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arXiv:2507.18349 · Physical Review Letters

Observation of Kibble-Zurek Behavior across Topological Transitions of a Chern Band in Ultracold Atoms

Huan Yuan, Chang-Rui Yi, Jia-Yu Guo, Xiang-Can Cheng, Rui-Heng Jiao, Jinyi Zhang, Shuai Chen, Jian-Wei Pan

Published Jul 14, 2025• 3 citations
arXivHTMLPDF

Abstract

The Kibble-Zurek (KZ) mechanism renders a theoretical framework for elucidating the formation of topological defects across continuous phase transitions. Nevertheless, it is not immediately clear whether the KZ mechanism applies to topological phase transitions. The direct experimental study for such a topic is hindered by quenching a certain parameter over orders of magnitude in topological materials. Instead, we investigate the KZ behavior across topological transitions of a Chern band in two-dimensional (2D) optical Raman lattices with quantum gases. Defined as the defects, excitation density is reconstructed via measuring the spin wave functions, with which the power-law scaling of total excitation density is extracted and such scaling could be interpreted within the KZ framework. Our work has heralded the commencement of experimentally exploring the KZ mechanism of the topological phase transitions.

DOI
10.1103/5j5s-946k

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The Kibble-Zurek (KZ) mechanism renders a theoretical framework for elucidating the formation of topological defects across continuous phase transitions. Nevertheless, it is not immediately clear whether the KZ mechanism applies to topological phase transitions. The direct experimental study for such a topic is hindered by quenching a certain parameter over orders of magnitude in topological materials. Instead, we investigate the KZ behavior across topological transitions of a Chern band in two-dimensional (2D) optical Raman lattices with quantum gases. Defined as the defects, excitation density is reconstructed via measuring the spin wave functions, with which the power-law scaling of total excitation density is extracted and such scaling could be interpreted within the KZ framework. Our work has heralded the commencement of experimentally exploring the KZ mechanism of the topological phase transitions.
The Kibble-Zurek (KZ) mechanism describes the scaling behavior when driving a system across a continuous symmetry-breaking transition. Previous studies have shown that the KZ-like scaling behavior also lies in the topological transitions in the Qi-Wu-Zhang model (2D) and the Su-Schrieffer-Heeger model (1D), although symmetry breaking does not exist in these systems. Both models with linear band crossings yield $\ensuremath{\nu}\ensuremath{\simeq}1$ and $z\ensuremath{\simeq}1$. A natural question is whether different critical exponents can emerge in topological transitions beyond the linear band crossings. In this paper, we look into the KZ behavior in a topological 2D checkerboard lattice with a quadratic band crossing. We investigate from dual perspectives: momentum distribution of the Berry curvature in clean systems for simplicity, and real-space analysis of domain-like local Chern marker configurations in disordered systems, which is a more intuitive analog to conventional KZ description. In equilibrium, we find the correlation length diverges at the transition with a power $\ensuremath{\nu}\ensuremath{\simeq}1/2$. Then, by slowly quenching the system across the topological phase transition, we find that the freeze-out time tf{t}_{\mathrm{f}}tf​ and the unfrozen length scale $\ensuremath{\xi}({t}_{\mathrm{f}})$ both satisfy the KZ scaling, verifying $z\ensuremath{\simeq}2$. We subsequently explore KZ behavior in topological phase transitions with other higher-order band crossings and find the relationship between the critical exponents and the order. Our results extend the understanding of the KZ mechanism and nonequilibrium topological phase transitions.
Abstract Out-of-equilibrium phenomena are a subject of considerable interest in many fields of physics. Ultracold quantum gases, which are extremely clean, well-isolated and highly controllable systems, offer ideal platforms to investigate this topic. The recent progress in tailoring trapping potentials now allows the experimental production of homogeneous samples in custom geometries, which is a key advance for studies of the emergence of coherence in interacting quantum systems. Here we review recent experiments in which temperature quenches have been performed across the Bose–Einstein condensation phase transition in an annular geometry and in homogeneous 3D and quasi-2D gases. Combined, these experiments comprehensively explore and validate the Kibble–Zurek (KZ) scenario through complementary measurements of correlation functions and density of topological defects. They allow the measurement of KZ scaling laws, the direct confirmation of the ‘freeze-out’ hypothesis that underlies the KZ theory, and the extraction of critical exponents of the Bose–Einstein condensation transition.
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.
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.
The Kibble-Zurek mechanism predicts a universal scaling behavior of the defect production when a system is slowly quenched across a critical phase transition point. Here, we discover that the universal scaling behavior across a higher-order topological phase transition does not conform to the traditional Kibble-Zurek mechanism. To explain the anomalous scaling exponent, we develop a solvable Landau-Zener model that takes into account the role of topological edge band that dominates the phase transition. For a two-dimensional boundary-obstructed higher-order topological system, the Kibble-Zurek scaling must be modified to adopt the effective dimension of topological edge band instead of the real physical dimension. We also find that across the boundary-obstructed higher-order topological phase transition, boundary conditions can drastically modify the scaling behaviors. For comparison, we investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with physical dimension.
Abstract We study the dynamics of second-order phase transitions that may have taken place in the early universe and analyze the Kibble-Zurek (KZ) scaling as well as the formation of topological defects emerging from a quench in the one-dimensional Bose-Hubbard model. We describe the universal dynamics of the KZ mechanism (KZM) and the topological defect formation by simulating the Bose–Hubbard model at zero temperature. We study the effects of thermalization on the ground state by analyzing the transition between Mott and superfluid phases. The out-of-equilibrium dynamics induced by a quench of the hopping parameter is presented. We find a KZ scaling behaviour at zero temperature and analyze the KZ dynamics.