Nonequilibrium phases of ultracold bosons with cavity-induced dynamic gauge fields

TL;DR

This paper explores the rich nonequilibrium dynamical phases, including limit cycles and chaos, in a cavity-mediated bosonic lattice system with dynamical gauge fields, revealing connections to time crystal behavior.

Contribution

It provides a comprehensive analysis of the phase diagram and stability of a minimal dynamical flux-lattice model with cavity-induced complex tunnelings, highlighting novel nonequilibrium phases.

Findings

Identification of limit-cycle and chaotic phases

Mapping of the dynamical phase diagram and phase transitions

Connection between limit cycles and time crystals

Abstract

Gauge fields are a central concept in fundamental theories of physics, and responsible for mediating long-range interactions between elementary particles. Recently, it has been proposed that dynamical gauge fields can be naturally engineered by photons in composite, neutral quantum gas--cavity systems using suitable atom-photon interactions. Here we comprehensively investigate nonequilibrium dynamical phases appearing in a two-leg bosonic lattice model with leg-dependent, dynamical complex tunnelings mediated by cavity-assisted two-photon Raman processes. The system constitutes a minimal dynamical flux-lattice model. We study fixed points of the equations of motion and their stability, the resultant dynamical phase diagram, and the corresponding phase transitions and bifurcations. Notably, the phase diagram features a plethora of nonequilibrium dynamical phases including limit-cycle and chaotic phases. In the end, we relate regular periodic dynamics (i.e., limit-cycle phases) of the system to time crystals.