Quantum Rabi Model with Two-Photon Relaxation

TL;DR

This paper investigates a cavity-QED system with a two-level atom and a cavity mode experiencing two-photon relaxation, revealing how parity symmetry influences dynamics and steady states in open quantum systems.

Contribution

It introduces a framework for analyzing non-Hermitian dynamics with two-photon dissipation in the Rabi model, highlighting the role of parity symmetry in open quantum systems.

Findings

Parity symmetry affects excitation and relaxation dynamics.

Initial parity states lead to distinct transient behaviors.

Parity-sensitive effects occur even at weak coupling.

Abstract

We study a cavity-QED setup consisting of a two-level system coupled to a single cavity mode with two-photon relaxation. The system dynamics is modeled via a Lindblad master equation consisting of the Rabi Hamiltonian and a two-photon dissipator. We show that an even-photon relaxation preserves the $Z_2$ symmetry of the Rabi model, and provide a framework to study the corresponding non-Hermitian dynamics in the number-parity basis. We discuss the role of different terms in the two-photon dissipator and show how one can extend existing results for the closed Rabi spectrum to the open case. Furthermore, we characterize the role of the $Z_2$ symmetry in the excitation-relaxation dynamics of the system as a function of light-matter coupling. Importantly, we observe that initial states with even-odd parity manifest qualitatively distinct transient and steady state behaviors, contrary to the Hermitian dynamics that is only sensitive to whether the initial state is parity-invariant. Moreover, the parity-sensitive dynamical behavior is not a creature of ultrastrong coupling and is present even at weak coupling values.