Chaotic spin-photonic states in an open periodically modulated quantum cavity

When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed 'chaotic`. Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here we consider quantum chaotic state emerging in a leaky cavity, when an intracavity photonic mode is coherently pumped with the intensity varying periodically in time. We show that a single spin, when placed inside the cavity and coupled to the mode, can moderate transitions between regular and chaotic regimes -- that are identified by using quantum Lyapunov exponents -- and thus can be used to control the degree of chaos. In an experiment, these transitions can be detected by analyzing photon emission statistics.