Jäger Simon B, Schmit Tom, Morigi Giovanna, Holland Murray J, Betzholz Ralf
Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, D-67663, Kaiserslautern, Germany.
JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA.
Phys Rev Lett. 2022 Aug 5;129(6):063601. doi: 10.1103/PhysRevLett.129.063601.
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.
我们提出了一种通用方法，用于推导与耗散玻色子模式耦合的子系统的林德布拉德主方程。该推导依赖于施里弗-沃尔夫变换，这使我们能够在自洽地确定玻色子自由度作为耦合量子系统函数的状态后消除这些自由度。我们将这种形式体系应用于耗散狄克模型，并推导了原子自旋的林德布拉德主方程，其中包括由玻色子模式介导的相干和耗散相互作用。该主方程准确地预测了狄克相变并给出了正确的稳态。此外，我们将使用精确对角化和主方程数值积分得到的动力学与半经典轨迹的预测进行了比较。我们最后通过研究NOON态的弛豫来测试我们形式体系的性能，并表明该动力学捕捉到了量子亚稳性。
