SU\G(𝔸)/K·U
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All published works (151)

Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point

2024-08-28
Bhavay Tyagi , Fumika Suzuki , Vladimir A. Chernyak +1 more
We propose and solve a minimal model of dynamic passage through a quantum second order phase transition in the presence of weak symmetry breaking interactions and no dissipation. The evolution … We propose and solve a minimal model of dynamic passage through a quantum second order phase transition in the presence of weak symmetry breaking interactions and no dissipation. The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry breaking term is. This suggests a potential mechanism for strong asymmetry in the production of particles with almost identical characteristics. The model's integrability also allows us to obtain exact Kibble-Zurek exponents for the scaling of the number of nonadiabatic excitations.
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Parametric tuning of dynamical phase transitions in ultracold reactions

2024-03-25
Nikolai A. Sinitsyn , Vijay Ganesh Sadhasivam , Fumika Suzuki +1 more
<title>Abstract</title> Advances in ultracold chemistry have led to the possibility of a coherent transformation between ultracold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the … <title>Abstract</title> Advances in ultracold chemistry have led to the possibility of a coherent transformation between ultracold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association of atoms at a Feshbach resonance which results in a passage through a quantum critical point. In this study, we show that the presence of generic interaction between the formed molecules can fundamentally alter the nature of the critical point, change the yield of the reaction and the order of the consequent phase transition. We find that the correlations introduced by this rather general interaction induce nontrivial many-body physics such as coherent oscillations between atoms and molecules, and a selective formation of squeezed molecular quantum states and quantum cat states. We provide analytical and numerical descriptions of these many-body effects, along with scaling laws for the reaction yield in both the adiabatic and non-adiabatic regimes, and highlight the potential experimental relevance in quantum sensing.
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Parametric tuning of dynamical phase transitions in ultracold reactions

2024-03-14
Vijay Ganesh Sadhasivam , Fumika Suzuki , Bin Yan +1 more
Advances in ultracold chemistry have led to the possibility of a coherent transformation between ultracold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association … Advances in ultracold chemistry have led to the possibility of a coherent transformation between ultracold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association of atoms at a Feshbach resonance which results in a passage through a quantum critical point. In this study, we show that the presence of generic interaction between the formed molecules can fundamentally alter the nature of the critical point, change the yield of the reaction and the order of the consequent phase transition. We find that the correlations introduced by this rather general interaction induce nontrivial many-body physics such as coherent oscillations between atoms and molecules, and a selective formation of squeezed molecular quantum states and quantum cat states. We provide analytical and numerical descriptions of these many-body effects, along with scaling laws for the reaction yield in both the adiabatic and non-adiabatic regimes, and highlight the potential experimental relevance in quantum sensing.
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Nonadiabatic transitions during a passage near a critical point

2024-02-16
Nikolai A. Sinitsyn , Vijay Ganesh Sadhasivam , Fumika Suzuki
The passage through a critical point of a many-body quantum system leads to abundant nonadiabatic excitations. Here, we explore a regime, in which the critical point is not crossed although … The passage through a critical point of a many-body quantum system leads to abundant nonadiabatic excitations. Here, we explore a regime, in which the critical point is not crossed although the system is passing slowly very close to it. We show that the leading exponent for the excitation probability can then be obtained by standard arguments of the Dykhne formula, but the exponential prefactor is no longer simple and behaves as a power law on the characteristic transition rate. We derive this prefactor for the nonlinear Landau-Zener model by adjusting Dykhne's approach. Then, we introduce an exactly solvable model of the transition near a critical point in the Stark ladder. We derive the number of excitations for it without approximations and find qualitatively similar results for the excitation scaling.
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Proximity-induced chiral quantum light generation in strain-engineered WSe2/NiPS3 heterostructures

2023-08-17
Xiangzhi Li , Andrew C. Jones , Junho Choi +7 more
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Topologically protected Grover's oracle for the partition problem

2023-08-14
Nikolai A. Sinitsyn , Bin Yan
The number partitioning problem (NPP) is one of the NP-complete (nondeterministic polynomial-time complete) computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is … The number partitioning problem (NPP) is one of the NP-complete (nondeterministic polynomial-time complete) computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in $\sqrt{N}$ quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with $N$ only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time dependence of the physical parameters or the choice of the annealing protocol. We also argue that our approach can solve many other famous NP-complete computational problems in $\sqrt{N}$ steps.
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Topologically protected Grover's oracle for the partition problem

2023-01-01
Nikolai A. Sinitsyn , Bin Yan
The Number Partitioning Problem (NPP) is one of the NP-complete computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here … The Number Partitioning Problem (NPP) is one of the NP-complete computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in $\sqrt{N}$ quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with $N$ only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time-dependence of the physical parameters or the choice of the annealing protocol.
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Mesoscopic critical fluctuations

2023-01-01
Saikat Banerjee , Nikolai A. Sinitsyn
We investigate the magnetic fluctuations in a mesoscopic critical region formed at the interface due to smooth time-independent spatial variations of a control parameter around its critical value. In the … We investigate the magnetic fluctuations in a mesoscopic critical region formed at the interface due to smooth time-independent spatial variations of a control parameter around its critical value. In the proximity of the spatial critical point, the order parameter fluctuations exhibit a mesoscopic nature, characterized by their significant size compared to the lattice constant, while gradually decaying away from the critical region. To explain this phenomenon, we present a minimal model that effectively captures this behavior and demonstrates its connection to the integrable Painlevé-II equation governing the local order parameter. By leveraging the well-established mathematical properties of this equation, we gain valuable insights into the nonlinear susceptibilities exhibited within this region.
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Phase transition in fluctuations of interacting spins at infinite temperature

2023-01-01
V. N. Gorshkov , Nikolai A. Sinitsyn , Dmitry Mozyrsky
The high temperature limit of interacting spins is usually not associated with ordering or critical phenomena. Nevertheless, spontaneous fluctuations of a local spin polarization at equilibrium have nontrivial dynamics even … The high temperature limit of interacting spins is usually not associated with ordering or critical phenomena. Nevertheless, spontaneous fluctuations of a local spin polarization at equilibrium have nontrivial dynamics even in this limit. Here, we demonstrate that the spin noise power spectrum of these fluctuations can undergo discontinuous changes as a function of an external magnetic field. As a simple illustration, we consider a model of Ising-like long range spin-spin interactions with a transverse magnetic field as a control parameter. This system undergoes a phase transition associated with disappearance of the noise power peak responsible for the most detrimental decoherence effect of the interactions. \end{abstract}
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Nonadiabatic transitions during a passage near a critical point

2023-01-01
Nikolai A. Sinitsyn , Vijay Ganesh Sadhasivam , Fumika Suzuki
The passage through a critical point of a many-body quantum system leads to abundant nonadiabatic excitations. Here, we explore a regime, in which the critical point is not crossed although … The passage through a critical point of a many-body quantum system leads to abundant nonadiabatic excitations. Here, we explore a regime, in which the critical point is not crossed although the system is passing slowly very close to it. We show that the leading exponent for the excitation probability then can be obtained by standard arguments of the Dykhne formula but the exponential prefactor is no longer simple, and behaves as a power law on the characteristic transition rate. We derive this prefactor for the nonlinear Landau-Zener (nLZ) model by adjusting the Dykhne's approach. Then, we introduce an exactly solvable model of the transition near a critical point in the Stark ladder. We derive the number of the excitations for it without approximations, and find qualitatively similar results for the excitation scaling.
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Benchmarking Information Scrambling

