Spin fluctuations in the dissipative phase transitions of the quantum Rabi model

We investigate the dissipative phase transitions of the anisotropic quantum Rabi model with cavity decay and demonstrate that large spin fluctuations persist in the stationary state, having important consequences on the phase diagram and the critical properties. In the second-order phase transition to the superradiant phase, there is a significant suppression of the order parameter and the appearance of non-universal factors, which directly reflect the spin populations. Furthermore, upon entering a parameter regime where mean-field theory predicts a tricritical phase, we find a first-order phase transition due to the unexpected collapse of superradiance. An accurate and physically transparent description going beyond mean-field theory is established by combining exact numerical simulations, the cumulant expansion, and analytical approximations based on reduced master equations and an effective equilibrium theory. Our findings, compared to the conventional thermodynamic limit of the Dicke model, indicate a general tendency of forming extreme non-equilibrium states in the single-spin system, thus have broad implications for dissipative phase transitions of few-body systems.