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arXiv:2112.05590 · Physical Review Letters

Universal Early Coarsening of Quenched Bose Gases

Junhong Goo, Yangheon Lee, Younghoon Lim, Dalmin Bae, Tenzin Rabga, Yong-il Shin

Published Apr 1, 2022• 19 citations
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Abstract

We investigate the early coarsening dynamics of an atomic Bose gas quenched into a superfluid phase. Using a two-step quench protocol, we independently control the two cooling rates during and after passing through the critical region, respectively, and measure the number of quantum vortices spontaneously created in the system. The latter cooling rate regulates the temperature during the condensate growth, consequently controlling the early coarsening dynamics in the defect formation. We find that the defect number shows a scaling behavior with the latter cooling rate regardless of the initial cooling rate, indicating universal coarsening dynamics in the early stage of condensate growth. Our results demonstrate that early coarsening not only reduces the defect density, but also affects its scaling with the quench rate, which is beyond the Kibble-Zurek mechanism.

DOI
10.1103/physrevlett.128.135701

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We investigate the early coarsening dynamics of an atomic Bose gas quenched into a superfluid phase. Using a two-step quench protocol, we independently control the two cooling rates during and after passing through the critical region, respectively, and measure the number of quantum vortices spontaneously created in the system. The latter cooling rate regulates the temperature during the condensate growth, consequently controlling the early coarsening dynamics in the defect formation. We find that the defect number shows a scaling behavior with the latter cooling rate regardless of the initial cooling rate, indicating universal coarsening dynamics in the early stage of condensate growth. Our results demonstrate that early coarsening not only reduces the defect density, but also affects its scaling with the quench rate, which is beyond the Kibble-Zurek mechanism.
We investigate the saturation of defect density in an atomic Bose gas rapidly cooled into a superfluid phase. The number of quantum vortices, which are spontaneously created in the quenched gas, exhibits a Poissonian distribution not only for a slow quench in the Kibble-Zurek (KZ) scaling regime but also for a fast quench, in which case the mean vortex number is saturated. This shows that the saturation is not caused by destructive vortex collisions, but by the early-time coarsening in an emerging condensate, which is further supported by the observation that the condensate growth lags the quenching in the saturation regime. Our results demonstrate that the defect saturation is an effect beyond the KZ mechanism, opening a path for studying critical phase transition dynamics using the defect number distribution.
Phase transitions abound in the physical world, from the subatomic length scales of quark condensation to the decoupling forces in the early universe. In the Bose-Einstein condensation phase transition, a gas of trapped bosonic atoms is cooled to a critical temperature. Below this temperature, a macroscopic number of atoms suddenly starts to occupy a single quantum state; these atoms comprise the Bose-Einstein condensate (BEC). The dynamics of the BEC phase transition are the focus of this dissertation and the experiments described here have provided new information on the details of BEC formation. New theoretical developments are proving to be valuable tools for describing BEC phase transition dynamics and interpreting new experimental results. With their amenability to optical manipulation and probing along with the advent of new microscopic theories, BECs provide an important new avenue for gaining insight into the universal dynamics of phase transitions in general.Spontaneous symmetry breaking in the system's order parameter may be one result of cooling through a phase transition. A potential consequence of this is the spontaneous formation of topological defects, which in a BEC appear as vortices. We experimentally observed and characterized the spontaneous formation of vortices during BEC growth. We attribute vortex creation to coherence length limitations during the initial stages of the phase transition. Parallel to these experimental observations, theory collaborators have used the Stochastic Gross-Pitaevski Equation formalism to simulate the growth of a condensate from a thermal cloud. The experimental and theoretical statistical results of the spontaneous formation of vortex cores during the growth of the condensate are in good quantitative agreement with one another, supporting our understanding of the dynamics of the phase transition. We believe that our results are also qualitatively consistent with the Kibble-Zurek mechanism, a universal model for topological defect formation.Ultimately, our understanding of the dynamics of the BEC phase transition may lead to a broader understanding of phase transitions in general, and provide new insight into the development of coherence in numerous systems.
We experimentally investigate the evolution of spatial phase correlations in a rapidly quenched inhomogeneous Bose gas of rubidium using off-resonant matter-wave interferometry. We measure the phase coherence length ℓ of the sample and directly probe its increase during the early stage of condensate growth before vortices are formed. Once the vortices are formed stably in the quenched condensate, the measured value of ℓ is shown to be linearly proportional to the mean distance between the vortex. These results confirm the presence of phase coarsening prior to vortex formation, which is crucial for a quantitative understanding of the resultant defect density in samples undergoing critical phase transitions. Published by the American Physical Society 2024
We study the vortex nucleation dynamics in inhomogeneous atomic Bose gases quenched into a superfluid phase and investigate the dependence of the Kibble-Zurek (KZ) scaling exponent on the underlying trap configuration. For samples in a number of different inhomogeneous traps, we observe the characteristic power-law scaling of the vortex number with the thermal quench rate, as well as an enhanced vortex suppression in the outer regions with lower particle density, in agreement with the causality effect as encapsulated in the inhomogeneous Kibble-Zurek mechanism (IKZM). However, the measured KZ scaling exponents show significant differences from the theoretical estimates, and furthermore their trends as a function of the underlying trap configuration deviate from the IKZM prediction. We also investigate the early-time coarsening effect using a two-step quench protocol as proposed in a recent study and show that the interpretation of the measurement results without including the causality effect might be misleading. This paper provides a comprehensive study of vortex formation dynamics in quenched Bose gases confined in inhomogeneous trapping potentials and calls for a refined theoretical framework for quantitative understanding of the phase transition and defect formation processes in such inhomogeneous systems.
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 emergence of order from an initially uncorrelated state across a phase transition is a central problem in quantum many-body physics, particularly in multicomponent systems where interactions between components lead to rich nonequilibrium dynamics. While defect formation is known to follow universal scaling laws, prior studies have focused mainly on defect density, leaving their spatial organization largely unexplored. Here we show that gradually tuning the chemical potential in a two-dimensional binary Bose gas drives condensation into either a miscible or immiscible phase. In the immiscible regime, domains form whose number, size, and boundary length obey Kibble-Zurek (KZ) scaling and evolve self-similarly. In the miscible regime, vortices emerge with KZ scaling. In both cases, the spatial distribution of vortices and domains is well described by a Poisson point process with KZ-determined density. These results reveal universal features of far-from-equilibrium dynamics and provide a framework to characterize stochastic geometry in multicomponent quantum systems. Driving a binary quantum gas mixture through a continuous phase transition can create domains or vortices, depending on the interaction regime. Here, the authors show that their formation universally follow Kibble-Zurek scaling and Poisson spatial statistics with predictions testable in ultracold atom experiments.