Spontaneous symmetry breaking in the laser transition
Spontaneous symmetry breaking in the laser transition
复制标题
激光跃迁中的自发对称性破缺
作者：
P. Gartner
在类比平衡相变，我们解决的不稳定性的问题，以破坏微扰的系统进行激光跃迁。讨论中的对称性是关于相位因子的U（1）不变性，微扰是耦合到激子的相干场E。在速率方程的水平，我们首先分析的情况下，一个腔包含一个单一的，两个级别的发射器，然后链的这种腔相互作用的光子跳跃过程。在这两种情况下，自发对称性破缺发生时，系统是在激光阶段。对于激光跃迁，热力学极限的类似物是消失的腔损耗和光-物质耦合的标度极限， o 0$，$g 0$，所以$g^2/kappa$保持有限。我们表明，在激光制度的异常平均坚持在$E o 0$ limit，前提是首先执行缩放限制。用数值方法比较了基于稳健反常平均的激光诊断与常用的相干性判据g^{（2）}（0）=1$，并讨论了前者的优点。
In analogy with equilibrium phase transitions, we address the problem of the instability to symmetry-breaking perturbations of systems undergoing a laser transition. The symmetry in question is the $U(1)$ invariance with respect to a phase factor, and the perturbation is a coherent field $E$, coupled to the exciton. At the rate equation level we analyze first the case of a cavity containing a single, two-level emitter, and then a chain of such cavities interacting by photon hopping processes. In both cases spontaneous symmetry breaking takes place when the system is in the lasing phase. For the laser transition, the analogue of the thermodynamic limit is the scaling limit of vanishing cavity loss and light-matter coupling, $kappa o 0$, $g o 0$, so that $g^2/kappa$ remains finite. We show that in the lasing regime anomalous averages persist in the $E o 0$ limit, provided that the scaling limit is performed first. Lasing diagnosis based on robust anomalous averages is compared numerically with the familiar coherence criterion $g^{(2)}(0)=1$, and the advantages of the former are discussed.