  We investigate the dynamical properties of the finite-size Dicke model
coupled to a photon reservoir in the dispersive regime. The system-reservoir
coupling in our Hamiltonian includes counter-rotating terms, which are relevant
in the strong atom-cavity coupling. Because the dispersive regime is
considered, the dynamics of low-energy states are described sufficiently
accurately within the finite-dimensional subspace of the dressed states. Using
the separation of the time scales between the system and the reservoir, we
derive the Markovian quantum master equation in the subspace without ignoring
the counter-rotating terms. The temporal evolution of the expectation of the
cavity mode shows that the bifurcation of the long-lived state corresponds to
the superradiant transition in the isolated model. The master equation
explicitly gives the steady state solution. The numerical results for the
first-order correlation function on the steady state indicate that the strong
atom-cavity coupling enhances the coherence and softens the dephasing in the
superradiant region.
