Physics and Astronomy Atomic and Molecular Physics, and Optics

Cold Atom Physics and Bose-Einstein Condensates

Description

This cluster of papers focuses on the study of many-body physics with ultracold gases, including topics such as quantum simulation, Bose-Einstein condensation, optical lattices, fermi gases, rydberg atoms, quantum information, mott insulators, dipole interactions, and superfluidity.

Keywords

Ultracold Gases; Quantum Simulation; Bose-Einstein Condensation; Optical Lattices; Fermi Gases; Rydberg Atoms; Quantum Information; Mott Insulator; Dipole Interactions; Superfluidity

The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of … The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the $s$-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of … When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a Lorentz-like force. In this Colloquium we present the physical principles at the basis of this artificial (synthetic) magnetism and relate the corresponding Aharonov-Bohm phase to the Berry's phase that emerges when the atom follows adiabatically one of its dressed states. We also discuss some manifestations of artificial magnetism for a cold quantum gas, in particular in terms of vortex nucleation. We then generalise our analysis to the simulation of non-Abelian gauge potentials and present some striking consequences, such as the emergence of an effective spin-orbit coupling. We address both the case of bulk gases and discrete systems, where atoms are trapped in an optical lattice.
Abstract We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and … Abstract We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy Citation1 Keywords: Ultracold atomic and molecular gasesHubbard ModelsDisordered systemsFrustrated systemsSpinor gasesQuantum information Acknowledgements This review is to a great extent based on ideas and discussions that we shared with our long lasting friends, close collaborators, and colleagues: Jan Arlt, Alain Aspect, Nuri Barberan, Michael Baranov, Indrani Bose, Immanuel Bloch, Kai Bongs, Sibylle Braungardt, Dagmar Bruß, Ignacio Cirac, Eugene Demler, Kai Eckert, Wolfgang Ertmer, Uli Everts, Henning Fehrmann, Massimo Inguscio, Jarosław Korbicz, Anna Kubasiak, Jonas Larson, Mikko Juhani Leskinen, Alem Mebrahtu, Chiara Menotti, Armand Niederberger, Belen Paredes, Eugene Polzik, Andreas Osterloh, Klaus Osterloh, Carles Rodó, Oriol Romero-Isart, Robert Roth, Kazimierz Rzazewski, Krzysztof Sacha, Laurent Sanchez-Palencia, Luis Santos, Klaus Sengstock, Gora Shlyapnikov, Christian Trefzger, Janek Wehr, Jakub Zakrzewski, Łukasz Zawitkowski, and Peter Zoller. We acknowledge support from the Deutsche Forschungsgemeinschaft (SFB 407, SPP1078 and SPP1116), the Spanish Ministerio de Ciencia y Tecnología grants BFM-2002-02588, FIS2005-04627, FIS2005-01497, FIS2005-01369, Consolider Ingenio 2010 CSD2006-00019 and Ramón y Cajal, the Alexander von Humboldt Foundation, the ESF Program QUDEDIS, the EU IP SCALA, and the U.S. Department of Energy. Notes †This statement has to be revised when the lattice is created inside of an optical cavity. As we discuss later, the presence of atoms may affect the cavity field. ‡Some authors go beyond this assumption. See for instance Ref. Citation156. †The studies of trapped FB gases concerned in particular FB phase separation Citation211, Citation212, the phase diagram Citation213, novel types of collective modes Citation212, Citation214, Fermi-Fermi interactions mediated by bosons Citation212, Citation215, the collapse of the Fermi cloud in the presence of attractive FB interactions Citation216, or the effects characteristic for the 1D FB mixtures Citation217. †The Majumdar-Ghosh model is one of the few frustrated spin models for which the exact ground states are known. See also, e.g. Citation452–455. †Since the submission of an earlier version of this review, the distributed case has also been considered Citation776, Citation783.
An analysis of leptonic decays based on unitary symmetry for strong interactions (eightfold way) and the V-A theory for weak interactions is presented. An explanation for the observed predominance of … An analysis of leptonic decays based on unitary symmetry for strong interactions (eightfold way) and the V-A theory for weak interactions is presented. An explanation for the observed predominance of the LAMBDA yields + e/sup -/ + nu decay over the LAMBDA /sup -/ yields n + e/sup -/ + nu decay is obtained. Branching ratios predicted for electron modes with DELTA S, 1 are presented; the ratios for the above decays agree well with experimental results. (D.C.W.)
