We investigate finite size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy-scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground-states. Both criteria can be computed using ground-state techniques that work for larger system sizes than full spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap which frequency is quenched, and the one-dimensional Bose-Hubbard model, that is known to be non-integrable and for which recent studies have uncovered remarkable non-equilibrium behaviors. The diagonal weights of the time-averaged density-matrix are computed and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the "thermalized" regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite size effects that render difficult a thorough comparison with statistical ensembles. In addition, we show that the non-thermalized regime, emerging on finite size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the non-interacting limit to the atomic limit.
We study the quench dynamics of the one-dimensional Hubbard model through the Quench Action formalism. We introduce a class of integrable initial states -- expressed as product states over two sites -- for which we can provide an exact characterisation of the late-time regime. This is achieved by finding a closed-form expression for the overlaps between our states and the Bethe ansatz eigenstates, which we check explicitly in the limits of low densities and infinite repulsion. Our solution gives access to the stationary values attained by local observables (we show the explicit example of the …
Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''
在他对Roux的论文[Phys. Rev. A 79，021608（R）（2009）]的评论[见前面的评论，Phys. Rev. A 82，037601（2010）]中，Rigol认为猝灭后的能量分布与标准统计系综无关，不能解释热化。后者被认为是源于他所谓的本征态热化假设，并归结为这样一个事实，即简单的可观测量预计是能量的平滑函数。在这篇回复中，我们表明，Roux的观察和讨论与Rigol讨论的预期热化情景之间没有矛盾或混淆。此外，我们还强调了其他一些重要的方面，特别是温度的定义和系综的等价性，尽管我们相信它们对热化的讨论是必不可少的，但它们更难以用数值来表示。这些评论可能是感兴趣的人在有限尺寸系统上获得的数据的解释感兴趣。
Using the time-dependent density matrix renormalization group method and exact diagonalization, we study the non-equilibrium dynamics of the one-dimensional Fermi-Hubbard model following a quantum quench or a ramp of the onsite interaction strength. For quenches from the non-interacting to the attractive regime, we investigate the dynamical emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which at finite spin polarizations are the dominant two-body correlations in the ground state, and their signatures in the pair quasi-momentum distribution function. We observe that the post…
Comment on "Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined" [arXiv:0810.3720]
在最近的一篇论文中，Roux [Phys. Rev. A 79，021608（R）（2009），arXiv：0810.3720]认为玻色-哈伯德系统中的热化在猝灭之后，遵循初始态和最终哈密顿量的本征态之间重叠的近似玻尔兹曼分布。我们在这里表明，重叠的分布一般不相关的正则（或微正则）分布，因此，它不能解释为什么热化发生在量子系统。
We present a scheme for measuring Rényi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random unitaries from random quenches, implemented using engineered time-dependent disorder potentials, and standard projective measurements, as realized by quantum gas microscopes. By analyzing the properties of the generated unitaries and the role of statistical errors, with respect to the size of the partition, we show that the protocol can be realized in exisiting AMO …
We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of Rényi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum…
We consider quantum quenches of harmonically trapped one-dimensional bosons from repulsive to attractive interactions, and the resulting breathing dynamics of the so-called `super-Tonks-Girardeau' (sTG) state. This state is highly excited compared to the ground state of the attractive gas, and is the lowest eigenstate where the particles are not bound or clustered. We analyze the dynamics from a spectral point of view, identifying the relevant eigenstates of the interacting trapped many-body system, and analyzing the nature of these quantum eigenstates. To obtain explicit eigenspectra, we use …
Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics
最近在光晶格中的凝聚态模型的实验实现激发了对其非平衡行为的研究。基于有效BCS哈密顿量，已经对配对相互作用突然猝灭后超导体的动力学进行了预测;然而，它们的实验验证需要沿着双重约束制备哈伯德模型的合适激发态：（i）充分非绝热的斜坡方案对于激发非平衡动力学是必要的，以及（ii）必须避免超过超导性的临界温度的过热。对于通常讨论的相互作用斜坡，相应的能量尺度没有明确的分离。在这里，我们表明，这两个条件的匹配被简化的超冷费米子系统的内在弛豫行为：对于一个特殊的例子，我们检查的线性斜坡的预热化的瞬态制度[M。Moeckel和S. Kehrein，Phys. Rev. Lett. 100，175702（2008）]在使用Keldysh微扰理论从突然切换到绝热切换的交叉下。的动量分布的实时分析表现出早期的能量弛豫和后来的热化散射事件的时间分离。对于长但有限的斜升时间，该间隔可能很大。在预热化制度的动量分布类似于零温度费米液体的能量插入的斜坡仍然位于高能量模式。因此，超冷费米子被证明对加热具有鲁棒性，这简化了光晶格中非平衡BCS动力学的观察。
We present a non-equilibrium Green's functional approach to study the dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The technique is based on the self-consistent solution of a set of equations which represents a particular case of the most general set of Hedin's equations for the interacting single-particle Green's function. We use the ladder approximation as a skeleton diagram for the two-particle scattering amplitude useful, through the self-energy in the Dyson equation, for finding the interacting single-particle Green's function. This scheme is then implemente…
We investigate a one-dimensional Bose-Hubbard model in a parametrically driven global harmonic trap. The delicate interplay of both the local atom interaction and the global driving allows to control the dynamical stability of the trapped quantum many-body state. The mechanism is illustrated for weak interaction by a discretized Gross-Pitaevskii equation within a Gaussian variational ansatz, yielding to a Mathieu equation for the condensate width. The parametric resonance condition can be tuned by the atom interaction strength. For stronger interaction, this mechanism is confirmed by results o…
