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本文基于量子开放系统理论，研究退相干效应在广义Dicke模型中的作用。通过构建平均场近似与二阶累积展开的方法，揭示系统发生超辐射相变的临界条件及其动力学特征。研究发现，与标准Dicke模型相同，广义Dicke模型在纯退相位环境下无法维持超辐射稳态，而通过引入自发辐射可以恢复超辐射态，阐明了退相干机制对量子相变的双重调控作用。更深入的分析表明，当旋波与反旋波相互作用不相等且光子耗散率较低的特定参数条件下，系统会随着退相干速率增加呈现超辐射相-正常相-超辐射相-正常相的再入相变现象，展现出量子耗散系统特有的多稳态竞争行为。
Abstract：Objective. Decoherence effects, ubiquitous in open quantum systems, arise from system-environment interactions and manifest primarily through two distinct channels: dephase and decay. While dephase disrupts quantum superposition without altering energy populations, decay directly modifies the energy-level occupation statistics. Prior studies have demonstrated that in the standard Dicke model, increasing decoherence rates generally suppress collective atomic correlations and prevent the onset of superradiant phase transitions, with the superradiant phase being entirely eradicated under pure dephase conditions. Given the enriched light-atom interaction configurations inherent to the generalized Dicke mode, it becomes imperative to systematically clarify the role of decoherence effects in such extended frameworks.Methods. In this work, we employ a combined methodology of mean-field approximation and second-order cumulant expansion to investigate the role of decoherence in the generalized Dicke model. Under the thermodynamic limit of atomic population, where dynamical correlations between the optical and matter fields become negligible, the mean-field approximation serves as an effective framework for characterizing both the system's dynamical evolution and steady-state properties. However, its validity becomes questionable in finite-N systems due to non-negligible quantum fluctuation effects. To systematically incorporate fluctuation corrections, we implement a second-order cumulant expansion of the dynamical equations, explicitly accounting for statistical correlations between physical observables.Results and discussions. Using the above two methods, we systematically analyze the role of decoherence in the generalized Dicke model and obtain the phase diagram of the system with different parameters. We find that, like the standard Dicke model, the steady state of the generalized Dicke model is always normal in the pure dephase condition, and the introduction of spin decay is able to restore the superradiant state, revealing the dual regulatory role of the decoherence mechanism on the quantum phase transition. A deeper analysis shows that under the characteristic parameters with unequal interaction between rotating-wave and counter-rotating-wave and low photon dissipation rate, the system can experience the reentry phase transition of superradiantnormal-superradiant-normal phase as the decoherence rate increases.Conclusions. We investigate the role of decoherence effects in the generalized Dicke model. By constructing a theoretical framework integrating mean-field approximation and second-order cumulant expansion, we systematically reveal the critical conditions and dynamical features of the superradiant phase transition. The results demonstrate that, consistent with the standard Dicke model, the generalized Dicke model fails to sustain a superradiant steady state under pure dephase condition, while the introduction of spin decay can reactivate the superradiant phase. Further analysis uncovers a striking reentrant phase transition sequence—superradiant phase → normal phase → superradiant phase → normal phase—emerging under specific parameter conditions characterized by asymmetric rotating-wave and counter-rotating-wave interactions combined with low photon dissipation rates. This phenomenon manifests the multistable competitive dynamics unique to quantum dissipative systems.
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基本信息:
中图分类号:O431.2
引用信息:
[1]刘治东,樊景涛,贾锁堂.广义Dicke模型中自旋退相干诱导的再入相变[J].量子光学学报,2025,31(04):23-35.
基金信息:
国家自然科学基金项目（12174233）; “1331工程”提质增效建设计划项目（晋教科[2021]4号）