channel selective on a 5 MHz frequency scale and tolerant to $\ifmmode\pm\else\textpm\fi{}0.5\mathrm{MHz}$ deviations of the transition frequency of ions within a single channel. Rotations in qubit space of arbitrary angles and phases are produced by sequences of $\ensuremath{\pi}$ pulses between the excited state of the ions and coherent superpositions of the qubit states.
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Noise-Enabled Precision Measurements of a Duffing Nanomechanical Resonator

2005-04-19
J. S. Aldridge , A. N. Cleland
We report quantitative measurements of the nonlinear response of a radio frequency mechanical resonator with a very high quality factor. We measure the noise-free transitions between the two basins of … We report quantitative measurements of the nonlinear response of a radio frequency mechanical resonator with a very high quality factor. We measure the noise-free transitions between the two basins of attraction that appear in the nonlinear regime, and find good agreement with theory. We measure the transition rate response to controlled levels of white noise, and extract the basin activation energy. This allows us to obtain precise values for the relevant frequencies and the cubic nonlinearity in the Duffing oscillator, with applications to parametric sensing.
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Tunneling Anisotropic Magnetoresistance: A Spin-Valve-Like Tunnel Magnetoresistance Using a Single Magnetic Layer

2004-09-09
C. Gould , C. Rüster , T. Jungwirth +6 more
We introduce a new class of spintronic devices in which a spin-valve-like effect results from strong spin-orbit coupling in a single ferromagnetic layer rather than from injection and detection of … We introduce a new class of spintronic devices in which a spin-valve-like effect results from strong spin-orbit coupling in a single ferromagnetic layer rather than from injection and detection of a spin-polarized current by two coupled ferromagnets. The effect is observed in a normal-metal-insulator-ferromagnetic-semiconductor tunneling device. This behavior is caused by the interplay of the anisotropic density of states in (Ga,Mn)As with respect to the magnetization direction and the two-step magnetization reversal process in this material.
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Nonadiabatic Dynamics of Two Strongly Coupled Nanomechanical Resonator Modes

2012-07-17
Thomas B. Faust , Johannes Rieger , Maximilian J. Seitner +3 more
The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here we present a classical mechanical model system exhibiting analogous … The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here we present a classical mechanical model system exhibiting analogous behaviour using two inversely tuneable, strongly coupled modes of the same nanomechanical beam resonator. In the adiabatic limit, the anticrossing between the two modes is observed and the coupling strength extracted. Sweeping an initialized mode across the coupling region allows mapping of the progression from diabatic to adiabatic transitions as a function of the sweep rate.
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Millikelvin cooling of an optically trapped microsphere in vacuum

2011-03-20
Tongcang Li , Simon Kheifets , Mark G. Raizen
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Completely integrable Hamiltonian systems connected with semisimple Lie algebras

1976-06-01
M. A. Olshanetsky , A. M. Perelomov

Sideband cooling of micromechanical motion to the quantum ground state

2011-07-01
John Teufel , Tobias Donner , Dale Li +7 more
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Detecting and characterizing frequency fluctuations of vibrational modes

2011-10-03
Z. А. Maizelis , M. L. Roukes , M. I. Dykman
We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of … We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the complex amplitude sensitively depend on the frequency noise statistics and its power spectrum. The analysis applies to classical and to quantum vibrations.
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Coupling Graphene Mechanical Resonators to Superconducting Microwave Cavities

2014-04-18
Peter Weber , J. Güttinger , Ioannis Tsioutsios +2 more
Graphene is an attractive material for nanomechanical devices because it allows for exceptional properties, such as high frequencies and quality factors, and low mass. An outstanding challenge, however, has been … Graphene is an attractive material for nanomechanical devices because it allows for exceptional properties, such as high frequencies and quality factors, and low mass. An outstanding challenge, however, has been to obtain large coupling between the motion and external systems for efficient readout and manipulation. Here, we report on a novel approach, in which we capacitively couple a high-Q graphene mechanical resonator ($Q \sim 10^5$) to a superconducting microwave cavity. The initial devices exhibit a large single-photon coupling of $\sim 10$ Hz. Remarkably, we can electrostatically change the graphene equilibrium position and thereby tune the single photon coupling, the mechanical resonance frequency and the sign and magnitude of the observed Duffing nonlinearity. The strong tunability opens up new possibilities, such as the tuning of the optomechanical coupling strength on a time scale faster than the inverse of the cavity linewidth. With realistic improvements, it should be possible to enter the regime of quantum optomechanics.
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Reduction of symplectic manifolds with symmetry

1974-02-01
Jerrold E. Marsden , Alan Weinstein
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