Out-of-time-order correlator in the quantum Rabi model

TL;DR

This paper studies chaos and equilibration in the quantum Rabi model, showing how out-of-time-order correlators indicate chaos in the superradiant phase and how the system equilibrates due to large effective dimension.

Contribution

It demonstrates the behavior of out-of-time-order correlators in the quantum Rabi model and links chaos signatures to the superradiant phase transition.

Findings

Out-of-time-order correlator saturates in the normal phase.

Exponential growth of correlator indicates chaos in the superradiant phase.

Large effective dimension leads to suppression of fluctuations and system equilibration.

Abstract

We investigate signatures of chaos and equilibration in the quantum Rabi model, which exhibits a quantum phase transition when the ratio of the atomic level-splitting to bosonic frequency grows to infinity. We show that out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase and reveals exponential growth in the superradiant phase which is associated with the onset of quantum chaos. Furthermore, we show that the effective time-averaged dimension of the quantum Rabi system can be large compared to the spin system size which leads to suppression of the temporal fluctuations and equilibration of the spin system.