We give a prescription to perform the continuum limit of the $d$-dimensional Hubbard model in the presence of a harmonic trap at zero temperature. We perform the continuum limit at fixed number of particles. In $d\geq3$ the lattice system of spin-1/2 particles is mapped into a non-interacting two-component Fermi gas in a harmonic trap. In $d=1$ and $d=2$ the particles with opposite spin interact via a Dirac delta interaction. We show that the properties of this continuum limit can be put in correspondence with those derived applying the Trap-Size scaling (TSS) formalism to the confined Hubbard…
In this paper we consider a recent experiment [Kang et al. PRA 95 053638 (2017)] in which an antiferromagnetic spin-1 condensate of 23Na atoms was quenched from the easy-axis polar phase into the easy-plane polar phase. We simulate the phase transition dynamics using a classical field method with noisy initial conditions and find good agreement to the experimental observations. We analyse the late-time dynamics in terms of phase ordering using the nematic order parameter that we have developed in earlier work [Symes et al. PRA 96, 013602 (2017)]. We show that these experiments are able to expl…
We study the spreading of correlations in space and time after a quantum quench in the Bose Hubbard model. We derive equations of motion for the single-particle Green's function within the contour-time formalism, allowing us to study dynamics in the strong coupling regime. We discuss the numerical solutions of these equations and calculate the single-particle density matrix for quenches in the Mott phase. We demonstrate light-cone like spreading of correlations in the Mott phase in one, two, and three dimensions and calculate propagation velocities in each dimension.
Considering a two-dimensional Bose-Hubbard spinor lattice with weak nearest neighbour interactions and no particle transfer between sites, we theoretically study the transport of energy from one initially excited dimer, to the rest of the lattice. Beyond a critical interaction strength, low energy on-site excitations are quickly dispersed throughout the array, while stronger excitations are self trapped, resulting in localized energy breathers and solitons. These structures are quasiparticle analogues to the discrete 2D solitons in photonic lattices. Full many-body simulations additionally dem…
Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field (Atala et al., Nature Physics \textbf{10}, 588 (2014)), we study the dynamics of bosons on a tight-binding two-leg ladder with complex hopping amplitudes. This system displays a quantum phase transition even without interactions. We study the non-equilibrium dynamics without and with interactions, in the presence of a harmonic trapping potential. In particular we consider dynamics induced by quenches of the trapping potential and of the magnitude of the rung hopping. We p…
Dynamically generated correlations in a trapped bosonic gas via frequency quenches
Raman Research Institute（拉曼研究所）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay（巴黎南大学萨克雷大学法国国家科学研究中心理论与统计物理实验室）
Prethermal cooling with many-body quantum quenches
Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息物质研究所）；Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；Institute for Theoretical Physics, Georg-August-Universität Göttingen（哥廷根大学理论物理研究所）
We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|ψ(0)\rangle=|\cdots 2020\cdots \rangle$ in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the the hopping energy. We d…
We study interaction quenches of the Fermi-Hubbard model initiated from various high-temperature and high-energy states, motivated by cold atom experiments, which currently operate above the ordering temperature(s). We analytically calculate the dynamics for quenches from these initial states, which are often strongly-interacting, to the non-interacting limit. Even for high-temperature uncorrelated initial states, transient connected correlations develop. These correlations share many features for all considered initial states. We observe light-cone spreading of intertwined spin and density co…
BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory
Charles University（查理大学）；São Paulo State University (UNESP)（圣保罗州立大学）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）
Thermodynamics of the three-dimensional Hubbard model: Implications for cooling cold atomic gases in optical lattices
本文对三维费米子哈伯德模型的热力学性质进行了全面的研究，并将其应用于受光晶格和囚禁势约束的冷费米子原子。我们的研究集中在当前实验感兴趣的温度范围内。我们采用两种理论方法-动态平均场论和高温系列-和执行比较基准，以界定各自的有效性范围。特别注意的是，致力于了解这个系统的热力学性质对冷却的影响。考虑到非均匀晶格中的局域占位分布函数，我们证明了，在绝热演化下，任何可观测的变化（例如，温度）可以方便地分解成两个不同的贡献。第一个贡献是由于演化过程中陷阱中原子的重新分布，而第二个贡献来自于可观测的内在变化。最后，我们提供了J. - S. Bernier等人，Phys. Rev. A 79，061601（2009）通过将该方法应用于理想化模型来计算。
We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate time-dependent observables such as the overlap between initial and final states and the expectation value of the separation between the two atoms. In the case where the interaction is quenched from the non-interacting regime to the strongly interacting regime, or vice versa, we are able to obtain analytic results. Examining the overlap between the initial a…
Comparative study of quantum dynamics of a few bosons in a one-dimensional split hard-wall trap: exact results versus Bose-Hubbard-model approximations