2022-07-26
Joseph Harris , Bin Yan , Nikolai A. Sinitsyn
Information scrambling refers to the rapid spreading of initially localized information over an entire system, via the generation of global entanglement. This effect is usually detected by measuring a temporal … Information scrambling refers to the rapid spreading of initially localized information over an entire system, via the generation of global entanglement. This effect is usually detected by measuring a temporal decay of the out-of-time order correlators. However, in experiments, decays of these correlators suffer from fake positive signals from various sources, e.g., decoherence due to inevitable couplings to the environment, or errors that cause mismatches between the purported forward and backward evolutions. In this work, we provide a simple and robust approach to single out the effect of genuine scrambling. This allows us to benchmark the scrambling process by quantifying the degree of the scrambling from the noisy backgrounds.
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Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model

2022-07-11
Rajesh K. Malla , Vladimir Chernyak , Chen Sun +1 more
We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution … We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate for both atoms-to-molecule pairing and molecular dissociation processes. We find that for the latter process with a linear energy dispersion of atomic modes, the emerging phase can have a thermalized energy distribution of noninteracting bosons with the temperature defined by the rate of the transition. This provides a simple interpretation of the phase transition in terms of the creation of equilibrium Bose-Einstein condensate.
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Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

2022-04-25
Bin Yan , Nikolai A. Sinitsyn
Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution … Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, HI. Here, we point to the existence of an analytical solution for such a problem for an arbitrary HI beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time T of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of HI, the solution also shows a considerable quantum speedup in computations.
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Quantum Algorithm Implementations for Beginners

2022-03-28
J. Abhijith , Adetokunbo Adedoyin , John Ambrosiano +7 more
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for … As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.
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Real-time simulation of light-driven spin chains on quantum computers

2022-03-11
Martin Rodriguez-Vega , Ella Carlander , Adrian Bahri +3 more
In this work, we study the real-time evolution of periodically driven (Floquet) systems on a quantum computer using IBM quantum devices. We consider a driven Landau-Zener model and compute the … In this work, we study the real-time evolution of periodically driven (Floquet) systems on a quantum computer using IBM quantum devices. We consider a driven Landau-Zener model and compute the transition probability between the Floquet steady states as a function of time. We find that for this simple one-qubit model, Floquet states can develop in real time, as indicated by the transition probability between Floquet states. Next, we model light-driven spin chains and compute the time-dependent antiferromagnetic order parameter. We consider models arising from light coupling to the underlying electrons as well as those arising from light coupling to phonons. For the two-spin chains, the quantum devices yield time evolutions that match the effective Floquet Hamiltonian evolution for both models once readout error mitigation is included. For three-spin chains, zero-noise extrapolation yields a time dependence that follows the effective Floquet time evolution. Therefore, the current IBM quantum devices can provide information on the dynamics of small Floquet systems arising from light drives once error mitigation procedures are implemented.
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Cross-correlation spectra in interacting quantum dot systems

2022-01-06
Andreas Fischer , Iris Kleinjohann , Nikolai A. Sinitsyn +1 more
Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the interquantum dot interactions. We investigate the spin cross-correlation function in a quantum dot … Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the interquantum dot interactions. We investigate the spin cross-correlation function in a quantum dot ensemble employing a modified semiclassical approach. Spin-correlation functions are calculated using a Hamilton quaternion approach that maintains local quantum mechanical properties of the spins. This method takes into account the effects of the nuclear-electric quadrupolar interactions, the randomness of the coupling constants, and the variation of the electron $g$ factor on the spin-noise power spectra. We demonstrate that the quantum dot ensemble can be mapped on an effective two-quantum dot problem and discuss how the characteristic length scale of the interdot interaction modifies the low-frequency cross-correlation spectrum. We argue that details on the interaction strength distribution can be extracted from the cross-correlation spectrum when applying a longitudinal or a transversal external magnetic field.
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Proximity Induced Chiral Quantum Light Generation in Strain-Engineered WSe2/NiPS3 Heterostructures

2022-01-01
Xiangzhi Li , Andrew Jones , Junho Choi +7 more
Quantum light emitters (QEs) capable of generating single photons of well-defined circular polarization could enable non-reciprocal single photon devices and deterministic spin-photon interfaces critical for realizing complex quantum networks. To … Quantum light emitters (QEs) capable of generating single photons of well-defined circular polarization could enable non-reciprocal single photon devices and deterministic spin-photon interfaces critical for realizing complex quantum networks. To date, emission of such chiral quantum light has been achieved via the application of intense external magnetic field electrical/optical injection of spin polarized carriers/excitons, or coupling with complex photonic/meta-structures. Here we report free-space generation of highly chiral single photons from QEs created in monolayer WSe2 - NiPS3 heterostructures at zero external magnetic field. These QEs emit in the 760-800 nm range with a degree of circular polarization and single photon purity as high as 0.71 and 80% respectively, independent of pump laser polarization. QEs are deterministically created by pressing a scanning probe microscope tip into a two-dimensional heterostructure comprising a WSe2 monolayer and a ~50 nm thick layer of the antiferromagnetic (AFM) insulator NiPS3. Temperature dependent magneto-photoluminescence studies indicate that the chiral quantum light emission arises from magnetic proximity interactions between localized excitons in the WSe2 monolayer and the out-of-plane magnetization of AFM defects in NiPS3, both of which are co-localized by the strain field arising from the nanoscale indentations.
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An adiabatic oracle for Grover's algorithm

2022-01-01
Bin Yan , Nikolai A. Sinitsyn
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is … Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design. Here, we propose a realization of Grover's oracle for a large class of searching problems using a quantum annealing step. The time of this step grows only logarithmically with the size of the database. This suggests an efficient path to application of Grover's algorithm to practically important problems, such as finding the ground state of a Hamiltonian with a spectral gap over its ground state.
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Randomized channel-state duality

2022-01-01
Bin Yan , Nikolai A. Sinitsyn
Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert … Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual state is generally mixed, it is described by a Hermitian matrix. In this article, we present a randomized channel-state duality. In other words, a quantum channel is represented by a collection of $N$ pure quantum states that are produced from a random source. The accuracy of this randomized duality relation is given by $1/N$, with regard to an appropriate distance measure. For large systems, $N$ is much smaller than the dimension of the exact dual matrix of the quantum channel. This provides a highly accurate low-rank approximation of any quantum channel, and, as a consequence of the duality relation, an efficient data compression scheme for mixed quantum states. We demonstrate these two immediate applications of the randomized channel-state duality with a chaotic $1$-dimensional spin system.
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Analytical solution for ground state estimation by a nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

2021-10-24
Bin Yan , Nikolai A. Sinitsyn
We point to the existence of an analytical solution to a general quantum annealing (QA) problem of finding low energy states of an arbitrary Ising spin Hamiltonian $H_I$ by implementing … We point to the existence of an analytical solution to a general quantum annealing (QA) problem of finding low energy states of an arbitrary Ising spin Hamiltonian $H_I$ by implementing time evolution with a Hamiltonian $H(t)=H_I+g(t) H_t$. We will assume that the nonadiabatic annealing protocol is defined by a specific decaying coupling $g(t)$ and a specific mixing Hamiltonian $H_t$ that make the model analytically solvable arbitrarily far from the adiabatic regime. In specific cases of $H_I$, the solution shows the possibility of a considerable quantum speedup of finding the Ising ground state. We then compare predictions of our solution to results of numerical simulations and argue that the solvable QA protocol produces the optimal performance in the limit of maximal complexity of the computational problem. Our solution demonstrates for the most complex spin glasses a power-law energy relaxation with the annealing time $T$ and uncorrelated from the $H_I$ annealing schedule. This proves the possibility for spin glasses of a faster than $\sim 1/\log^{\beta} T$ energy relaxation.
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Benchmarking Information Scrambling

