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arXiv:2507.07092 · Physical Review A

Non-Gaussian phase transition and cascade of instabilities in the dissipative quantum Rabi model

Mingyu Kang, Yikang Zhang, Kenneth R. Brown, Thomas Barthel

Published May 6, 2026• 2 citations
arXivHTMLPDF

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.

DOI
10.1103/q6xb-8t1j

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This study investigates phase-driven symmetry breaking leading to superradiance phase transitions in cascaded non-Hermitian quantum Rabi cavities. Non-Hermiticity is introduced via the phase coupling $\ensuremath{\varphi}$ between the atom and the optical field. In the thermodynamic limit of the quantum harmonic oscillator, we analytically derive the superradiance phase boundary, validated by observables. An unconventional quantum phase transition without a Hermitian analog arises when $|\ensuremath{\varphi}|=\frac{\ensuremath{\pi}}{4}$ or $\frac{3\ensuremath{\pi}}{4}$, where the phase boundary is uniquely determined by the cavity coupling, at J=12\mathcal{J}=\frac{1}{2}J=21​ (J\mathcal{J}J is the ratio of the cavity coupling strength JJJ to the optical field frequency ${\ensuremath{\omega}}_{p}$, and $\mathcal{J}=\frac{J}{{\ensuremath{\omega}}_{p}}$), independent of the atom-photon coupling strength ggg. For other $\ensuremath{\varphi}$, the phase boundary relies on both J\mathcal{J}J and ggg, similar to the scenario observed in Hermitian systems. Furthermore, we identify phase-driven first- and second-order superradiance phase transitions, focusing on the quantum criticality of the second-order transition by determining the critical exponents and the universality class. The feasibility of experimental realization is also discussed, aiming to inspire further studies on non-Hermitian superradiance quantum phase transitions.
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We demonstrate a novel mechanism driving complex critical phenomena in open light-atom interacting systems by investigating a parametrically amplified quantum Rabi model (QRM) subject to both single- and two-photon decay. In the classical oscillator limit, four composite phases emerge, arising from the possible normal or superradiant regimes across the upper and lower spin branches. A mean-field analysis reveals that the two-photon decay activates the intrinsic nonlinearity of the QRM. The synergy of the coherent and dissipative two-photon processes, together with the spin-boson coupling, constitutes an ``inverted" regime where superradiance emerges exclusively at weak coupling. This regime features first- and second-order superradiant DPTs separated by a tricritical point. Utilizing an adiabatic approach and the semi-classical Langevin formalism, we further study the steady-state structure beyond the mean-field level. The universality classes of the DPTs are identified, with the corresponding critical and finite-size scaling exponents derived and a scaling ansatz proposed to describe the critical behavior.