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition … The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension ${d}_{c}$ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on $^{4}\mathrm{He}$ absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical … This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.
Evidence for Bose-Einstein condensation of a gas of spin-polarized ${}^{7}$Li atoms is reported. Atoms confined to a permanent-magnet trap are laser cooled to 200 \ensuremath{\mu}K and are then evaporatively cooled … Evidence for Bose-Einstein condensation of a gas of spin-polarized ${}^{7}$Li atoms is reported. Atoms confined to a permanent-magnet trap are laser cooled to 200 \ensuremath{\mu}K and are then evaporatively cooled to lower temperatures. Phase-space densities consistent with quantum degeneracy are measured for temperatures in the range of 100 to 400 nK. At these high phase-space densities, diffraction of a probe laser beam is observed. Modeling shows that this diffraction is a sensitive indicator of the presence of a spatially localized condensate. Although measurements of the number of condensate atoms have not been performed, the measured phase-space densities are consistent with a majority of the atoms being in the condensate, for total trap numbers as high as $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms. For ${}^{7}$Li, the spin-triplet $s$-wave scattering length is known to be negative, corresponding to an attractive interatomic interaction. Previously, Bose-Einstein condensation was predicted not to occur in such a system.
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This … Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
We have observed condensation of fermionic atom pairs in the BCS-BEC crossover regime. A trapped gas of fermionic 40K atoms is evaporatively cooled to quantum degeneracy and then a magnetic-field … We have observed condensation of fermionic atom pairs in the BCS-BEC crossover regime. A trapped gas of fermionic 40K atoms is evaporatively cooled to quantum degeneracy and then a magnetic-field Feshbach resonance is used to control the atom-atom interactions. The location of this resonance is precisely determined from low-density measurements of molecule dissociation. In order to search for condensation on either side of the resonance, we introduce a technique that pairwise projects fermionic atoms onto molecules; this enables us to measure the momentum distribution of fermionic atom pairs. The transition to condensation of fermionic atom pairs is mapped out as a function of the initial atom gas temperature T compared to the Fermi temperature T(F) for magnetic-field detunings on both the BCS and BEC sides of the resonance.
We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated ``cigar''-shaped atomic trap. We … We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated ``cigar''-shaped atomic trap. We show that, in the low-energy scattering regime, the scattering process degenerates to a total reflection, suggesting an experimental realization of a famous model in theoretical physics---a one-dimensional gas of impenetrable bosons (``Tonks'' gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.
We establish the general form of the generator of a completely positive dynamical semigroup of an N-level quantum system, and we apply the result to derive explicit inequalities among the … We establish the general form of the generator of a completely positive dynamical semigroup of an N-level quantum system, and we apply the result to derive explicit inequalities among the physical parameters characterizing the Markovian evolution of a 2-level system.
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and … The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. … The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap, and in optical superlattices are presented.
A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the … A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant, $\ensuremath{\gamma}$. When $\ensuremath{\gamma}$ is small, Bogoliubov's perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of $\ensuremath{\gamma}$ and show that it is analytic for all $\ensuremath{\gamma}$, except $\ensuremath{\gamma}=0$. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum---not one as is ordinarily supposed.
The short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case. The ground-state energy, wave function, and the chemical potentials are obtained, … The short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case. The ground-state energy, wave function, and the chemical potentials are obtained, and it is found that the ground state exhibits no conductor-insulator transition as the correlation strength is increased.
The behavior of the electrons in a dense electron gas is analyzed quantum-mechanically by a series of canonical transformations. The usual Hamiltonian corresponding to a system of individual electrons with … The behavior of the electrons in a dense electron gas is analyzed quantum-mechanically by a series of canonical transformations. The usual Hamiltonian corresponding to a system of individual electrons with Coulomb interactions is first re-expressed in such a way that the long-range part of the Coulomb interactions between the electrons is described in terms of collective fields, representing organized "plasma" oscillation of the system as a whole. The Hamiltonian then describes these collective fields plus a set of individual electrons which interact with the collective fields and with one another via short-range screened Coulomb interactions. There is, in addition, a set of subsidiary conditions on the system wave function which relate the field and particle variables. The field-particle interaction is eliminated to a high degree of approximation by a further canonical transformation to a new representation in which the Hamiltonian describes independent collective fields, with ${n}^{\ensuremath{'}}$ degrees of freedom, plus the system of electrons interacting via screened Coulomb forces with a range of the order of the inter electronic distance. The new subsidiary conditions act only on the electronic wave functions; they strongly inhibit long wavelength electronic density fluctuations and act to reduce the number of individual electronic degrees of freedom by ${n}^{\ensuremath{'}}$. The general properties of this system are discussed, and the methods and results obtained are related to the classical density fluctuation approach and Tomonaga's one-dimensional treatment of the degenerate Fermi gas.
