We consider an open Dicke model comprising a single infinite-component vector spin and a single-mode harmonic oscillator which are connected by Jaynes–Cummings-type interaction between them. This open quantum model is referred to as the OISD (Open Infinite-component Spin Dicke) model. The algebraic structure of the OISD Liouvillian is studied in terms of superoperators acting on the space of density matrices. An explicit invertible superoperator (precisely, a completely positive trace-preserving map) is obtained that transforms the OISD Liouvillian into a sum of two independent Liouvillians, one generated by a dressed spin only, the other generated by a dressed harmonic oscillator only. The time evolution generated by the OISD Liouvillian is shown to be asymptotically equivalent to that generated by an adjusted decoupled Liouvillian with some synchronized frequencies of the spin and the harmonic oscillator. This asymptotic equivalence implies that the time evolution of the OISD model dissipates completely in the presence of any (tiny) dissipation.

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关于由无限分量向量自旋生成的开迪克型模型

我们考虑一个开放的 Dicke 模型，包括一个无限分量矢量自旋和一个单模谐振子，它们之间通过 Jaynes-Cummings 型相互作用连接。这种开放量子模型被称为 OISD（开放无限分量自旋迪克）模型。OISD Liouvillian 的代数结构是根据作用在密度矩阵空间上的超级算子来研究的。获得了一个明确的可逆超级算子（准确地说，是一个完全正的保迹图），它将 OISD 刘维良转换为两个独立的刘维良的和，一个仅由修整自旋生成，另一个仅由修整谐振子生成。由 OISD Liouvillian 产生的时间演化被证明是渐近地等价于由具有自旋和谐振子的一些同步频率的调整解耦 Liouvillian 产生的。这种渐近等价意味着 OISD 模型的时间演化在存在任何（微小）耗散的情况下会完全耗散。