Nonequilibrium Phase Transitions in Rydberg Atom Gases with Collective Dissipation*

This work investigates nonequilibrium phase transitions in a Rydberg atomic system with collective dissipation. ^[15,16] By combining mean-field theory ^[26] and Liouvillian spectral analysis ^{[23-27,29,30]}, we reveal novel nonequilibrium phases induced by collective dissipation and compare the results from both approaches. Our findings demonstrate that collective dissipation not only generates interatomic correlations but also sustains persistent periodic oscillations ^[18,32] and a distinctive form of bistability, where the system may either evolve to a stationary state or sustain self-consistent oscillatory dynamics. This study highlights the rich nonequilibrium phenomena present in quantum many-body systems and provides an extensible spectral framework for exploring dissipative phases in Rydberg and related systems.<br>Recent experiments ^[10-13] have reported persistent oscillations in thermal Rydberg atomic ensembles, yet a theoretical consensus on their origin remains elusive. Motivated by these observations, we introduce a collective dissipation mechanism and employ both mean-field approximations and the Liouvillian spectrum method to systematically explore nonequilibrium phase transitions. Our results show that collective dissipation effectively induces interatomic correlations and sustains persistent periodic oscillations, whereas under the same parameters, independent dissipation leads the system to relax to a stationary state. Furthermore, the nonlinear effects arising from collective dissipation give rise to a novel type of bistability, in which the system can either converge to a fixed point or maintain self-consistent periodic oscillations. This mechanism is distinctly different from conventional bistability induced by Rydberg interactions, which involves two stationary states. Moreover, the Liouvillian spectral method, based on the quantum master equation, successfully captures features of nonequilibrium phase transitions even in finite-dimensional systems, and the results agree well with those obtained from mean-field approximation in the thermodynamic limit.<br>Our work not only provides a theoretical explanation for recently observed oscillatory phenomena but also predicts novel bistable states and rich nonequilibrium phase structures. It further verifies the effectiveness of the Liouvillian spectral approach in studying quantum many-body systems, contributing significantly to the understanding of microscopic mechanisms underlying nonequilibrium phase transitions.