Alternatives to eigenstate thermalization

An isolated quantum many-body system in an initial pure state will come to thermal equilibrium if it satisfies the eigenstate thermalization hypothesis (ETH). We consider alternatives to ETH that have been proposed. We first show that von Neumann's quantum ergodic theorem relies on an assumption that is essentially equivalent to ETH. We also investigate whether, following a sudden quench, special classes of pure states can lead to thermal behavior in systems that do not obey ETH, namely, integrable systems. We find examples of this, but only for initial states that obeyed ETH before the quench.     

Thermalization of strongly coupled field theories

Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.     

Experimental study of the role of atomic interactions on quantum transport

We report an experimental study of quantum transport for atoms confined in a periodic potential and compare between thermal and Bose-Einstein condensation (BEC) initial conditions. We observe ballistic transport for all values of well depth and initial conditions, and the measured expansion velocity for thermal atoms is in excellent agreement with a single-particle model. For weak wells, the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature. We observe a crossover to a new regime for the BEC case as the well depth is increased, indicating the importance of interactions on quantum transport.     

Identifying the closeness of eigenstates in quantum many-body systems

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis(ETH) which explains the thermalization in quantum many-body systems.     

Tunneling and Self-Trapping of Superfluid Fermi Gases in BCS-BEC Crossover

We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the
tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.     

Coherent state approach to the cross-collisional effects in the population dynamics of a two-mode Bose–Einstein condensate

We reanalyze the non-linear population dynamics of a Bose–Einstein condensate (BEC) in a double well trap considering a semiclassical approach based on a time dependent variational principle applied to coherent states associated to SU(2) group. Employing a two-mode local approximation and hard sphere type interaction, we show in the Schwinger’s pseudo-spin language the occurrence of a fixed point bifurcation that originates a separatrix of motion on a sphere. This separatrix corresponds to the borderline between two dynamical regimes of Josephson oscillations and mesoscopic self-trapping. We also consider the effects of interaction between particles in different wells, known as cross-collisions. Such terms are usually neglected for traps sufficiently far apart, but recently it has been shown that they contribute to the effective tunneling constant with a factor growing linearly with the particle number. This effect changes considerably the effective tunneling of the system for sufficiently large number of trapped atoms, in perfect accord with experimental data. Finally, we identify analytically the transition parameter associated to the bifurcation in the generalized phase space of the model with cross-collision terms, and show how the dynamical regime depends on the initial conditions of the system and the collisional parameters values.     

Interaction of Short Laser Pulses in Wavelength Range from Infrared to X‐ray with Metals,Semiconductors, and Dielectrics

Laser‐matter interaction is defined by an electronic band structure of condensed matter and frequency ω_L of electromagnetic radiation. In the range of moderate fluences, the energy absorbed by electrons from radiation finally thermalizes in the ion thermal energy. The thermalization processes are different for optical as compared with X‐ray quanta and for metals relative to semiconductors and dielectrics, since the light absorption and electron‐electron, electron‐ion dynamics are sensitive to the electron population in a conduction band and the width of a forbidden gap. Although the thermalization processes are different, the final state is simply a heated matter. Laser heating creates powerful stresses in a target if duration of a laser pulse τ_L is short in acoustic time scale. Nucleation and material removal take place under such stresses. Such way of removal is called here the spallative ablation. Thus the spallative ablation is an ablation mechanism universally important for qualitatively different materials and quanta (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of the vortex state in the BCS-BEC crossover of a quasi two-dimensional superfluid Fermi gas

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional(2D) Fermi superfluid system trapped in an optical lattice potential.Within the framework of mean-field theory,the cooper pair density,the atom number density,and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime.Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime.Meanwhile,the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional(3D) to 2D case.Furthermore,using a simple re-normalization procedure,we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G_c which is obtained as a function of the lattice potential's parameter.Finally,we investigate the vortex core size and find that it grows with increasing interaction strength.In particular,by analyzing the behavior of the vortex core size in both BCS and BEC regimes,we find that the vortex core size behaves quite differently for positive and negative chemical potentials.     

Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice

We study the exact Bloch states of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) held in an optical lattice. Under a natural condition of the symmetry between the two species, we obtain two different forms of exact solutions corresponding to different existing conditions. Then, we analytically demonstrate that (a) the average atomic number per well can enlarge the region area (consisting of instability and stability parameter regions) existing exact solutions; (b) the sizes of the instability and stability parameter regions exhibit opposite variation trend with the increase in Rabi coupling strength, and the results of different solutions are just opposite. Besides, we find that spin-orbit coupling (SOC) results in the generation of spin-motion entanglement for the Bloch states, the SOC strength and lattice depth can influence the population transfer between two BEC components, and varying the SOC strength and lattice depth can also reveal the dynamical superfluid-insulator transition from the superfluid state to the critical insulating state. These results present a feasible scheme to manipulate the stable superfluid currents, which will be useful to control quantum transport of BEC.

