Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model

TL;DR

This paper investigates a non-Gaussian phase transition in the dissipative quantum Rabi model, revealing cascades of instabilities and a jump in qubit polarization due to oscillator dephasing, using various theoretical methods.

Contribution

It uncovers a non-Gaussian phase transition and cascade of instabilities caused by oscillator dephasing, expanding understanding of dissipative quantum phase transitions.

Findings

Identification of a non-Gaussian phase transition.

Discovery of cascade of instabilities for bosonic operators.

Observation of a jump in steady-state qubit polarization.

Abstract

The open quantum Rabi model describes a two-level system coupled to a harmonic oscillator. A Gaussian phase transition for the nonequilibrium steady states has been predicted when the bosonic mode is soft and subject to damping. We show that oscillator dephasing is a relevant perturbation, which leads to a non-Gaussian phase transition and an intriguing cascade of instabilities for $k$-th order bosonic operators, as well as a jump in the steady-state qubit polarization. For the soft-mode limit, the equations of motion form a closed hierarchy and spectral properties can be efficiently studied. To this purpose, we establish a fruitful connection to non-Hermitian Hamiltonians. The results for the phase diagram, stability boundaries, and relevant observables are based on mean-field analysis, exact diagonalization, perturbation theory, and Keldysh field theory.