Universal non-equilibrium dynamics in Bose condensed atomic gases undergoing spontaneous symmetry breaking

Spontaneous symmetry breaking (SSB) is a ubiquitous physical phenomenon in nature, ranging from the formation of cosmic galaxies to the generation of the vortices in superfluid, which widely occurs in cosmology, condensed matter physics, and atomic and molecular optical physics. Universal critical dynamics associated with the SSB can be described by the Kibble-Zurek mechanism (KZM), which describes the scaling of the non-adiabatic excitations when driving the system crossing the phase transition. The KZM was first described in the context of finite temperature transitions in the region of cosmology, and then extended to the condensed matter physics by Zurek. KZM was confirmed by experiments in superfluid helium, liquid crystals, both high-T-c and low-T-c superconductors and ultracold atomic gases. Due to the advantages of clean environment, robust coherence and highly controllable parameters, ultracold atomic gases become one of ideal simulation platforms for researching the universal non-equilibrium critical dynamics. In this review, we investigate the critical dynamics associated with the SSB phase transition, introducing two typical universal non-equilibrium dynamics in Bose condensed atomic gases undergoing spontaneous symmetry breaking: (1) Universal non-equilibrium dynamics induced by the gapless Higgs modes; (2) universal non-equilibrium dynamics induced by the soft phonon modes. In the first part, we investigate the universal non-equilibrium dynamics induced by the gapless Higgs modes. Considering the coupled two-component Bose-Einstein condensation (BEC), we explore its static symmetry breaking transition and its mean-field quenching dynamics. In the equilibrium transitions, the maximum probability of the full quantum states corresponds to the mean-field ground state. In the non-equilibrium dynamical transitions, as the Higgs mode vanishes at the critical point, the mean-field dynamics display critical phenomena obeying the KZM. Both the mean-field and the full quantum defect modes show damped oscillation as driving the coupling strength crossing the critical point. Furthermore, we consider the coupled two-component BEC confined in a one-dimensional optical lattice potential, and then explore its ground-state properties and real-time quenching dynamics. Through driving the system crossing from the symmetric Rabi oscillation to the broken symmetry self-trapping, the universal non-equilibrium dynamics, which is induced by the gapless Higgs mode at the critical point, will result in the generation of the domains and appearance of the phase transition delay. On the other hand, we investigate the universal non-equilibrium dynamics induced by the soft phonon modes. Here, by considering an atomic BEC ladder subjected to a synthetic magnetic field, we reveal that the spontaneous superfluidity breakdown induced by the soft phonon mode obeys the KZM. The critical exponents are extracted from the Landau critical velocity, which determines the systematic correlation length. Meanwhile, the numerical critical exponents are extracted from the universal non-equilibrium dynamics of the phase transition delay and the spontaneous vortex creation. Furthermore, we consider the universal non-equilibrium dynamics of the two-component BEC. By driving the atom-atom interaction strength crossing the critical point, the system occurs spontaneous superfluidity breakdown induced by the soft phonon mode, and the numerical simulation shows the spontaneous domain generation and its temporal delay. The studies of the universal non-equilibrium critical dynamics can not only deepen our understanding of the formation and evolution of complex structures in early universe, but also help us find out the suitable adiabatic pathway. and shorten the time for quantum state preparation and quantum control.

Automated summary

This article investigates the critical dynamics associated with spontaneous symmetry breaking (SSB) phase transition and introduces two typical universal non-equilibrium dynamics in Bose condensed atomic gases. Through experiments and numerical simulations, the important role of the Kibble-Zurek mechanism in these phase transitions is revealed.