2021-10-24
Joseph Harris , Bin Yan , Nikolai A. Sinitsyn
Information scrambling refers to the rapid spreading of initially localized information over an entire system, via the generation of global entanglement. This effect is usually detected by measuring a temporal … Information scrambling refers to the rapid spreading of initially localized information over an entire system, via the generation of global entanglement. This effect is usually detected by measuring a temporal decay of the out-of-time order correlators. However, in experiments, decays of these correlators suffer from fake positive signals from various sources, e.g., decoherence due to inevitable couplings to the environment, or errors that cause mismatches between the purported forward and backward evolutions. In this work, we provide a simple and robust approach to single out the effect of genuine scrambling. This allows us to benchmark the scrambling process by quantifying the degree of the scrambling from the noisy backgrounds.
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Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

2021-04-07
Rajesh K. Malla , Vladimir Chernyak , Nikolai A. Sinitsyn
We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We … We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-St\"uckelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that provides analytical approximation for the transition probabilities in these models for all parameter values. The results predict a dynamic phase transition, and show that similarly looking models belong to different topological classes.
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Nonadiabatic Phase Transition with Broken Chiral Symmetry

2021-02-19
Bin Yan , Vladimir Chernyak , Wojciech H. Zurek +1 more
We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through … We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sublattices are suppressed in the nearly adiabatic regime exponentially. Thus, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.Received 2 September 2020Accepted 25 January 2021DOI:https://doi.org/10.1103/PhysRevLett.126.070602© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDynamical phase transitionsNonequilibrium statistical mechanicsPhase transitionsQuantum phase transitionsQuantum quenchPhysical Systems1-dimensional spin chainsTechniquesIsing modelSpin chainsStatistical PhysicsCondensed Matter, Materials & Applied Physics
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Integrability in the multistate Landau-Zener model with time-quadratic commuting operators

2021-02-09
Vladimir Chernyak , Nikolai A. Sinitsyn
Abstract All currently known exactly solvable multistate Landau–Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also … Abstract All currently known exactly solvable multistate Landau–Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with the MLZ Hamiltonians but depend on time quadratically. We show that, among the MLZ systems, such time-quadratic operators are much more common. We demonstrate then that such operators generally lead to constraints on the independent variables that parametrize the scattering matrix. Such constraints lead to asymptotically exact expressions for the transition probabilities in the adiabatic limit of a three-level MLZ model. New more complex fully solvable MLZ systems are also found.
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Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

2020-07-24
Bin Yan , Nikolai A. Sinitsyn
A time-reversed dynamics unwinds information scrambling, which is induced during the time-forward evolution with a complex Hamiltonian. We show that if the scrambled information is, in addition, partially damaged by … A time-reversed dynamics unwinds information scrambling, which is induced during the time-forward evolution with a complex Hamiltonian. We show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.
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Integrable multistate Landau–Zener models with parallel energy levels

2020-05-19
Vladimir Chernyak , Fuxiang Li , Chen Sun +1 more
We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/\tau$-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive … We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/\tau$-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ models from this class must contain bands of parallel diabatic energy levels. The structure of the scattering matrix and other properties are found to be the same as in the previously discussed completely solvable MLZ Hamiltonians.
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Multitime Landau–Zener model: classification of solvable Hamiltonians

2020-03-13
Vladimir Chernyak , Nikolai A. Sinitsyn , Chen Sun
We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution … We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number $N$ of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system's dynamics. Due to the possibility of such a detailed classification, the multitime Landau-Zener (MTLZ) model defines a useful special function of theoretical physics.
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Operator scrambling, hypersensitivity, and quantum Lyapunov spectrum

2020-03-06
Bin Yan , Nikolai A. Sinitsyn , Wojciech H. Zurek

Integrability in the multistate Landau-Zener model with time-quadratic commuting operators

2020-01-01
Vladimir Chernyak , Nikolai A. Sinitsyn
Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy … Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with the MLZ Hamiltonians but depend on time quadratically. We show that, among the MLZ systems, such time-quadratic operators are much more common. We demonstrate then that such operators generally lead to constraints on the independent variables that parametrize the scattering matrix. We show how such constraints lead to asymptotically exact expressions for the transition probabilities in the adiabatic limit of a three-level MLZ model. New fully solvable MLZ systems are also found.
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Dynamic spin localization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi></mml:math> -magnets

2019-12-20
Vladimir Chernyak , Nikolai A. Sinitsyn , Chen Sun
We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for … We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for all qubits. We show that at least the simplest such models, which can be realized with localized states in Dirac materials, satisfy integrability conditions that we use to describe pseudospin dynamics in a linearly time-dependent magnetic field. Generalizing to an arbitrary number of qubits, we construct a spin Hamiltonian, which we call the gamma-magnet. This system does not conserve polarization of any spin and the net spin polarization. Nevertheless, for arbitrarily strong interactions, nonadiabatic dynamics, and any initial eigenstate, we find that quantum interference suppresses spin-flips. This behavior resembles many-body localization but occurs in phase space of many spins rather than real space. This effect may not have a counterpart in classical physics and can be a signature of a new type of spin ordering, which is different from both disordered spin glasses and ordered phases of spin lattices.
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Multitime Landau-Zener model

2019-11-27
Vladimir Chernyak , Nikolai A. Sinitsyn , Chen Sun
We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution … We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number $N$ of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system's dynamics. Due to the possibility of such a detailed classification, the multitime Landau-Zener (MTLZ) model defines a useful special function of theoretical physics.
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Cooperative Light Emission in the Presence of Strong Inhomogeneous Broadening

2019-09-20
Chen Sun , Vladimir Chernyak , Andrei Piryatinski +1 more
We study photon emission by an ensemble of two-level systems, with strong inhomogeneous broadening and coupled to a cavity mode whose frequency has linear time dependence. The analysis shows that, … We study photon emission by an ensemble of two-level systems, with strong inhomogeneous broadening and coupled to a cavity mode whose frequency has linear time dependence. The analysis shows that, regardless of the distribution of energy level splittings, a sharp phase transition occurs between the weak and strong cooperative emission phases near a critical photonic frequency sweeping rate. The associated scaling exponent is determined. We suggest that this phase transition can be observed in an ensemble of negatively charged ${\mathrm{NV}}^{\ensuremath{-}}$ centers in diamond interacting with a microwave half-wavelength cavity mode even in the regime of weak coupling and at strong disorder of two-level splittings.
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Dynamic spin localization