     

偶极玻色-爱因斯坦凝聚体在类方势阱中的Bénard-von Kármán涡街

对偶极玻色-爱因斯坦凝聚体（Bose-Einstein condensate,BEC）在类方势阱中的Bénard-von Kármán涡街现象进行了数值研究.结果表明,当障碍势在BEC中的运动速度与尺寸在适当范围内时,系统中会出现稳定的两列涡旋对阵列,即Bénard-von Kármán涡街.研究了偶极相互作用强弱、障碍势尺寸以及运动速度对尾流中产生的涡旋结构的影响,得到了相图结构.对障碍势所受拖拽力进行计算,分析了涡旋对产生的力学机理.     

Thermalization in nature and on a quantum computer

In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.     

Stabilities of one-dimensional stationary states of Bose-Einstein condensates

We explore the dynamical stabilities of a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) consisting of fixed N atoms with time-independent external potential. For the stationary states with zero flow density the general solution of the perturbed time evolution equation is constructed, and the stability criterions concerning the initial conditions and system parameters are established. Taking the lattice potential case as an example, the stability and instability regions on the parameter space are found. The results suggest a method for selecting experimental parameters and adjusting initial conditions to suppress the instabilities.     

1D stability analysis of filtering and controlling the solitons in Bose-Einstein condensates

We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating the external potential well in the three-dimensional (3D) Gross–Pitaevskii equation (GPE). Within the framework of this method, under suitable conditions, the GPE can be exactly decomposed into a pair of coupled equations: a transverse two-dimensional (2D) linear Schr?dinger equation and a one-dimensional (1D) longitudinal nonlinear Schr?dinger equation (NLSE) with, in a general case, a time-dependent nonlinear coupling coefficient. We review the general idea how to filter and control localized solutions of the GPE. Then, the 1D longitudinal NLSE is numerically solved with suitable non-ideal controlling potentials that differ from the ideal one so as to introduce relatively small errors in the designed spatial profile. It is shown that a BEC with an asymmetric initial position in the confining potential exhibits breather-like oscillations in the longitudinal direction but, nevertheless, the BEC state remains confined within the potential well for a long time. In particular, while the condensate remains essentially stable, preserving its longitudinal soliton-like shape, only a small part is lost into “radiation”.     

Classically induced suppression of energy growth in a chaotic quantum system

Recent experiments with Bose–Einstein condensates (BEC) in traps and speckle potentials have explored the dynamical regime in which the evolving BEC clouds localize due to the influence of classical dynamics. The growth of their mean energy is effectively arrested. This is in contrast with the well-known localization phenomena that originate due to quantum interferences. We show that classically induced localization can also be obtained in a classically chaotic, non-interacting system. In this work, we study the classical and quantum dynamics of non-interacting particles in a double-barrier structure. This is essentially a non-KAM system and, depending on the parameters, can display chaotic dynamics inside the finite well between the barriers. However, for the same set of parameters, it can display nearly regular dynamics above the barriers. We exploit this combination of two qualitatively different classical dynamical features to obtain saturation of energy growth. In the semiclassical regime, this classical mechanism strongly influences the quantum behaviour of the system.     

Error Covariance Matrix Estimation of Noisy and Dynamically Coupled Time Series

We estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors. We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. The estimation of the covariance matrix of the errors is made using a noise reduction algorithm that efficiently exploits the information contained jointly in the dynamically coupled noisy time series. The method is particularly powerful for short length time series with high uncertainties.     

Behaviors of thermalization for the Fermi–Pasta–Ulam–Tsingou system with small number of particles

We study the behaviors of thermalization in Fermi–Pasta–Ulam–Tsingou(FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_(eq) depending on system's energy density ε scales as t_(eq) ∝ε~(-4) only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε~(-4) will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.     

Josephson dynamics for coupled polariton modes under the atom–field interaction in the cavity

We consider a new approach to the problem of Bose–Einstein condensation (BEC) of polaritons for atom–field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons. PACS 03.75.Lm; 71.36.+c; 42.50.Fx     

Photon emission as a source of coherent behavior of polaritons

We show that the combined effect of photon emission and Coulomb interactions may drive an exciton-polariton system towards a dynamical coherent state, even without phonon thermalization or any other relaxation mechanism. Exact diagonalization results for a finite system (a multilevel quantum dot interacting with the lowest-energy photon mode of a microcavity) are presented in support of this statement.