As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom–photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.

顾名思义，周期轨道是一个动态系统的解决方案，它在时间上自我重复。在规则状态下，周期轨道是稳定的，而在混沌状态下，它们变得不稳定。不稳定周期轨道的存在与量子疤痕现象直接相关，这会限制本征态的离域程度并导致动力学的恢复。在这里，我们研究了超辐射阶段的 Dicke 模型并确定了两组基本周期轨道。这种可通过实验实现的原子-光子模型在低能时是规则的，在高能时是混沌的。我们研究了规则和混沌状态下周期轨道对本征态结构的影响，并获得了它们的量子化能量。