规范不变Dicke模型的基态：非经典态中的光子凝聚
Ground state of the gauge invariant Dicke model: condensation of the photons in non-classical states
AI总结：
该研究对比两种修正Dicke模型的基态特性，发现自旋1/2粒子体系可发生经典场非零的相变，而规范不变两能级体系序参量为零但存在非经典压缩态光子凝聚，揭示了两类系统的定性差异。
摘要：
我们研究了两种具有物理动机的Dicke模型修正形式的基态。第一种修正对应相空间仅包含两个态的粒子，例如自旋1/2粒子或人工制备的量子比特（qubit）。第二种修正描述的是两能级系统，它是将原子的完整希尔伯特空间截断为与电磁场共振的两个能级后得到的，由规范不变Dicke模型描述。我们证明这两种系统的行为在定性上存在差异。具体而言，在第一种情形中，系统可能发生相变，进入经典场振幅非零的状态；而在第二种情形中，表征场向发生光子凝聚的相干态相变的所谓序参量$η= \braket{\u0026#226;}$为零。与此同时，平均光子数$\bar{n} = \braket{\u0026#226;^\u2020 \u0026#226;} \neq 0$，且系统中的集体激发表现出场的非经典“压缩”态。我们在参数变化的大范围内分析了两种系统的可观测特征。
英文摘要：
We investigate the ground state of two physically motivated modifications of the Dicke model. The first modification corresponds to particles whose phase space contains only two states, for example, particles with spin 1/2 or artificially created qubits. The second modification describes two-level systems that arise as a result of truncating the full Hilbert space of atoms to two levels that are in resonance with the electromagnetic field and are described by the gauge-invariant Dicke model. We demonstrate that the behavior of these systems is qualitatively distinct in both cases. In particular, in the first scenario, a phase transition into the state with a non-zero amplitude of the classical field is possible, while in the second case, the so-called order parameter $η= \braket{\hat{a}}$ of the field's phase transition into a coherent state with photon condensation is zero. At the same time, the average number of photons $\bar{n} = \braket{\hat{a}^\dagger \hat{a}} \neq 0$, and the collective excitation in the system manifests a non-classical "squeezed" state of the field. We analyze the observable characteristics of both systems in a wide range of variation of their parameters.
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