The repulsive $\ensuremath{\delta}$ interaction problem in one dimension for $N$ particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as … The repulsive $\ensuremath{\delta}$ interaction problem in one dimension for $N$ particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations $R$ of the permutation group ${S}_{N}$. For some $R'\mathrm{s}$ this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-\textonehalf{} fermions is reduced to a generalized Fredholm equation.
A quantum gas of ultracold polar molecules, with long-range and anisotropic interactions, not only would enable explorations of a large class of many-body physics phenomena but also could be used … A quantum gas of ultracold polar molecules, with long-range and anisotropic interactions, not only would enable explorations of a large class of many-body physics phenomena but also could be used for quantum information processing. We report on the creation of an ultracold dense gas of potassium-rubidium ( 40 K 87 Rb) polar molecules. Using a single step of STIRAP (stimulated Raman adiabatic passage) with two-frequency laser irradiation, we coherently transfer extremely weakly bound KRb molecules to the rovibrational ground state of either the triplet or the singlet electronic ground molecular potential. The polar molecular gas has a peak density of 10 12 per cubic centimeter and an expansion-determined translational temperature of 350 nanokelvin. The polar molecules have a permanent electric dipole moment, which we measure with Stark spectroscopy to be 0.052(2) Debye (1 Debye = 3.336 × 10 –30 coulomb-meters) for the triplet rovibrational ground state and 0.566(17) Debye for the singlet rovibrational ground state.
A density-functional formalism comparable to the Hohenberg-Kohn-Sham theory of the ground state is developed for arbitrary time-dependent systems. It is proven that the single-particle potential $v(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}t)$ leading to a given … A density-functional formalism comparable to the Hohenberg-Kohn-Sham theory of the ground state is developed for arbitrary time-dependent systems. It is proven that the single-particle potential $v(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}t)$ leading to a given $v$-representable density $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}t)$ is uniquely determined so that the corresponding map $v\ensuremath{\rightarrow}n$ is invertible. On the basis of this theorem, three schemes are derived to calculate the density: a set of hydrodynamical equations, a stationary action principle, and an effective single-particle Schr\"odinger equation.
Micron-sized particles have been accelerated and trapped in stable optical potential wells using only the force of radiation pressure from a continuous laser. It is hypothesized that similar accelerations and … Micron-sized particles have been accelerated and trapped in stable optical potential wells using only the force of radiation pressure from a continuous laser. It is hypothesized that similar accelerations and trapping are possible with atoms and molecules using laser light tuned to specific optical transitions. The implications for isotope separation and other applications of physical interest are discussed.
An exactly soluble model of a one-dimensional many-fermion system is discussed. The model has a fairly realistic interaction between pairs of fermions. An exact calculation of the momentum distribution in … An exactly soluble model of a one-dimensional many-fermion system is discussed. The model has a fairly realistic interaction between pairs of fermions. An exact calculation of the momentum distribution in the ground state is given. It is shown that there is no discontinuity in the momentum distribution in this model at the Fermi surface, but that the momentum distribution has infinite slope there. Comparison with the results of perturbation theory for the same model is also presented, and it is shown that, for this case at least, the perturbation and exact answers behave qualitatively alike. Finally, the response of the system to external fields is also discussed.
The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with … The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species. Topics covered include the definition of and conditions for BEC in an interacting system, the replacement of the true interatomic potential by a zero-range pseudopotential, the time-independent and time-dependent Gross-Pitaevskii equations, superfluidity and rotational properties, the Josephson effect and related phenomena, and the Bogoliubov approximation.
