TY - JOUR

T1 - Dynamical phase transition in Floquet optical bistable systems

T2 - An approach from finite-size quantum systems

AU - Shirai, Tatsuhiko

AU - Todo, Synge

AU - Miyashita, Seiji

N1 - Funding Information:
This research was supported by MEXT as the Exploratory Challenge on Post-K Computer project (Challenge of Basic Science-Exploring Extremes through Multi-Physics and Multi-Scale Simulations), Grants-in-Aid for Scientific Research C (Grant No. 18K03444) from MEXT of Japan, and the Elements Strategy Initiative Center for Magnetic Materials (ESICMM), Grant No. JPMXP0112101004, through MEXT. The authors also thank the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo, for the use of the facilities.

PY - 2020/1/10

Y1 - 2020/1/10

N2 - 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 a 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 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 paper provides a systematic way of studying a dynamical phase transition observed in time-periodically driven open systems in terms of the Floquet dissipative map.

AB - 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 a 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 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 paper provides a systematic way of studying a dynamical phase transition observed in time-periodically driven open systems in terms of the Floquet dissipative map.

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U2 - 10.1103/PhysRevA.101.013809

DO - 10.1103/PhysRevA.101.013809

M3 - Article

AN - SCOPUS:85078107538

VL - 101

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 013809

ER -