标题： 拓扑--卡明斯模型中的热态结构及介观量子系综的快速模拟 显示英文标题

标题： Thermal state structure in the Tavis--Cummings model and rapid simulations in mesoscopic quantum ensembles

摘要： 由N个自旋-1/2粒子组成的混合量子系统，这些粒子与电磁场均匀相互作用，例如被限制在腔体中的系统，在量子信息处理器的发展中非常重要，并且在计量学以及集体行为的测试中也将是有用的。 这类系统通常由Tavis-Cummings模型进行建模，为了理解它们在现实环境中的行为，需要准确理解该系统的热行为。 在本工作中，我们定量地表明，有时过于轻易地使用了Dicke子空间近似，具体来说，我们表明存在一个温度，高于该温度时系统的简并性占主导地位，而Dicke子空间则几乎不被占据。 这种转变发生的温度低于之前考虑的温度。 当处于这种温度范围内时，运动的关键常数是自旋系统和腔体之间的总激发计数以及自旋系统的集体角动量。 这些使得可以基于所谓Lamb位移（在此处称为“着衣态的能量位移”）对热性质进行微扰展开。 这些方法能够高效地获取某些以$O(\sqrt{N})$为尺度的参数，因此效率非常高。 这些方法还提供了近似和界定这些系统性质的方法，以及表征主要占据区域的方法，包括在微扰噪声下的情况。 在更强的自旋-自旋耦合 regime 中，微扰超过了展开级数项，可能需要使用低效的方法来模拟，从而失去了模拟此类系统的计算效率。 本工作中的结果也可以用于相关系统，如耦合腔阵列、腔介导的集体自旋系综耦合以及集体自旋系统。 显示英文摘要

摘要： Hybrid quantum systems consisting of a collection of N spin-1/2 particles uniformly interacting with an electromagnetic field, such as one confined in a cavity, are important for the development of quantum information processors and will be useful for metrology, as well as tests of collective behavior. Such systems are often modeled by the Tavis-Cummings model and having an accurate understanding of the thermal behaviors of this system is needed to understand the behavior of them in realistic environments. We quantitatively show in this work that the Dicke subspace approximation is at times invoked too readily, in specific we show that there is a temperature above which the degeneracies in the system become dominant and the Dicke subspace is minimally populated. This transition occurs at a lower temperature than priorly considered. When in such a temperature regime, the key constants of the motion are the total excitation count between the spin system and cavity and the collective angular momentum of the spin system. These enable perturbative expansions for thermal properties in terms of the energy shifts of dressed states, called Lamb shifts herein. These enable efficient numeric methods for obtaining certain parameters that scale as $O(\sqrt{N})$, and is thus highly efficient. These provide methods for approximating, and bounding, properties of these systems as well as characterizing the dominant population regions, including under perturbative noise. In the regime of stronger spin-spin coupling the perturbations outweigh the expansion series terms and inefficient methods likely are needed to be employed, removing the computational efficiency of simulating such systems. The results in this work can also be used for related systems such as coupled-cavity arrays, cavity mediated coupling of collective spin ensembles, and collective spin systems.