Electric dipole transitions within the $4f$ shell of a rare-earth ion are permitted if the surroundings of the ion are such that its nucleus is not situated at a center … Electric dipole transitions within the $4f$ shell of a rare-earth ion are permitted if the surroundings of the ion are such that its nucleus is not situated at a center of inversion. An expression is found for the oscillator strength of a transition between two states of the ground configuration $4{f}^{N}$, on the assumption that the levels of each excited configuration of the type $4{f}^{N}{n}^{\ensuremath{'}}d$ or $4{f}^{N}{n}^{\ensuremath{'}}g$ extend over an energy range small as compared to the energy of the configuration above the ground configuration. On summing over all transitions between the components of the ground level ${\ensuremath{\psi}}_{J}$ and those of an excited level ${{\ensuremath{\psi}}^{\ensuremath{'}}}_{{J}^{\ensuremath{'}}}$, both of $4{f}^{N}$, the oscillator strength $P$ corresponding to the transition ${\ensuremath{\psi}}_{J}\ensuremath{\rightarrow}{{\ensuremath{\psi}}^{\ensuremath{'}}}_{{J}^{\ensuremath{'}}}$ of frequency $\ensuremath{\nu}$ is found to be given by $P=\ensuremath{\Sigma}{T}_{\ensuremath{\lambda}}\ensuremath{\nu}{({\ensuremath{\psi}}_{J}\ensuremath{\parallel}{U}^{(\ensuremath{\lambda})}\ensuremath{\parallel}{{\ensuremath{\psi}}^{\ensuremath{'}}}_{{J}^{\ensuremath{'}}})}^{2},$ where ${\mathrm{U}}^{(\ensuremath{\lambda})}$ is a tensor operator of rank $\ensuremath{\lambda}$, and the sum runs over the three values 2, 4, and 6 of $\ensuremath{\lambda}$. Transitions that also involve changes in the vibrational modes of the complex comprising a rare-earth ion and its surroundings, provide a contribution to $P$ of precisely similar form. It is shown that sets of parameters ${T}_{\ensuremath{\lambda}}$ can be chosen to give a good fit with the experimental data on aqueous solutions of Nd${\mathrm{Cl}}_{3}$ and Er${\mathrm{Cl}}_{3}$. A calculation on the basis of a model, in which the first hydration layer of the rare-earth ion does not possess a center of symmetry, leads to parameters ${T}_{\ensuremath{\lambda}}$ that are smaller than those observed for ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Er}}^{3+}$ by factors of 2 and 8, respectively. Reasons for the discrepancies are discussed.
The general expression for the exact forces on the nuclei (negative derivatives of the total energy with respect to the nuclear coordinates) is applied for Hartree-Fock wavefunctions. It is suggested … The general expression for the exact forces on the nuclei (negative derivatives of the total energy with respect to the nuclear coordinates) is applied for Hartree-Fock wavefunctions. It is suggested that force constants should be calculated by differentiating the forces numerically. This method, called the force method, is numerically more accurate and requires less computation than the customary one of differentiating the energy numerically twice. It permits the quick determination of the equilibrium geometry by relaxing the nuclear coordinates until the forces vanish. The unreliability of the methods using the Hellmann-Feynman forces is re-emphasized. The question of which force constants can be best calculated ab initio is discussed.
The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by … The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.
We have observed Bose-Einstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phase-space density by … We have observed Bose-Einstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phase-space density by 6 orders of magnitude within seven seconds. Condensates contained up to 5\ifmmode\times\else\texttimes\fi{}${10}^{5}$ atoms at densities exceeding ${10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of \ensuremath{\sim}2\ensuremath{\mu}K. The distribution consisted of an isotropic thermal distribution and an elliptical core attributed to the expansion of a dense condensate.
Using a focused laser beam we stir a Bose-Einstein condensate of 87Rb confined in a magnetic trap and observe the formation of a vortex for a stirring frequency exceeding a … Using a focused laser beam we stir a Bose-Einstein condensate of 87Rb confined in a magnetic trap and observe the formation of a vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to four vortices are simultaneously present. We have also measured the lifetime of the single vortex state after turning off the stirring laser beam.
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. … The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by DMRG.
Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale as ${n}^{3}$. It was proposed a decade … Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale as ${n}^{3}$. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.
First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a … First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.
In 1925 Einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. This gaseous state, a Bose–Einstein condensate, was produced in the … In 1925 Einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. This gaseous state, a Bose–Einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates has become one of the most active areas in contemporary physics. The study of Bose–Einstein condensates in dilute gases encompasses a number of different subfields of physics, including atomic, condensed matter, and nuclear physics. The authors of this graduate-level textbook explain this exciting new subject in terms of basic physical principles, without assuming detailed knowledge of any of these subfields. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problem sets are also included in each chapter.