2019-05-13
Vladimir Chernyak , Nikolai A. Sinitsyn , Chunfang Sun
We construct an explicitly solvable model of interacting quantum spins under the action of linearly time-dependent magnetic field. The Hamiltonian, which we call the gamma-magnet, does not conserve polarization of … We construct an explicitly solvable model of interacting quantum spins under the action of linearly time-dependent magnetic field. The Hamiltonian, which we call the gamma-magnet, does not conserve polarization of any spin and the net spin polarization. Nevertheless, for arbitrarily strong interactions, nonadiabatic dynamics, and any initial state, we find that quantum interference suppresses spin-flips, so that the system at the end is essentially close to the initial state. This phenomenon resembles many-body localization but occurs in the phase space of many spins rather than real space and does not need disorder.
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Gamma-Magnets and Dynamic Spin Localization

2019-05-13
Vladimir Chernyak , Nikolai A. Sinitsyn , Chengjun Sun
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Quantum Annealing and Thermalization: Insights from Integrability

2018-11-06
Fuxiang Li , Vladimir Chernyak , Nikolai A. Sinitsyn
We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap … We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap during the whole evolution, and a programmable computational problem that is encoded by parameters of the Ising part of the spin Hamiltonian. Our solution enables exact nonperturbative characterization of final nonadiabatic excitations, including a scaling of their number with the annealing rate and the system size. We prove that quantum correlations can accelerate computations and, at the end of the annealing protocol, lead to the perfect Gibbs distribution of all microstates.
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Broadband Spectroscopy of Thermodynamic Magnetization Fluctuations through a Ferromagnetic Spin-Reorientation Transition

2018-09-21
Andrew Balk , Fuxiang Li , Ian Gilbert +3 more
We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise," in an archetypal ferromagnetic film that can be smoothly tuned through a … We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise," in an archetypal ferromagnetic film that can be smoothly tuned through a spin-reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar+ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise S(ν) exhibits a remarkably robust ν−3/2 power law over frequencies ν from 1 kHz to 1 MHz. As the SRT region is traversed, however, S(ν) spectra develop a steadily increasing critical frequency ν0, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.Received 26 January 2018DOI:https://doi.org/10.1103/PhysRevX.8.031078Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasKerr effectMagnetic phase transitionsPhysical SystemsMagnetic multilayersTechniquesSpin noise spectroscopyCondensed Matter, Materials & Applied Physics
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Integrable Time-Dependent Quantum Hamiltonians

2018-05-11
Nikolai A. Sinitsyn , Emil A. Yuzbashyan , Vladimir Chernyak +2 more
We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge … We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
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A large class of solvable multistate Landau–Zener models and quantum integrability

2018-05-10
Vladimir Chernyak , Nikolai A. Sinitsyn , Chen Sun
The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402). Within the multistate Landau–Zener (MLZ) … The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor. 50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.
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Quantum Algorithm Implementations for Beginners

2018-04-10
Patrick J. Coles , Stephan Eidenbenz , Scott Pakin +7 more
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for … As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

Integrability in multistate Landau-Zener and Landau-Zener-Coulomb problems

2018-03-08
Nikolai A. Sinitsyn , Emil A. Yuzbashyan , Vladimir Chernyak +2 more

A large class of solvable multistate Landau-Zener models and quantum integrability

2018-03-08
Chen Sun , Nikolai A. Sinitsyn

Computing with a single qubit faster than the computation quantum speed limit

2017-12-23
Nikolai A. Sinitsyn
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Multistate Landau-Zener models with all levels crossing at one point

2017-08-04
Fuxiang Li , Chen Sun , Vladimir Chernyak +1 more
We discuss common properties and reasons for integrability in the class of multistate Landau-Zener models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that … We discuss common properties and reasons for integrability in the class of multistate Landau-Zener models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that each previously solved model has a dual one, whose scattering matrix can be also obtained analytically. For applications, we demonstrate how our results can be used to study conversion of molecular into atomic Bose condensates during passage through the Feshbach resonance, and provide purely algebraic solutions of the bowtie and special cases of the driven Tavis-Cummings model.
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Nearly optimal quantum control: an analytical approach

2017-07-18
Chen Sun , Avadh Saxena , Nikolai A. Sinitsyn
We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a … We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for optimization. This optimization strategy can be preferred in practice because it is physically transparent and does not lead to combinatorial complexity in multistate problems. For demonstration, we design optimized control protocols that achieve switching between orthogonal states of a naturally biased quantum two-level system.
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The quest for solvable multistate Landau-Zener models

2017-05-24
Nikolai A. Sinitsyn , Vladimir Chernyak
Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs … Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. In addition, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.
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Constraints on scattering amplitudes in multistate Landau-Zener theory

2017-01-30
Nikolai A. Sinitsyn , Jeffmin Lin , Vladimir Chernyak
We derive a set of constraints, which we will call hierarchy constraints, on scattering amplitudes of an arbitrary multistate Landau-Zener model (MLZM). The presence of additional symmetries can transform such … We derive a set of constraints, which we will call hierarchy constraints, on scattering amplitudes of an arbitrary multistate Landau-Zener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix.
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Is there a quantum limit on speed of computation

2017-01-19
Nikolai A. Sinitsyn
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are … The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this resource can be used to accelerate information-processing without relying on entanglement or any other type of quantum correlations. In fact, there are computational problems that can be solved much faster, in comparison to currently used classical schemes, by saving intermediate information in nonorthogonal states of just a single qubit. There are also error correction strategies that protect such computations.
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Computing with a single qubit faster than the quantum speed limit

2017-01-19
Nikolai A. Sinitsyn
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Surface oxidation and thermoelectric properties of indium-doped tin telluride nanowires

2017-01-01
Zhen Li , Enzhi Xu , Yaroslav Losovyj +7 more
The recent discovery of excellent thermoelectric properties and topological surface states in SnTe-based compounds has attracted extensive attention in various research areas. Indium doped SnTe is of particular interest because, … The recent discovery of excellent thermoelectric properties and topological surface states in SnTe-based compounds has attracted extensive attention in various research areas. Indium doped SnTe is of particular interest because, depending on the doping level, it can either generate resonant states in the bulk valence band leading to enhanced thermoelectric properties, or induce superconductivity that coexists with topological states. Here we report on the vapor deposition of In-doped SnTe nanowires and the study of their surface oxidation and thermoelectric properties. The nanowire growth is assisted by Au catalysts, and their morphologies vary as a function of substrate position and temperature. Transmission electron microscopy characterization reveals the formation of an amorphous surface in single crystalline nanowires. X-ray photoelectron spectroscopy studies suggest that the nanowire surface is composed of In2O3, SnO2, Te and TeO2 which can be readily removed by argon ion sputtering. Exposure of the cleaned nanowires to atmosphere leads to rapid oxidation of the surface within only one minute. Characterization of electrical conductivity σ, thermopower S, and thermal conductivity κ was performed on the same In-doped nanowire which shows suppressed σ and κ but enhanced S yielding an improved thermoelectric figure of merit ZT compared to the undoped SnTe.
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The theory of spin noise spectroscopy: a review

2016-09-12
Nikolai A. Sinitsyn , Yuriy V. Pershin
Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of … Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical Spin Noise Spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside with examples of their applications.
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Common Coauthors

