Lindblad Master Equations for Quantum Systems Coupled to Dissipative Bosonic Modes
Lindblad Master Equations for Quantum Systems Coupled to Dissipative Bosonic Modes
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DOI：
10.1103/physrevlett.129.063601
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发表时间：
2022-08-02
影响因子：
8.6
通讯作者：
Betzholz, Ralf
中科院分区：
文献类型：
--
作者：
Jaeger, Simon B.;Schmit, Tom;Betzholz, Ralf
我们提出了一个一般的方法来获得Lindblad主方程的子系统，其动力学耦合到耗散玻色子模式。推导依赖于一个Schriffl-Wolff变换，它使我们能够消除玻色子自由度后，自洽地确定其状态作为耦合量子系统的函数。我们将这种形式主义的耗散迪凯模型，并推导出Lindblad主方程的原子自旋，其中包括介导的玻色子模式的相干和耗散的相互作用。这个主方程准确地预测了迪凯相变，并给出了正确的稳态。此外，我们比较动力学使用精确对角化和数值积分的主方程的半经典轨迹的预测。最后，我们通过研究NOON态的弛豫来测试我们的形式主义的性能，并表明动态捕获量子亚稳态。
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.