  We propose an experimental setup, feasible with present day technology,
involving two highquality- factor cavities, one Ramsey zone and a two-level
atom which interacts with them. The dynamics in the cavities is modeled by a
dissipative dispersive Jaynes-Cummings model. Analytical expresions for the
evolution superoperator in each part of the proposed setup and for the
concurrence between the atom and the first cavity are given, and the pairwise
entanglement of the subsystems is calculated numerically. We consider initial
separable states given by the tensor product of a superposition of the two
atomic relevant states and coherent states for the fields. We show that for
realistic model parameters (including dissipation), when the dissipation rates
are smaller than the dispersive frequencies (the ratio between the squared
vacuum Rabi frequencies and the detunings), the final state of the cavity
fields remains entangled.
