Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer

We investigate semiclassical dynamics of coupled atom-photon interacting system described by a dimer of anisotropic Dicke model in the presence of photon loss, exhibiting a rich variety of non-linear dynamics. Based on symmetries and dynamical classification, we characterize and chart out various dynamical phases in a phase diagram. A key feature of this system is the multistability of different dynamical states, particularly the coexistence of various superradiant phases as well as limit cycles. Remarkably, this dimer system manifests self-trapping phenomena, resulting in a photon population imbalance between the cavities. Such a self-trapped state arises from saddle-node bifurcation, which can be understood from an equivalent Landau-Ginzburg description. Additionally, we identify a unique class of oscillatory dynamics self-trapped limit cycle hosting self-trapping of photons. The absence of stable dynamical phases leads to the onset of chaos, which is diagnosed using the saturation value of the decorrelator dynamics. Moreover, in a narrow region, the self-trapped states can coexist with chaotic attractor, which may have intriguing consequences in quantum dynamics. Finally, we discuss the experimental relevance of our findings, which can be tested in cavity and circuit quantum electrodynamics setups.