Coauthor Papers Together
Vladimir Chernyak 31
Fuxiang Li 12
A. H. MacDonald 11
Chen Sun 11
Jairo Sinova 10
S. A. Crooker 10
Ilya Nemenman 9
Avadh Saxena 8
Bin Yan 8
Dibyendu Roy 7
T. Jungwirth 6
Soumya Kundu 6
Bin Yan 5
Scott Backhaus 5
Yuriy V. Pershin 5
Stephan Eidenbenz 5
Fumika Suzuki 5
Vijay Ganesh Sadhasivam 4
Yan Li 4
Luyi Yang 4
D. L. Smith 4
John R. Klein 4
Andrew Mugler 3
Tamara S. Nunner 3
Wiet Hendrik de Ronde 3
Mario F. Borunda 3
Diego A. R. Dalvit 3
Benjamin Sims 3
Jie Ren 3
A. Greilich 3
Carsten Timm 3
Qian Niu 3
Andrei Piryatinski 3
Bryan C. Daniels 3
V. A. Slipko 3
V. L. Pokrovsky 3
Scott Pakin 2
Pieter Swart 2
Hristo Djidjev 2
Dimitrie Culcer 2
Adetokunbo Adedoyin 2
Boram Yoon 2
Vigneshwaran Chandrasekaran 2
Nandakishore Santhi 2
Jonathan J. Finley 2
Susan M. Mniszewski 2
Richard J. Zamora 2
V. K. Dugaev 2
Marc Vuffray 2
Carleton Coffrin 2

Commonly Cited References

Multiparticle Landau-Zener problem: Application to quantum dots

2002-11-06
Nikolai A. Sinitsyn
We propose a simple ansatz that allows us to generate new exactly solvable multistate Landau-Zener models. It is based on a system of two decoupled two-level atoms whose levels vary … We propose a simple ansatz that allows us to generate new exactly solvable multistate Landau-Zener models. It is based on a system of two decoupled two-level atoms whose levels vary with time and cross at some moments. Then we consider multiparticle systems with Heisenberg equations for annihilation operators having a similar structure as the Shr\"odinger equation for amplitudes in multistate Landau-Zener models and show that the corresponding Shr\"odinger equation in the multiparticle sector belongs to the multistate Landau-Zener class. This observation allows us to generate new exactly solvable models from already known ones. We discuss possible applications of the new solutions in the problem of the driven charge transport in quantum dots.
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Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model

2005-12-09
Jacek Dziarmaga
The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a … The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.
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The Berry phase and the pump flux in stochastic chemical kinetics

2007-02-15
Nikolai A. Sinitsyn , Ilya Nemenman
We study a classical two-state stochastic system in a sea of substrates and products (absorbing states), which can be interpreted as a single Michaelis-Menten catalyzing enzyme or as a channel … We study a classical two-state stochastic system in a sea of substrates and products (absorbing states), which can be interpreted as a single Michaelis-Menten catalyzing enzyme or as a channel on a cell surface.We introduce a novel general method and use it to derive the expression for the full counting statistics of transitions among the absorbing states.For the evolution of the system under a periodic perturbation of the kinetic rates, the latter contains a term with a purely geometrical (the Berry phase) interpretation.This term gives rise to a pump current between the absorbing states, which is due entirely to the stochastic nature of the system.We calculate the first two cumulants of this current, and we argue that it is observable experimentally.
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Quantum effects on curve crossing in a Bose-Einstein condensate

2002-03-21
Vladimir Yurovsky , A. Ben‐Reuven , Paul S. Julienne
Formation of atomic pairs by the dissociation of a molecular condensate or by inelastic collisions in an atomic condensate due to a time-dependent curve crossing process is studied beyond the … Formation of atomic pairs by the dissociation of a molecular condensate or by inelastic collisions in an atomic condensate due to a time-dependent curve crossing process is studied beyond the mean-field approximation. The number of atoms formed by the spontaneous process is described by a Landau-Zener formula multiplied by an exponential amplification factor due to quantum many-body effects. The atomic pairs are formed in an entangled (squeezed) state. The rate of stimulated processes depends on the relative phase of the two fields.
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Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings

2004-10-21
Nikolai A. Sinitsyn
We generalize the Brundobler–Elser hypothesis in the multistate Landau–Zener problem to the case when instead of a state with the highest slope of the diabatic energy level there is a … We generalize the Brundobler–Elser hypothesis in the multistate Landau–Zener problem to the case when instead of a state with the highest slope of the diabatic energy level there is a band of states with an arbitrary number of parallel levels having the same slope. We argue that the probabilities of counterintuitive transitions among such states are exactly zero.
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Nonadiabaticity and large fluctuations in a many-particle Landau-Zener problem

2009-04-02
Alexander Altland , Victor Gurarie , Thomas Kriecherbauer +1 more
We consider the behavior of an interacting many-particle system under slow external driving---a many-body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to … We consider the behavior of an interacting many-particle system under slow external driving---a many-body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single-particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are ``nonadiabatic'' in that even at very slow driving it is exceedingly difficult to push the center of the distribution toward the limit of full ground-state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.
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Spin Noise Spectroscopy in GaAs

2005-11-17
M. Oestreich , Michael Römer , R. J. Haug +1 more
We observe the noise spectrum of electron spins in bulk GaAs by Faraday-rotation noise spectroscopy. The experimental technique enables the undisturbed measurement of the electron-spin dynamics in semiconductors. We measure … We observe the noise spectrum of electron spins in bulk GaAs by Faraday-rotation noise spectroscopy. The experimental technique enables the undisturbed measurement of the electron-spin dynamics in semiconductors. We measure exemplarily the electron-spin relaxation time and the electron Landé g factor in -doped GaAs at low temperatures and find good agreement of the measured noise spectrum with a theory based on Poisson distribution probability.
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Quantum integrability in the multistate Landau–Zener problem

2015-05-27
Aniket Patra , Emil A. Yuzbashyan
We analyze Hamiltonians linear in the time variable for which the multistate Landau-Zener problem is known to have an exact solution. We show that they either belong to families of … We analyze Hamiltonians linear in the time variable for which the multistate Landau-Zener problem is known to have an exact solution. We show that they either belong to families of mutually commuting Hamiltonians polynomial in time or reduce to the 2 x 2 Landau-Zener problem, which is considered trivially integrable. The former category includes the equal slope, bow-tie, and generalized bow-tie models. For each of these models we explicitly construct the corresponding families of commuting matrices. The equal slope model is a member of an integrable family that consists of the maximum possible number (for a given matrix size) of commuting matrices linear in time. The bow-tie model belongs to a previously unknown, similarly maximal family of quadratic commuting matrices. We thus conjecture that quantum integrability understood as the existence of nontrivial parameter-dependent commuting partners is a necessary condition for the Landau-Zener solvability. Descendants of the 2 x 2 Landau-Zener Hamiltonian are e.g. general SU(2) and SU(1,1) Hamiltonians, time-dependent linear chain, linear, nonlinear, and double oscillators. We explicitly obtain solutions to all these Landau-Zener problems from the 2 x 2 case.
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Spin noise of conduction electrons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-type bulk GaAs

