In a view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) non-stationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model, we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete ${\mathbb{Z}}_2$ symmetry), and that of (anti-) and Tavis-Cummings $U(1)$ models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of photon number take universal values. We also find a temperature scales below which one approaches zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss Bethe ansatz solution for integrable $U(1)$ limits.

中文翻译：

---

接近超辐射相变的广义Dicke模型中的普遍涨落和压缩

鉴于最近提出的在诸如（i）非平稳或电感和电容耦合的超导量子位，（ii）交叉场中的原子和（iii）具有自旋轨道的半导体异质结构等平台上实现各向异性光物质相互作用的建议在相互作用中，旋转波项和反向旋转波项的耦合强度不相等的广义Dicke模型概念引起了极大的兴趣。对于此模型，当温度和二级系统的数量都是有限的时，我们研究了从正常到超辐射相变的关键区域中的光子涨落。在这种情况下，在显示两种临界行为的相图中，超辐射量子相变会更改为波动区域。这些是Dicke模型的状态（具有离散${\mathbb{Z}}_2$ 对称性）和（反）和Tavis-Cummings $ü（\mathrm{1个}）$楷模。我们表明，在这些情况下，光子冷凝物的压缩参数显示出不同的温度标度。此外，光子数的相对波动具有通用值。我们还发现了一个温度标度，在该温度标度以下，接近零温度量子相变，其中量子涨落占主导地位。我们的有效理论是由凝结模式的非金石函数和Pauli算子的Majorana表示提供的。我们还将讨论Bethe ansatz可集成解决方案$ü（\mathrm{1个}）$ 限制。