We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using … We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference technique, we map the phase of the vortex state to confirm that it possesses angular momentum. We can create vortices in either of the two components and have observed differences in the dynamics and stability.
Since an atomic Bose-Einstein condensate, predicted by Einstein in 1925, was first produced in the laboratory in 1995, the study of ultracold Bose and Fermi gases has become one of … Since an atomic Bose-Einstein condensate, predicted by Einstein in 1925, was first produced in the laboratory in 1995, the study of ultracold Bose and Fermi gases has become one of the most active areas in contemporary physics. This book explains phenomena in ultracold gases from basic principles, without assuming a detailed knowledge of atomic, condensed matter, and nuclear physics. This new edition has been revised and updated, and includes new chapters on optical lattices, low dimensions, and strongly-interacting Fermi systems. This book provides a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problems are included at the end of each chapter.
Symmetry is known to strongly influence the course of a chemical reaction. It has also been found to play a key role in vibrational strong coupling (VSC), where it can … Symmetry is known to strongly influence the course of a chemical reaction. It has also been found to play a key role in vibrational strong coupling (VSC), where it can influence the outcome of chemical reactions or alter chemical equilibria. However, the precise nature of this effect and its extent remains elusive. To further explore the role of vibrational symmetry, we have investigated the equilibrium constants of different charge transfer complexes, in particular of isomers of trimethyl benzene belonging to different point groups from which a general symmetry rule emerges. We describe the strongly coupled system by a direct product of irreducible representations associated with the complexes and the cavity. As a consequence, the coupled vibration is associated with a new irreducible representation that projects differently on the reaction coordinate of the charge transfer complexation, reflecting the changes in the equilibrium constants. This phenomenological symmetry rule points to a general underlying framework for predicting the outcome of chemical reactivity under VSC.
Abstract The vortex dynamics after the initial ring dark solitons in two-component ultracold Rydberg atomic systems have been investigated. The two parameters characterizing the Rydberg long-range interaction|namely, the Rydberg strength … Abstract The vortex dynamics after the initial ring dark solitons in two-component ultracold Rydberg atomic systems have been investigated. The two parameters characterizing the Rydberg long-range interaction|namely, the Rydberg strength and the blockade radius|along with the initial depth, are identified as the main factors that affect the vortex dynamics. In the absence of Rydberg soft-core potential and spin-orbit coupling, the late vortex dipoles move along x - or y -axis first. While this work demonstrates that the Rydberg nonlocal nonlinear interaction shorten the lifetime of late vortices, it also shows that, with certain Rydberg strength and blockade radius, the late vortex dipoles move towards the edge at an oblique angle to the coordinate axes. When the intra-component and inter-component Rydberg strengths are different, the backgrounds of the two components gradually complement each other, and the lifetime of late vortices is significantly shortened. The presented results show that the Rydberg dressing breaks the rule that the initial average depth determines the number and paths of vortices. The motion features of vortex dipoles in ultracold Rydberg atomic system have been ascertained, and their directions of movement can be predicted to some degree based on the rotation directions and initial positions of the vortices.
Nearly a decade’s worth of data went into the first direct observation of sputtering on Mars, which researchers believe contributed to the loss of the Red Planet’s atmosphere. Nearly a decade’s worth of data went into the first direct observation of sputtering on Mars, which researchers believe contributed to the loss of the Red Planet’s atmosphere.
NULL AUTHOR_ID | Physical review. B./Physical review. B
Flat-band systems provide an ideal platform for exploring exotic quantum phenomena, where the strongly suppressed kinetic energy in these flat energy bands suggests the potential for exotic phases driven by … Flat-band systems provide an ideal platform for exploring exotic quantum phenomena, where the strongly suppressed kinetic energy in these flat energy bands suggests the potential for exotic phases driven by geometric structure, disorder, and interactions. While intriguing phenomena and physical mechanisms have been unveiled in theoretical models, synthesizing such systems within scalable quantum platforms remains challenging. Here, we present the experimental realization of a π-flux rhombic system using a two-dimensional superconducting qubit array with tunable coupling. We experimentally observe characteristic dynamics, e.g., π-flux driven destructive interference, and demonstrate the protocol for eigenstate preparation in this rhombic array with coupler-assisted flux. Our results provide future possibilities for exploring the interplay of geometry, interactions, and quantum information encoding in such degenerate systems.