The formation of an equilibrium quantum state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of non-equilibrium many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously-generated defects, whose emergence obeys a universal scaling law with the quench duration. Much less is known about the ensuing re-equilibrating or "coarse-graining" stage, which is governed by the evolution and interactions of such defects under system-specific and external constr…
Observations of center of mass dynamics offer a straightforward method to identify strongly interacting quantum phases of atoms placed in optical lattices. We theoretically study the dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time scale mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results…
We probe the transition between superfluid and Bose glass phases using quantum quenches of disorder in an ultracold atomic lattice gas that realizes the disordered Bose-Hubbard model. Measurements of excitations generated by the quench exhibit threshold behavior in the disorder strength indicative of a phase transition. Ab-initio quantum Monte Carlo simulations confirm that the appearance of excitations coincides with the equilibrium superfluid--Bose-glass phase boundary at different lattice potential depths. By varying the quench time, we demonstrate the disappearance of an adiabatic timescal…
Quantum degenerate gases trapped in optical lattices are ideal testbeds for fundamental physics because these systems are tunable, well characterized, and isolated from the environment. Controlled disorder can be introduced to explore suppression of quantum diffusion in the absence of conventional dephasing mechanisms such as phonons, which are unavoidable in experiments on electronic solids. Recent experiments use transport of degenerate Fermi gases in optical lattices (Kondov et al. Phys. Rev. Lett. 114, 083002 (2015)) to probe a particularly extreme regime of strong interaction in what can …
Leibniz University Hannover（汉诺威莱布尼茨大学）；Université Paris-Saclay（巴黎萨克雷大学）；Ulm University（乌尔姆大学）；German Aerospace Center (DLR)（德国航空航天中心）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Bates College（贝茨学院）
We address the effects of quenched disorder averaging in the time-evolution of systems of ultracold atoms in optical lattices in the presence of noise, imposed by of an environment. For bosonic systems governed by the Bose-Hubbard Hamiltonian, we quantify the response of disorder in Hamiltonian parameters in terms of physical observables, including bipartite entanglement in the ground state and report the existence of disorder-induced enhancement in weakly interacting cases. For systems of two-species fermions described by the Fermi-Hubbard Hamiltonian, we find similar results. In both cases, …
We study the expansion dynamics of harmonically trapped bosons in a two-dimensional lattice within the extended Bose-Hubbard model. We evaluate the dynamics of the system following a sudden removal of the confining potential, starting with a cloud mostly in n = 1 Mott state. We show that the nearest neighbour interactions have a strong influence on the dynamics of ultracold bosons on an optical lattice. Also we conclude that validity of the widely used contact potential approximation is questionable in the presence of Feschbach resonances.
We introduce a one-dimensional (1D) spatially inhomogeneous Bose-Hubbard model (BHM) with the strength of the onsite repulsive interactions growing, with the discrete coordinate $z_{j}$, as $|z_{j}|^{α}$ with $α>0$. Recently, the analysis of the mean-field (MF) counterpart of this system has demonstrated self-trapping of robust unstaggered discrete solitons, under condition $α>1$. Using the numerically implemented method of the density matrix renormalization group (DMRG), we demonstrate that, in a certain range of interaction, the BHM also self-traps, in the ground state, into a soliton-like c…
We study the spontaneous formation of defects in the order parameter of a trapped ultracold bosonic gas while crossing the critical temperature for Bose-Einstein Condensation (BEC) at different rates. The system has the shape of an elongated ellipsoid, whose transverse width can be varied to explore dimensionality effects. For slow enough temperature quenches we find a power-law scaling of the average defect number with the quench rate, as predicted by the Kibble-Zurek mechanism. A breakdown of such a scaling is found for fast quenches, leading to a saturation of the average defect number. We …
We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with tra…
We apply Quantum Monte Carlo technique to analyze the non equlibrium state of a trapped 1d Bose gas just after the quenching of the confining potential. As a matter of fact we solve the time dependent Schroedinger equation for the system of one-dimensional bosons interacting via delta potential in an infinite square well (namely Lieb-Liniger model) using Feynman-Kac path integral Monte Carlo technique. These 1d systems are extremely interesting and worth investigating in the context of non-equilibrium dynamics of interacting many body systems. Even though the systems can be realized experiment…
The question of how the low-energy properties of disordered quantum systems may be connected to exotic localization phenomena at high energy is a key open question in the context of quantum glasses and many-body localization. In arXiv:2105.05774 we have shown that key features of the excitation spectrum of a disordered system can be efficiently probed from out-of-equilibrium dynamics following a quantum quench, providing distinctive signatures of the various phases. Here, we extend this work by providing a more in-depth study of the behavior of the quench spectral functions associated to diffe…
