Dynamical phase transition in Floquet optical bistable systems: An approach from finite-size quantum systems

TL;DR

This paper investigates a dynamical phase transition in Floquet-driven optical bistable systems, revealing finite-size effects and spinodal phenomena through the analysis of a Floquet dissipative map.

Contribution

It introduces a systematic approach using Floquet dissipative maps to study dynamical phase transitions in finite quantum systems under periodic driving.

Findings

Decay rate behavior changes across the transition

Finite-size scaling reveals spinodal phenomena

Single limit cycle persists in finite systems due to tunneling

Abstract

We study a dynamical phase transition in optical bistable systems subject to a time-periodic driving field. The phase transition occurs in the structure of limit cycle as a function of the frequency of the driving field. In the thermodynamic limit, a single limit cycle is divided into two separated limit cycles at the transition point. In finite-size systems, however, there is always a single limit cycle due to the quantum tunneling effect. We use a Floquet dissipative map, which is a time-evolution operator over one period in a dynamics given by a quantum master equation, and discuss the decay rate of relaxation dynamics into the limit cycle based on the dominant eigenvalue of the map. We found that the decay rate exhibits qualitatively different system-size dependence before and after the phase transition, and it shows a finite-size scaling of spinodal phenomena around the transition point. The present work provides a systematic way of studying dynamical phase transition observed in time-periodically driven open systems in terms of the Floquet dissipative map.