  We explore the long-time dynamics of Rabi model in a driven-dissipative
setting and show that, as the atom-cavity coupling strength becomes larger than
the cavity frequency, a new time scale emerges. This time scale, much larger
than the natural relaxation time of the atom and the cavity, leads to
long-lived metastable states susceptible to being observed experimentally. By
applying a Floquet-Liouville approach to the time-dependent master equation, we
systematically investigate the set of possible metastable states. We find that
the properties of the metastable states can differ drastically from those of
the steady state and relate these properties to the energy spectrum of the Rabi
Hamiltonian.
