  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.
