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arXiv:2310.05437

Observation of universal Kibble-Zurek scaling in an atomic Fermi superfluid

Kyu‐Hwan Lee, Sol Kim, Taehoon Kim, Yong-il Shin

Published Oct 9, 2023• 1 citation
arXivHTMLPDF

Abstract

Half a century ago, T. Kibble proposed a scenario for topological defect formation from symmetry breaking during the expansion of the early Universe. W. Zurek later crystallized the concept to superfluid helium, predicting a power-law relation between the number of quantum vortices and the rate at which the system passes through the lambda transition. Here, we report the observation of Kibble-Zurek scaling in a homogeneous, strongly interacting Fermi gas undergoing a superfluid phase transition. We investigate the superfluid transition using two distinct control parameters: temperature and interaction strength. The microscopic physics of condensate formation is markedly different for the two quench parameters, signaled by their two orders of magnitude difference in the condensate formation timescale. However, regardless of the thermodynamic direction in which the system passes through a phase transition, the Kibble-Zurek exponent is identically observed to be about 0.68 and shows good agreement with theoretical predictions that describe superfluid phase transitions. This work demonstrates the gedanken experiment Zurek proposed for liquid helium that shares the same universality class with strongly interacting Fermi gases.

DOI
10.48550/arxiv.2310.05437

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Half a century ago, T. Kibble proposed a scenario for topological defect formation from symmetry breaking during the expansion of the early Universe. W. Zurek later crystallized the concept to superfluid helium, predicting a power-law relation between the number of quantum vortices and the rate at which the system passes through the lambda transition. Here, we report the observation of Kibble-Zurek scaling in a homogeneous, strongly interacting Fermi gas undergoing a superfluid phase transition. We investigate the superfluid transition using two distinct control parameters: temperature and interaction strength. The microscopic physics of condensate formation is markedly different for the two quench parameters, signaled by their two orders of magnitude difference in the condensate formation timescale. However, regardless of the thermodynamic direction in which the system passes through a phase transition, the Kibble-Zurek exponent is identically observed to be about 0.68 and shows good agreement with theoretical predictions that describe superfluid phase transitions. This work demonstrates the gedanken experiment Zurek proposed for liquid helium that shares the same universality class with strongly interacting Fermi gases.
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.
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.
The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect density as a function of the quench time. We focus on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter. These predictions are verified in several paradigmatic scenarios in both the classical and quantum domains.
Kibble-Zurek theory models the dynamics of spontaneous symmetry breaking, which plays an important role in a wide variety of physical contexts, ranging from cosmology to superconductors. We explored these dynamics in a homogeneous system by thermally quenching an atomic gas with short-range interactions through the Bose-Einstein phase transition. Using homodyne matter-wave interferometry to measure first-order correlation functions, we verified the central quantitative prediction of the Kibble-Zurek theory, namely the homogeneous-system power-law scaling of the coherence length with the quench rate. Moreover, we directly confirmed its underlying hypothesis, the freezing of the correlation length near the transition. Our measurements agree with a beyond-mean-field theory and support the expectation that the dynamical critical exponent for this universality class is z = 3/2.
When a system is swept through a quantum critical point, the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp timescale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a noncritical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality. © 2026 authors. Published by the American Physical Society.
When a second-order phase transition is crossed at finite speed, domains with independent order parameters can appear in the system, with the consequent formation of defects at the domain boundaries. The Kibble-Zurek theory provides a description for this universal phenomenon, which applies to many different systems in nature, and it predicts a power-law dependence of the defect density on the quench rate. This thesis reports on the results of the experimental study of the Kibble-Zurek mechanism in elongated Bose-Einstein condensates of atomic sodium gases, following the observations on the spontaneous formation of defects after temperature quenches across the BEC transition. The power-law scaling of the defect number with the quench speed was observed and characterized for the first time in ultracold gases. The characterization of the density and phase profiles of the defects allowed their identification as solitonic vortices, representing the first direct experimental evidence for this kind of long living excitation, which sets a link between solitons and vortices. The measurements reported in this thesis provide a novel approach to the study of the critical phenomena happening at phase transitions, and introduce to the possibility of exploring the turbulent dynamics of quenched systems through the spontaneous production of solitonic vortices.