Lindblad Master Equations for Quantum Systems Coupled to Dissipative Bosonic Modes,Physical Review Letters

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Lindblad Master Equations for Quantum Systems Coupled to Dissipative Bosonic Modes
Physical Review Letters ( IF 8.1 ) Pub Date : 2022-08-02 , DOI: 10.1103/physrevlett.129.063601
Simon B Jäger _{1,

2} , Tom Schmit ₃ , Giovanna Morigi ₃ , Murray J Holland ₂ , Ralf Betzholz _{4,

5}

Affiliation

We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows us to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke phase transition and gives the correct steady state. In addition, we compare the dynamics using exact diagonalization and numerical integration of the master equation with the predictions of semiclassical trajectories. We finally test the performance of our formalism by studying the relaxation of a NOON state and show that the dynamics captures quantum metastability.

中文翻译：

耦合耗散玻色子模式的量子系统 Lindblad 主方程

我们提出了一种通用方法来推导动力学耦合到耗散玻色子模式的子系统的 Lindblad 主方程。推导依赖于 Schrieffer-Wolff 变换，它允许我们在自洽地确定它们的状态作为耦合量子系统的函数之后消除玻色子自由度。我们将这种形式应用于耗散 Dicke 模型，并推导出原子自旋的 Lindblad 主方程，其中包括由玻色子模式介导的相干和耗散相互作用。这个主方程准确地预测了 Dicke 相变并给出了正确的稳态。此外，我们将使用主方程的精确对角化和数值积分的动力学与半经典轨迹的预测进行比较。

更新日期：2022-08-02

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