Ergodic-nonergodic transition with cold spinless fermions in a cavity

Abstract

We consider a one-dimensional spinless Fermi gas coupled to an optical cavity. Using exact diagonalization, we numerically study the model and find that the system can undergo the ergodic-nonergodic transition, which depends on the cavity-fermion coupling strength and the fermion-fermion interacting strength. We demonstrate that the cavity-fermion coupling strength, which breaks the integrability of the system, can lead to the ergodic phase in the strong-interaction regime. It is shown that the ergodic-nonergodic transition is characterized by static statistical methods, including level-spacing distribution and the average ratio of consecutive level spacing. To experimentally observe the transition, we also study the dynamic properties of the system, including the out-of-time-ordered correlator, the time evolution of the occupancy imbalance, and the survival probability, which manifest different behaviors in different phases. In addition, we find that even though the system contains long-range interactions, it does not exhibit information fast scrambling whether in the ergodic phase or the nonergodic phase.