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arXiv:2205.07551 · Physical Review A

Dynamical emergence of a Kosterlitz-Thouless transition in a disordered Bose gas following a quench

Thibault Scoquart, Dominique Delande, Nicolas Cherroret

Published Aug 11, 2022• 5 citations
arXivHTMLPDF

Abstract

Following a quantum quench, two-dimensional Bose gases dynamically evolve toward a thermal state exhibiting a Kosterlitz-Thouless transition. Here the authors theoretically characterize this nonequilibrium phenomenon in the presence of spatial disorder, a scenario that could be realized either in ultracold atomic gases or in nonlinear paraxial optics.

DOI
10.1103/physreva.106.l021301

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Following a quantum quench, two-dimensional Bose gases dynamically evolve toward a thermal state exhibiting a Kosterlitz-Thouless transition. Here the authors theoretically characterize this nonequilibrium phenomenon in the presence of spatial disorder, a scenario that could be realized either in ultracold atomic gases or in nonlinear paraxial optics.
The quenched dynamics of an ultracold homogeneous atomic two-dimensional Bose gas subjected to periodic quenches across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition are discussed.Specifically, we address the effect of periodic cycling of the effective atomic interaction strength between a thermal disordered state above and a highly ordered state below the critical BKT interaction strength, by means of numerical simulations of the stochastic projected Gross-Pitaevskii equation.Probing the emerging dynamics as a function of the frequency of sinusoidal driving from low to high frequencies reveals diverse dynamical features, including phase-lagged quasiadiabatic reversible condensate formation, resonant excitation consistent with an intrinsic system relaxation timescale, and the gradual establishment of dynamically recurring or time-averaged nonequilibrium states with enhanced coherence, which are neither condensed nor thermal.Our study paves the way for experimental observation of such driven nonequilibrium ultracold superfluid states.
We study the dynamics of a two-dimensional Bose gas after an instantaneous quench of an initially ultracold thermal atomic gas across the Berezinskii-Kosterlitz-Thouless phase transition, confirming via stochastic simulations that the system undergoes phase-ordering kinetics and fulfills the dynamical scaling hypothesis at late-time dynamics. Specifically, we find in that regime the vortex number decaying in time as $\ensuremath{\langle}{N}_{\mathrm{v}}\ensuremath{\rangle}\ensuremath{\propto}{t}^{\ensuremath{-}1}$, consistent with a dynamical critical exponent $z\ensuremath{\approx}2$ for both temperature and interaction quenches. Focusing on finite-size boxlike geometries, we demonstrate that such an observation is within current experimental reach.
This thesis manuscript is devoted to different aspects of the non-equilibrium dynamics of a moving two-dimensional ultra-cold Bose gas, under the simultaneous action of a spatially disordered potential and interactions between particles. In the absence of interactions, the momentum distribution of the gas is the sum of two well-known components: a classical, diffusive background made of particles multiply scattered by the disorder, and a coherent backscattering interference peak (CBS peak), consequence of the weak localization phenomenon. In the presence of weak interactions, mean field simulations show that these two contributions evolve in time. This evolution is described by two coupled kinetic equations, which we derive using a microscopic quantum transport theory. These predict the destruction of the CBS peak by an effective dephasing mechanism, and the thermalization of the diffusive background. As the interaction strength increases, the effects of disorder become negligible, and the dynamics of the gas resembles that of a superfluid. In this regime, the gas quickly enters a so-called "pre-thermal" state: the spatial correlations g_1 decrease algebraically and propagate along a light cone, in accordance with theoretical predictions. Finally, at long times, our simulations describe the global evolution of the system towards a thermal equilibrium state, characterized by a Kosterlitz-Thouless transition separating a normal fluid state from a superfluid state. Some properties of this phase transition, resulting from the non-equilibrium evolution in the presence of disorder, are discussed.
The understanding of nonequilibrium dynamics in many-body quantum systems is a fundamental issue in statistical physics. Experiments that probe universal properties of these systems can address such foundational questions. In this study, we report the measurement of universal dynamics triggered by a quench from the superfluid to normal phase across the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional (2D) Bose gas. We reduced the density by splitting the 2D gas in two, realizing a quench across the critical point. The subsequent relaxation dynamics were probed with matter-wave interferometry to measure the local phase fluctuations. We show that the time evolution of both the phase correlation function and vortex density obeys universal scaling laws. This conclusion is supported by classical-field simulations and interpreted by means of real-time renormalization group theory.
We propose a realistic experiment to demonstrate a dynamic Kosterlitz-Thouless transition in ultracold atomic gases in two dimensions. With a numerical implementation of the truncated Wigner approximation we simulate the time evolution of several correlation functions, which can be measured via matter wave interference. We demonstrate that the relaxational dynamics is well described by a real-time renormalization-group approach and argue that these experiments can guide the development of a theoretical framework for the understanding of critical dynamics.
Thermal fluctuations, the microscopic fluctuations of things due to their temperature, counteract order in many-body systems. Thermal fluctuations often lead to high-temperature disordered phases and low-temperature ordered ones. In lower dimensions, thermal fluctuations are relatively stronger with two-dimensional materials being just on the brink of thermal fluctuations destroying their order. Twodimensional materials therefore display unique behaviour, for example undergoing a superfluid phase transition driven by point-like topological defects. In this work, we realise two-dimensional bosonic quantum gases of the isotope Rb-87 in precisely controlled potentials to study how quantum-tunnelling and spatially disordered potentials affect the phases of matter they form. We also present a new scheme for cooling quantum gases directly in the finely tuned radiofrequency-dressed traps confining the gases in our experiments. To study tunnel-coupled gases, this work utilises a novel method to read out information from bilayer quantum gas experiments by analysing noise patterns arising from interference effects. We find that quantum-tunnelling between the two layers in a bilayer system can cause both layers to remain superfluid at higher temperatures than without quantum tunnelling. We compare our results to predictions using renormalisation-group theory and numerical simulations. We experimentally observe the predicted double-layer superfluid phase, a novel phase where the U(1) symmetry of the relative phase is broken and relative excitations are suppressed. Separately, we investigate the topological Berezinskii-Kosterlitz-Thouless phase transition in disordered two-dimensional Bose gases. We find that such systems can be driven across this phase transition by increasing the strength of an applied disordered potential. We experimentally map out the phase diagram for a continuous 2D Bose gas in the presence of disorder, which has not previously been carried out to the best of our knowledge. We find that the presence of disorder increases the number of topological defects at a given temperature while reducing the rate at which the number of defects increases with temperature. The experimental results for 2D disordered Bose gases are in qualitative agreement with numerical simulations for the parameter regime studied.