2009-01-29
S. A. Crooker , Lili Cheng , D. L. Smith
We report a comprehensive study of stochastic electron spin fluctuations -- spin noise -- in lightly doped ($n$-type) bulk GaAs, which are measured using sensitive optical magnetometry based on off-resonant … We report a comprehensive study of stochastic electron spin fluctuations -- spin noise -- in lightly doped ($n$-type) bulk GaAs, which are measured using sensitive optical magnetometry based on off-resonant Faraday rotation. Frequency spectra of electron spin noise are studied as a function of electron density, magnetic field, temperature, probe laser wavelength and intensity, and interaction volume. Electron spin lifetimes $\tau_s$ are inferred from the width of the spin noise spectra, and are compared with direct measurements of $\tau_s$ using conventional Hanle effect methods. Both methods reveal a strong and similar dependence of $\tau_s$ on the wavelength and intensity of the probe laser, highlighting the undesired influence of sub-bandgap absorption effects on the nominally `non-perturbative' spin noise measurements. As a function of temperature, the spin noise power increases approximately linearly from 1.5 K to 30 K, as expected for degenerate electrons obeying Fermi-Dirac statistics, but with an additional zero-temperature offset. Finally, as the cross-sectional area of the probe laser shrinks and fewer electrons are probed, the measured Faraday rotation fluctuations due to electron spin noise are shown to increase, as expected.
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Intrinsic Spin Fluctuations Reveal the Dynamical Response Function of Holes Coupled to Nuclear Spin Baths in (In,Ga)As Quantum Dots

2012-05-03
Yan Li , Nikolai A. Sinitsyn , D. L. Smith +5 more
The problem of how single "central" spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to … The problem of how single "central" spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to the many-body couplings involved. Different models yield widely varying timescales and dynamical responses (exponential, power-law, Gaussian, etc). Here we detect the small random fluctuations of central spins in thermal equilibrium (holes in singly-charged (In,Ga)As quantum dots) to reveal the timescales and functional form of bath-induced spin relaxation. This spin noise indicates long (400 ns) spin correlation times at zero magnetic field, that increase to $\sim$5 $\mu$s as hole-nuclear coupling is suppressed with small (100 G) applied fields. Concomitantly, the noise lineshape evolves from Lorentzian to power-law, indicating a crossover from exponential to inverse-log dynamics.
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Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance

2004-09-01
S. A. Crooker , D.G. Rickel , Alexander V. Balatsky +1 more
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Landau-Zener transitions in chains

2013-03-04
Nikolai A. Sinitsyn
We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the … We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the dissipationless quantum mechanical regime. In particular, we show that the statistics of particles in a new phase demonstrate scaling behavior. Our results also reveal a symmetry that we claim is a property of a large class of multistate LZ models, whose explicit solutions are not presently known. We support our arguments by direct numerical simulations.
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Landau-Zener transitions in a linear chain

2002-04-04
V. L. Pokrovsky , Nikolai A. Sinitsyn
We present an exact asymptotic solution for electron transition amplitudes in an infinite linear chain driven by an external homogeneous time-dependent electric field. This solution extends the Landau-Zener theory for … We present an exact asymptotic solution for electron transition amplitudes in an infinite linear chain driven by an external homogeneous time-dependent electric field. This solution extends the Landau-Zener theory for the case of infinite number of states in discrete spectrum. In addition to transition amplitudes we calculate an effective diffusion constant.
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Integrable Time-Dependent Quantum Hamiltonians

2018-05-11
Nikolai A. Sinitsyn , Emil A. Yuzbashyan , Vladimir Chernyak +2 more
We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge … We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
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Counterintuitive transitions between crossing energy levels

2005-11-10
Andon A. Rangelov , Jyrki Piilo , Nikolay V. Vitanov
We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the … We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the other two states in a chainwise linkage pattern with constant couplings of finite duration. The probability for a counterintuitive transition is found to increase with the square of the coupling and decrease with the squares of the interaction duration, the energy splitting between the parallel energies, and the tilt (chirp) rate. Physical examples of this model can be found in coherent atomic excitation and optical shielding in cold atomic collisions.
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No-go theorem for bands of potential curves in multistate Landau–Zener model

2005-03-16
M. V. Volkov , V N Ostrovsky
In the multistate Landau–Zener model all diabatic potential curves are linear functions of time. We consider the case where there is a band of parallel potential curves with slope larger … In the multistate Landau–Zener model all diabatic potential curves are linear functions of time. We consider the case where there is a band of parallel potential curves with slope larger (smaller) than any of the other slopes in the system. In such a situation transitions from a lower (higher) lying state within the band to any upper (lower) state are counterintuitive, since in the simple semiclassical picture they are possible only via propagation backwards in time. We rigorously prove that the probabilities of such transitions are exactly zero. In other words the energy of states within the band can only decrease (increase). The theoretical method employed is based on analysis of perturbation theory series to arbitrary order.

Full counting statistics of charge transfer in Coulomb blockade systems

2003-02-27
Д. А. Багрец , Yuli V. Nazarov
Full counting statistics (FCS) of charge transfer in mesoscopic systems has recently become a subject of significant interest, since it proves to reveal an important information about the system which … Full counting statistics (FCS) of charge transfer in mesoscopic systems has recently become a subject of significant interest, since it proves to reveal an important information about the system which can be hardly assessed by other means. While the previous research mostly addressed the FCS of noninteracting systems, the present paper deals with the FCS in the limit of strong interaction. In this Coulomb blockade limit the electron dynamics is known to be governed by a master equation. We develop a general scheme to evaluate the FCS in such case, this being the main result of the work presented. We illustrate the scheme, by applying it to concrete systems. For generic case of a single resonant level we establish the equivalence of scattering and master equation approach to FCS. Further we study a single Coulomb blockade island with two and three leads attached and compare the FCS in this case with our recent results concerning an open dot either with two and three terminals. We demonstrate that Coulomb interaction suppresses the relative probabilities of large current fluctuations.
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Spin Noise of Electrons and Holes in Self-Assembled Quantum Dots

2010-01-22
S. A. Crooker , J. Brandt , Christian Sandfort +5 more
We measure the frequency spectra of random spin fluctuations, or ``spin noise,'' in ensembles of $(\mathrm{In},\mathrm{Ga})\mathrm{As}/\mathrm{GaAs}$ quantum dots (QDs) at low temperatures. We employ a spin noise spectrometer based on … We measure the frequency spectra of random spin fluctuations, or ``spin noise,'' in ensembles of $(\mathrm{In},\mathrm{Ga})\mathrm{As}/\mathrm{GaAs}$ quantum dots (QDs) at low temperatures. We employ a spin noise spectrometer based on a sensitive optical Faraday rotation magnetometer that is coupled to a digitizer and field-programmable gate array, to measure and average noise spectra from 0--1 GHz continuously in real time with $\mathrm{\text{subnanoradian}}/\sqrt{\mathrm{Hz}}$ sensitivity. Both electron and hole spin fluctuations generate distinct noise peaks, whose shift and broadening with magnetic field directly reveal their $g$ factors and dephasing rates within the ensemble. A large, energy-dependent anisotropy of the in-plane hole $g$ factor is clearly exposed, reflecting systematic variations in the average QD confinement potential.
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Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets

2018-02-01
Emil A. Yuzbashyan
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Universal Geometric Theory of Mesoscopic Stochastic Pumps and Reversible Ratchets

2007-11-30
Nikolai A. Sinitsyn , Ilya Nemenman
We construct a unifying theory of geometric effects in mesoscopic stochastic kinetics. We demonstrate that the adiabatic pump and the reversible ratchet effects, as well as similar new phenomena in … We construct a unifying theory of geometric effects in mesoscopic stochastic kinetics. We demonstrate that the adiabatic pump and the reversible ratchet effects, as well as similar new phenomena in other domains, such as in epidemiology, all follow from very similar geometric phase contributions to the effective action in the stochastic path integral representation of the moment generating function. The theory provides the universal technique for identification, prediction, and calculation of pumplike phenomena in an arbitrary mesoscopic stochastic framework.
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Exact results for models of multichannel quantum nonadiabatic transitions

