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arXiv:1905.05263 · Physical Review A

Quench dynamics of an ultracold two-dimensional Bose gas

P. Comaron, F. Larcher, F. Dalfovo, Nick P. Proukakis

Published Sep 27, 2019• 27 citations
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Abstract

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.

DOI
10.1103/physreva.100.033618

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•Jan 1, 2016•0 citations
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⟨Nv\ensuremath⟩\ensuremath∝t\ensuremath−1\ensuremath{\langle}{N}_{\mathrm{v}}\ensuremath{\rangle}\ensuremath{\propto}{t}^{\ensuremath{-}1}\ensuremath⟨Nv​\ensuremath⟩\ensuremath∝t\ensuremath−1, consistent with a dynamical critical exponent z\ensuremath≈2z\ensuremath{\approx}2z\ensuremath≈2 for both temperature and interaction quenches. Focusing on finite-size boxlike geometries, we demonstrate that such an observation is within current experimental reach.
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 investigate the phase ordering dynamics of a uniform two-dimensional Bose gas quenched to a finite temperature in the superfluid phase. Starting from a defect-rich, far-from-equilibrium state, we model the subsequent evolution with the projected Gross-Pitaevskii equation, which conserves both energy and particle number. By tuning the initial energy, we control the effective post-quench temperature and examine its role in the equilibration dynamics. We find that the gas exhibits universal behaviour at all temperatures, evidenced by spatio-temporal scaling of correlation functions and power-law growth of the correlation length ∼t1/z\sim t^{1/z}∼t1/z, with zzz the dynamical critical exponent. We find zzz to be temperature dependent, with z≈1.5z \approx 1.5z≈1.5 for post-quench temperatures just below the Berezinskii-Kosterlitz-Thouless (BKT) transition, and z≈1.9z \approx 1.9z≈1.9 for quenches to near-zero temperature. Analysis of the Porod tail of the momentum distribution suggests a temperature-dependent competition between vortices and sound waves in the coarsening process. The two-time correlation function also exhibits universal scaling, decaying as ∼t−λ/z\sim t^{-λ/z}∼t−λ/z, with autocorrelation exponent λλλ. Near the BKT transition we obtain λ≈2λ\approx 2λ≈2, whereas λλλ is found to diverge as the effective temperature approaches zero.
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.
In this work we investigate the unique properties of ultracold Bose gases in one and two dimensions. In two dimensions, we present simulations of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using the projected Gross-Pitaevskii equation formalism. We confirm the presence of the BKT phase by observing algebraic decay in the first-order correlation function, unbinding of vortex pairs, and behaviour of the superfluid fraction. In one dimension we use a transverse Gaussian ansatz and the Lagrangian approach to derive an effective equation of motion for the one dimensional Bose gas at zero temperature.
Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.
In this thesis, we study numerically critical dynamics in the ultracold Bose gas in one and two spatial dimensions. We concentrate on two specific setups, both amenable for experimental realisation: Hamiltonian parameter quenches in a two-component Bose gas in one spatial dimension and a driven-dissipative single-component gas in two spatial \ndimensions. The setups are chosen to excite critical dynamics, either via quenches close to a quantum critical point or via nucleation of vortex defects. The goal is to identify critical scaling and universal scaling forms in the time evolution of the respective systems. The analysis for the two-component Bose gas reveals that short-time quench dynamics can be described by a universal crossover function, where the quench-induced energy appears as the relevant energy scale. For the single-component gas, we find a new universal phase of time evolution, characterised by an anomalously slow phase ordering process of vortex defects. We discuss our results in the light of concepts of prethermalisation, generalised Gibbs ensembles and non-thermal fixed points, for universal critical \nphenomena far from thermal equilibrium.