NULL AUTHOR_ID | Physical review. A/Physical review, A
Abstract A limiting case is considered in which the causal action principle for causal fermion systems describing Minkowski space gives rise to the linear Fock space dynamics of quantum electrodynamics. … Abstract A limiting case is considered in which the causal action principle for causal fermion systems describing Minkowski space gives rise to the linear Fock space dynamics of quantum electrodynamics. The quantum nature of the bosonic field is a consequence of the stochastic description of a multitude of fluctuating fields coupled to non-commuting operators, taking into account dephasing effects. The scaling of all error terms is specified. Our analysis leads to the concept of holographic mixing, which is introduced and explained in detail.
Understanding quantum tunneling in many-body systems is crucial for advancing quantum technologies and nanoscale device design. Despite extensive studies of quantum tunneling, the role of interactions in determining directional transport … Understanding quantum tunneling in many-body systems is crucial for advancing quantum technologies and nanoscale device design. Despite extensive studies of quantum tunneling, the role of interactions in determining directional transport through asymmetric barriers in discrete quantum systems remains unclear. Here we show that noninteracting fermions exhibit symmetric tunneling probabilities regardless of barrier orientation, while inter-particle interactions break this symmetry and create pronounced asymmetric tunneling behavior. We explore the dependence of tunneling behavior on the initial spin configurations of two spin-1/2 fermions: spin-triplet states preserve tunneling symmetry, while spin-singlet states show strong asymmetry. We identify regimes where interactions mediate tunneling through under-barrier resonant trapping and enhance tunneling via many-body resonant tunneling - a phenomenon arising solely from inter-particle interactions and being fundamentally different from traditional single-particle resonant tunneling. Our results may be applied to the design of nanoscale devices with tailored transport properties, such as diodes and memristors.
Abstract Conducting experiments in extreme conditions has long been the aim of the levitated mechanics field, as it allows for the investigation of new fundamental physics phenomena. Sending these experiments … Abstract Conducting experiments in extreme conditions has long been the aim of the levitated mechanics field, as it allows for the investigation of new fundamental physics phenomena. Sending these experiments into the micro-g environment of space has been one such milestone, with multiple proposals calling for such a platform. At the same time, levitated sensors have demonstrated a high sensitivity to external stimuli, such as electric, magnetic and gravitational forces, which will only improve in low-vibrational conditions. This paper describes the development of a technology demonstrator for optical and magnetic trapping experiments in space. Our payload represents the first concrete step towards future missions with aims of probing fundamental physical questions: matter-wave interferometry of nanoparticles to probe the limits of macroscopic quantum mechanics, detection of Dark Matter candidates and gravitational waves to test physics beyond the Standard Model, and accelerometry for Earth-observation.
NULL AUTHOR_ID | Physical review. D/Physical review. D.
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In recent years, neural quantum states have emerged as a powerful variational approach, achieving state-of-the-art accuracy when representing the ground-state wave function of a great variety of quantum many-body systems, … In recent years, neural quantum states have emerged as a powerful variational approach, achieving state-of-the-art accuracy when representing the ground-state wave function of a great variety of quantum many-body systems, including spin lattices, interacting fermions or continuous-variable systems. However, accurate neural representations of the ground state of interacting bosons on a lattice have remained elusive. We introduce a neural backflow Jastrow Ansatz, in which occupation factors are dressed with translationally equivariant many-body features generated by a deep neural network. We show that this neural quantum state is able to faithfully represent the ground state of the 2D Bose-Hubbard Hamiltonian across all values of the interaction strength. We scale our simulations to lattices of dimension up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>20</mml:mn><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>&amp;#x00D7;</mml:mo></mml:mrow><mml:mn>20</mml:mn></mml:math> while achieving the best variational energies reported for this model. This enables us to investigate the scaling of the entanglement entropy across the superfluid-to-Mott quantum phase transition, a quantity hard to extract with non-variational approaches.