2014-12-11
Nikolai A. Sinitsyn
We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}(t)=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}+\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{B}t+\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{C}/t$, where $t$ is time and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A},\phantom{\rule{0.16em}{0ex}}\stackrel{\ifmmode … We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}(t)=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}+\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{B}t+\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{C}/t$, where $t$ is time and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A},\phantom{\rule{0.16em}{0ex}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{B},\phantom{\rule{0.16em}{0ex}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{C}$ are Hermitian $N\ifmmode\times\else\texttimes\fi{}N$ matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. This allows one to continue such solutions analytically to $t\ensuremath{\rightarrow}+\ensuremath{\infty}$, and connect their asymptotic behavior at $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ and $t\ensuremath{\rightarrow}+\ensuremath{\infty}$. This property becomes particularly useful when a model shows additional discrete symmetries. In particular, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems.
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Solvable four-state Landau-Zener model of two interacting qubits with path interference

2015-11-30
Nikolai A. Sinitsyn
I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system … I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria of integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.
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Universal Intrinsic Spin Hall Effect

2004-03-25
Jairo Sinova , Dimitrie Culcer , Qian Niu +3 more
We describe a new effect in semiconductor spintronics that leads to dissipationless spin-currents in paramagnetic spin-orbit coupled systems. We argue that in a high mobility two-dimensional electron system with substantial … We describe a new effect in semiconductor spintronics that leads to dissipationless spin-currents in paramagnetic spin-orbit coupled systems. We argue that in a high mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin-current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the spin-Hall conductivity has a universal value.
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Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges

2010-08-18
G. Müller , M. Oestreich , Michael Römer +1 more
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Solvable multistate model of Landau-Zener transitions in cavity QED

2016-06-29
Nikolai A. Sinitsyn , Fuxiang Li
We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin … We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy-level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener transitions leads to coflips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.
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Coherent Particle Transfer in an On-Demand Single-Electron Source

2008-11-07
Jonathan Keeling , A. V. Shytov , Leonid Levitov
Electron transfer from a localized state in a quantum dot into a ballistic conductor generally results in particle-hole excitations. We study this effect, considering a resonance level with time-dependent energy … Electron transfer from a localized state in a quantum dot into a ballistic conductor generally results in particle-hole excitations. We study this effect, considering a resonance level with time-dependent energy coupled to particle states in the Fermi sea. We find that, as the resonance level is driven through the Fermi-level, particle-hole excitations can be suppressed for certain driving protocols. In particular, such noiseless transfer occurs if the level moves with constant rapidity, its energy changing linearly with time. A scheme to study the coherence of particle transfer is proposed.
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Directed Flow in Nonadiabatic Stochastic Pumps

2008-10-02
Saar Rahav , Jordan M. Horowitz , Christopher Jarzynski
We analyze the operation of a molecular machine driven by the nonadiabatic variation of external parameters. We derive a formula for the integrated flow from one configuration to another, obtain … We analyze the operation of a molecular machine driven by the nonadiabatic variation of external parameters. We derive a formula for the integrated flow from one configuration to another, obtain a ``no-pumping theorem'' for cyclic processes with thermally activated transitions, and show that in the adiabatic limit the pumped current is given by a geometric expression.
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Stochastic Path Integral Formulation of Full Counting Statistics

2003-05-20
S. Pilgram , Andrew N. Jordan , Eugene V. Sukhorukov +1 more
We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point … We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle-point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semiclassical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.
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The quest for solvable multistate Landau-Zener models

2017-05-24
Nikolai A. Sinitsyn , Vladimir Chernyak
Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs … Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. In addition, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.
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Dissipationless Quantum Spin Current at Room Temperature

2003-08-12
Shuichi Murakami , Naoto Nagaosa , Shoucheng Zhang
Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is … Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this irreversibility that leads to intrinsic dissipations in electronic devices and limits the possibility of quantum computation. We theoretically predict that the electric field can induce a substantial amount of dissipationless quantum spin current at room temperature, in hole-doped semiconductors such as Si, Ge, and GaAs. On the basis of a generalization of the quantum Hall effect, the predicted effect leads to efficient spin injection without the need for metallic ferromagnets. Principles found here could enable quantum spintronic devices with integrated information processing and storage units, operating with low power consumption and performing reversible quantum computation.
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Production efficiency of Feshbach molecules in fermion systems

2005-10-11
B. Dobrescu , V. L. Pokrovsky
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Nonadiabatic Landau-Zener tunneling in Fe <sub>8</sub> molecular nanomagnets

2000-05-15
Wolfgang Wernsdorfer , Roberta Sessoli , Andréa Caneschi +2 more
The Landau Zener method allows to measure very small tunnel splittings \Delta in molecular clusters Fe_8. The observed oscillations of \Delta as a function of the magnetic field applied along … The Landau Zener method allows to measure very small tunnel splittings \Delta in molecular clusters Fe_8. The observed oscillations of \Delta as a function of the magnetic field applied along the hard anisotropy axis are explained in terms of topological quantum interference of two tunnel paths of opposite windings. Studies of the temperature dependence of the Landau Zener transition rate P gives access to the topological quantum interference between exited spin levels. The influence of nuclear spins is demonstrated by comparing P of the standard Fe_8 sample with two isotopically substituted samples. The need of a generalized Landau Zener transition rate theory is shown.
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Landau-Zener transitions in a multilevel system: An exact result

2004-11-17
A. V. Shytov
We study the $S$ matrix for the transitions at an avoided crossing of several energy levels, which is a multilevel generalization of the Landau-Zener problem. We demonstrate that, by extending … We study the $S$ matrix for the transitions at an avoided crossing of several energy levels, which is a multilevel generalization of the Landau-Zener problem. We demonstrate that, by extending the Schr\"odinger evolution to complex time, one can obtain an exact answer for some of the transition amplitudes. Similar to the Landau-Zener case, our result covers both the adiabatic (slow evolution) and the diabatic (fast evolution) regimes. The form of the exact transition amplitude coincides with that obtained in a sequential pairwise level crossing approximation, in accord with the conjecture of Brundobler and Elser [J. Phys. A 26, 1211 (1993)].

Exact transition probabilities in a 6-state Landau–Zener system with path interference

2015-04-23
Nikolai A. Sinitsyn
We identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model … We identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the LZ formula. We discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.
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Role of Nuclear Quadrupole Coupling on Decoherence and Relaxation of Central Spins in Quantum Dots

2012-10-18
Nikolai A. Sinitsyn , Yan Li , S. A. Crooker +2 more
Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling … Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling (QC) on the spin correlators of electron and hole "central" spins localized in such dots. We show that when the QC strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential. We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots.
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Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

1999-06-15
Ganesh Sundaram , Qian Niu
We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first-order … We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first-order gradient correction and obtain all kinds of Berry phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking interband couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.
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Dynamics of a many-particle Landau-Zener model: Inverse sweep

