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 constraints. In this work we perform a detailed numerical characterization of the entire non-equilibrium process, addressing subtle issues in condensate growth dynamics and demonstrating the quench-induced decoupling of number and coherence growth during the re-equilibration process. Our unique visualizations not only reproduce experimental measurements in the relevant regimes, but also provide valuable information in currently experimentally-inaccessible regimes.
We address the physics of equilibration in ultracold atomic gases following a quench of the interaction parameter. We focus on the momentum distribution of the excitations, $n_{\mathbf k}$, and observe that larger ${\mathbf k}$ modes will equilibrate faster, as has been claimed in recent experimental work. We identify three time regimes. At short times $n_{\mathbf k}$ exhibits oscillations; these are damped out at intermediate times where the system appears to be in a false-equilibrium. Finally, at longer times, full equilibration occurs. This false-equilibrium is associated with the necessari…
We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of phase imprinting and localized density depletion perturbations, both of which initially are found to produce "phase walls". These planar defects are associated with a sharp gradient in the phase. Importantly they relax following a quite general sequence. Our studies, based on simulations of the complex time-dependent Ginzburg-Landau equation, address the challenge posed by these experiments: how a superfluid eventually eliminates a spatially extended…
We study the response of trapped two dimensional cold bosons to time dependent lattices. We find that in lattice ramps from 11 (superfluid, $\hbar/U_{\text{i}} = 3$ms, $\hbar/J_{\text{i}} = 45$ms) to 16 recoils (Mott, $\hbar/U_{\text{f}} = 2$ms, $\hbar/J_{\text{f}} = 130$ms) the local number fluctuations remains at their equilibrium values if ramps are slower than 3 ms. Global transport, however, is much slower (1s), especially in the presence of Mott shells. This separation of timescales has practical implications for cold atom experiments and cooling protocols.
The dynamical evolution of an inhomogeneous ultracold atomic gas quenched at different controllable rates through the Bose-Einstein condensation phase transition is studied numerically in the premise of a recent experiment in an anisotropic harmonic trap. Our findings based on the stochastic (projected) Gross-Pitaevskii equation are shown to be consistent at early times with the predictions of the homogeneous Kibble-Zurek mechanism. This is demonstrated by collapsing the early dynamical evolution of densities, spectral functions and correlation lengths for different quench rates, based on an a…
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…
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 derive a non-equilibrium finite-temperature kinetic theory for a binary mixture of two interacting atomic Bose-Einstein condensates and use it to explore the degree of hydrodynamicity attainable in realistic experimental geometries. Based on the standard separation of timescale argument of kinetic theory, the dynamics of the condensates of the multi-component system are shown to be described by dissipative Gross-Pitaevskii equations, self-consistently coupled to corresponding Quantum Boltzmann equations for the non-condensate atoms: on top of the usual mean field contributions, our scheme i…
We study the quenched dynamics of the momentum distribution of a unitary Bose gas under isotropic harmonic confinement within a time-dependent density functional approach based on our recently calculated Monte Carlo (MC) bulk equation of state. In our calculations the inter-atomic s-wave scattering length of the trapped bosons is suddenly increased to a very large value and the real-time evolution of the system is studied. Prompted by the very recent experimental data of $^{85}$Rb atoms at unitarity [Nature Phys. 10, 116 (2014)] we focus on the momentum distribution as a function of time. Our …
We explore the time evolution of two impurities in a trapped one-dimensional Bose gas that follows a change of the boson-impurity interaction. We study the induced impurity-impurity interactions and their effect on the quench dynamics. In particular, we report on the size of the impurity cloud, the impurity-impurity entanglement, and the impurity-impurity correlation function. The presented numerical simulations are based upon the variational multilayer multiconfiguration time-dependent Hartree method for bosons. To analyze and quantify induced impurity-impurity correlations, we employ an effe…
We show that a composite spin-1/2 Kondo system can be formed by coupling a superconducting quantum interference device (SQUID) to the internal hyperfine states of a trapped ultracold atomic Fermi gas. Here, the SQUID, or flux qubit, acts as an effective magnetic impurity that induces spin-flip scattering near the Fermi energies of the trapped gas. Although the ultracold gas and SQUID are at vastly different temperatures, the formation of a strongly correlated Kondo state between the two systems is found when the gas is cooled below the Kondo temperature; this temperature regime is within curre…
We study the sensitivity of coupled condensate formation dynamics on the history of initial stochastic domain formation in the context of instantaneously quenched elongated harmonically-trapped immiscible two-component atomic Bose gases. The spontaneous generation of defects in the fastest condensing component, and subsequent coarse-graining dynamics, can lead to a deep oscillating microtrap into which the other component condenses, thereby establishing a long-lived composite defect in the form of a dark-bright solitary wave. We numerically map out diverse key aspects of these competing growth…
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…
By quenching the strength of interactions in a partially condensed Bose gas we create a "super-saturated" vapor which has more thermal atoms than it can contain in equilibrium. Subsequently, the number of condensed atoms ($N_0$) grows even though the temperature ($T$) rises and the total atom number decays. We show that the non-equilibrium evolution of the system is isoenergetic and for small initial $N_0$ observe a clear separation between $T$ and $N_0$ dynamics, thus explicitly demonstrating the theoretically expected "two-step" picture of condensate growth. For increasing initial $N_0$ valu…
We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions after a quench and we find its occurrence analytically for an infinitely repulsive pair of atoms. We further show this phenomena is related to the fundamental excitations that dictate the dynamics from the spectral function. We establish a clear qualitative link between the amount of (irreversible) work performed on the system and the est…
We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases which are in good agreement with recent, independent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase imprinting tilt angle, and illustrate their dramatic effects. The former causes vor…
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions in instances of quantum simulations. This article provides an overview on the progress in understanding dynamical equilibration and thermalisation of closed quantum many-body systems out of equilibrium due to quenches, ramps and periodic driving. It also addresses topics such as the eigenstate thermalisation hypothesis, typicality, transport, many-body locali…
By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occur…
We investigate the equilibration dynamics of string order in one-dimensional quantum systems. After initializing a spin-1 chain in the Haldane phase, the time evolution of non-local correlations following a sudden quench is studied by means of matrix-product-state-based algorithms. Thermalization occurs only for scales up to a horizon growing at a well defined speed, due to the finite maximal velocity at which string correlations can propagate, related to a Lieb-Robinson bound. The persistence of string ordering at finite times is non-trivially related to symmetries of the quenched Hamiltonian…
In phase transition dynamics involving symmetry breaking, topological defects can be spontaneously created but it is suppressed in a spatially inhomogeneous system due to the spreading of the ordered phase information. We demonstrate the defect suppression effect in a trapped atomic Bose gas which is quenched into a superfluid phase. The spatial distribution of created defects is measured for various quench times and it is shown that for slower quenches, the spontaneous defect production is relatively more suppressed in the sample's outer region with higher atomic density gradient. The power-l…
Thermalization is a ubiquitous process of statistical physics, in which details of few-body observables are washed out in favor of a featureless steady state. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a uniformly increasing field -- b…
In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter, and could evolve into a "cavity glass microscope" for frustrated quantum systems out-of-equilibrium. Here we develop the non-equilibrium theory of the multimode Dicke model with quenched disorder…