<title>Abstract</title> The ground state of spin-$1/2$ fermions with contact $s$-wave inter- and $p$-wave intra-species interactions is discussed. Particularly, we formulate the mean field scheme for calculating thermodynamic properties of the … <title>Abstract</title> The ground state of spin-$1/2$ fermions with contact $s$-wave inter- and $p$-wave intra-species interactions is discussed. Particularly, we formulate the mean field scheme for calculating thermodynamic properties of the system in arbitrary dimension $D&lt;2$ and discuss in detail the phase diagram in the 1D case. Except for clean phases with either singlet or triplet Cooper pairings, we have identified two mixed phases (one stable and another metastable) of the one-dimensional two-component fermions where both pairing mechanisms coexist. PACS numbers: 67.85.-d
Resonance-enhanced multiphoton ionization (REMPI) is used to characterize Rydberg states of 174YbF. Assignment of these Rydberg states to series that converge to various rotational and vibrational levels of the 174YbF+ … Resonance-enhanced multiphoton ionization (REMPI) is used to characterize Rydberg states of 174YbF. Assignment of these Rydberg states to series that converge to various rotational and vibrational levels of the 174YbF+ cation leads to an accurate value for the ionization energy IE = 48706.57(8) cm-1 of YbF. The values for the rotational constants of the YbF+ X1Σ+ ground state are found as Bν = 0+ = 0.257(1) cm-1 and Bν = 1+ = 0.255(3) cm-1, while the vibrational transition energy is ΔG1/2 = 598.86(15) cm-1. Photoinduced Rydberg ionization (PIRI) measurements via a high-lying Rydberg state have been performed using an infrared free electron laser, confirming the ΔG1/2 value.
A magneto-optical trap of cesium atoms was generated by applying a circularly polarized cooling laser beam onto a reflective two-dimensional diffraction grating with an aperture and by retroreflecting the incident … A magneto-optical trap of cesium atoms was generated by applying a circularly polarized cooling laser beam onto a reflective two-dimensional diffraction grating with an aperture and by retroreflecting the incident beam passing through the aperture while reversing the circular polarization. The cooling laser beams comprised the incident, retroreflected, and four diagonally diffracted beams at an angle of 50° with respect to the normal direction of the grating surface. The intensity of the retroreflected beam was carefully adjusted to balance the radiation forces acting on the atoms. A significant number of cold atoms (7.0 × 106) were captured, in spite of the difficulty in a magneto-optical trap of cesium atoms, using nonorthogonal cooling beams owing to the high nuclear spin. The significance of the retroreflected beam in the trapping process was highlighted when the intensity of the retroreflected beam was reduced, resulting in the absence of trapped atoms. Notably, the cold atom cloud was generated near the edge of the region, where all the cooling beams were overlapped. The phenomenon is explained by the numerical calculations of the radiation forces considering all the Zeeman sublevels in the cooling transition and the Gaussian intensity profile of the incident beam.
NULL AUTHOR_ID | Physical review. B./Physical review. B
Buffer gas cooling, one of the most relevant direct cooling techniques for cooling molecules, relies on dissipating the energy of the molecule via collisions with a buffer gas. The cooling … Buffer gas cooling, one of the most relevant direct cooling techniques for cooling molecules, relies on dissipating the energy of the molecule via collisions with a buffer gas. The cooling efficiency hinges on the molecule-atom scattering properties, concretely, on the transport properties. This work presents a global study on the interactions, collision dynamics, and transport properties of monofluoride molecules (X–F), with X being a metal, in the presence of a cold He buffer gas. The interactions are calculated using ab initio quantum chemistry methods, and the dynamics is treated fully quantal, assuming the monofluoride molecule is a rigid rotor. The resulting thermalization and rotational quenching rates are analyzed in light of the distorted-wave Born approximation, yielding an explanation based on the elemental physical properties of the molecule under consideration. Therefore, our findings contribute to understanding the rotational quenching of molecules in a cold buffer gas.
Among interesting applications of cold atoms, quantum simulations attract a lot of attention. In this context, rare-earth ultracold atoms are particularly appealing for such simulators due to their numerous Fano–Feshbach … Among interesting applications of cold atoms, quantum simulations attract a lot of attention. In this context, rare-earth ultracold atoms are particularly appealing for such simulators due to their numerous Fano–Feshbach resonances and magnetic dipole moments in the ground state. Creating a quantum gas microscope requires a large optical access that may be achieved using the transport of atoms between separate vacuum volumes. We demonstrate that in the case of the transport of magnetic atoms, the magnetic field can be directly measured and adjusted to reduce additional losses after the transport, therefore increasing the efficiency of subsequent evaporation cooling. This approach allows to transfer over 85% of the atoms from the main chamber to the scientific chamber, located 38 cm away with moderate laser power of 26 W without atomic polarization decay.