2009-05-18
A. P. Itin , Päivi Törmä
We consider dynamics of a slowly time-dependent Dicke model, which represents a many-body generalization of the Landau-Zener model. In particular, the model describes narrow Feshbach resonance passage in an ultracold … We consider dynamics of a slowly time-dependent Dicke model, which represents a many-body generalization of the Landau-Zener model. In particular, the model describes narrow Feshbach resonance passage in an ultracold gas of Fermi atoms. Adiabaticity is destroyed when a parameter crosses a critical value, even at very slow sweeping rates of a parameter. The dynamics crucially depends on direction of the sweep. We apply our recent analysis (A. P. Itin and P. T\"orm\"a, e-print arXiv:0901.4778) to the ``inverse'' sweep through the resonance, corresponding (in a context of Feshbach resonance passage) to dissociation of molecules. On a level of the mean-field approximation, the dynamics is equivalent to a molecular condensate formation from Bose atoms within a two-mode model. Mapping the system to a Painlev\'e equation allows us to calculate deviation from adiabaticity at very slow sweeps analytically.
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The stochastic pump current and the non-adiabatic geometrical phase

2008-02-26
Jun Ohkubo
We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and … We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and under a periodic perturbation of the kinetic rates, it gives rise to a pump current between the two-state system and the absorbing states. In order to calculate the pump current, the Floquet theory for the non-adiabatic geometrical phase is extended from a Hermitian case to a non-Hermitian case. The dependence of the pump current on the frequency of the perturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior is obtained.
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Anomalous Hall Effect in Ferromagnetic Semiconductors

2002-05-06
T. Jungwirth , Qian Niu , A. H. MacDonald
We present a theory of the anomalous Hall effect in ferromagnetic (III, Mn)V semiconductors. Our theory relates the anomalous Hall conductance of a homogeneous ferromagnet to the Berry phase acquired … We present a theory of the anomalous Hall effect in ferromagnetic (III, Mn)V semiconductors. Our theory relates the anomalous Hall conductance of a homogeneous ferromagnet to the Berry phase acquired by a quasiparticle wave function upon traversing closed paths on the spin-split Fermi surface. The quantitative agreement between our theory and experimental data in both (In, Mn)As and (Ga, Mn)As systems suggests that this disorder independent contribution to the anomalous Hall conductivity dominates in diluted magnetic semiconductors. The success of this model for (III, Mn)V materials is unprecedented in the longstanding effort to understand origins of the anomalous Hall effect in itinerant ferromagnets.
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Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

2016-09-07
Chen Sun , Nikolai A. Sinitsyn
We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent … We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and $q$-deformed binomial statistics.
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Gauging a Quantum Heat Bath with Dissipative Landau-Zener Transitions

2006-11-17
Martijn Wubs , Keiji Saito , Sigmund Kohler +2 more
We calculate the exact Landau-Zener transitions probabilities for a qubit with arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the … We calculate the exact Landau-Zener transitions probabilities for a qubit with arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of a diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
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Spin Noise Spectroscopy in GaAs (110) Quantum Wells: Access to Intrinsic Spin Lifetimes and Equilibrium Electron Dynamics

2008-11-11
G. Müller , Michael Römer , Dieter Schuh +3 more
In this Letter, the first spin noise spectroscopy measurements in semiconductor systems of reduced effective dimensionality are reported. The nondemolition measurement technique gives access to the otherwise concealed intrinsic, low … In this Letter, the first spin noise spectroscopy measurements in semiconductor systems of reduced effective dimensionality are reported. The nondemolition measurement technique gives access to the otherwise concealed intrinsic, low temperature electron spin relaxation time of n-doped GaAs (110) quantum wells and to the corresponding low temperature anisotropic spin relaxation. The Brownian motion of the electrons within the spin noise probe laser spot becomes manifest in a modification of the spin noise line width. Thereby, the spatially resolved observation of the stochastic spin polarization uniquely allows to study electron dynamics at equilibrium conditions with a vanishing total momentum of the electron system.
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Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior

2007-06-29
Keiji Saito , Martijn Wubs , Sigmund Kohler +2 more
We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula is derived that is applicable to models with a non-degenerate ground state. We … We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula is derived that is applicable to models with a non-degenerate ground state. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard LZ probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.
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Many Body Generalization of the Landau-Zener Problem

2008-02-15
Alexander Altland , Victor Gurarie
We formulate and approximately solve a specific many body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground … We formulate and approximately solve a specific many body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.
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Pumping Restriction Theorem for Stochastic Networks

2008-10-15
Vladimir Chernyak , Nikolai A. Sinitsyn
We formulate an exact result, which we refer to as the pumping restriction theorem (PRT). It imposes strong restrictions on the currents generated by periodic driving in a generic dissipative … We formulate an exact result, which we refer to as the pumping restriction theorem (PRT). It imposes strong restrictions on the currents generated by periodic driving in a generic dissipative system with detailed balance, and provides a universal nonperturbative approach to explore the stochastic pump effect in nonadiabatically driven systems.
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Assisted Finite-Rate Adiabatic Passage Across a Quantum Critical Point: Exact Solution for the Quantum Ising Model

2012-09-13
Adolfo del Campo , Marek M. Rams , Wojciech H. Zurek
The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of the critical slowing down in the neighborhood of the critical point. … The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of the critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point that allows one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.
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Optical Spectroscopy of Spin Noise

2013-04-23
V. S. Zapasskiĭ , A. Greilich , S. A. Crooker +6 more
Spontaneous fluctuations of the magnetization of a spin system in thermodynamic equilibrium (spin noise) manifest themselves as noise in the Faraday rotation of probe light. We show that the correlation … Spontaneous fluctuations of the magnetization of a spin system in thermodynamic equilibrium (spin noise) manifest themselves as noise in the Faraday rotation of probe light. We show that the correlation properties of this noise over the optical spectrum can provide clear information about the composition of the spin system that is largely inaccessible for conventional linear optics. Such optical spectroscopy of spin noise, e.g., allows us to clearly distinguish between optical transitions associated with different spin subsystems, to resolve optical transitions that are unresolvable in the usual optical spectra, to unambiguously distinguish between homogeneously and inhomogeneously broadened optical bands, and to evaluate the degree of inhomogeneous broadening. These new possibilities are illustrated by theoretical calculations and by experiments on paramagnets with different degrees of inhomogeneous broadening of optical transitions [atomic vapors of 41K and singly charged (In,Ga)As quantum dots].
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Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory

2007-02-20
M. V. Volkov , V N Ostrovsky
Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A new technique for analysis of the series is developed. Analytical expressions for probabilities of survival … Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A new technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. New expressions for some state-to-state transition probabilities are derived in degenerate cases.
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Quantum Spin Hall Effect in Graphene

2005-11-23
C. L. Kane , E. J. Melé
We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime … We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are non chiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed.
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High Bandwidth Atomic Magnetometery with Continuous Quantum Nondemolition Measurements

2010-01-05
Vishal Shah , Georgios Vasilakis , Michael Romalis
We describe an experimental study of spin-projection noise in a high sensitivity alkali-metal magnetometer. We demonstrate a fourfold improvement in the measurement bandwidth of the magnetometer using continuous quantum nondemolition … We describe an experimental study of spin-projection noise in a high sensitivity alkali-metal magnetometer. We demonstrate a fourfold improvement in the measurement bandwidth of the magnetometer using continuous quantum nondemolition measurements. Operating in the scalar mode with a measurement volume of 2 cm3 we achieve magnetic field sensitivity of 22 fT/Hz(1/2) and a bandwidth of 1.9 kHz with a spin polarization of only 1%. Our experimental arrangement is naturally backaction evading and can be used to realize sub-fT sensitivity with a highly polarized spin-squeezed atomic vapor.
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