  A model is presented to describe the recently proposed experiment (J.
Raimond,
  M. Brune and S. Haroche Phys. Rev. Lett {\bf 79}, 1964 (1997)) where a
mesoscopic superposition of radiation states is prepared in a high-Q cavity
which is coupled to a similar resonator. The dynamical coherence loss of such
state in the absence of dissipation is reversible and can in principle be
observed. We show how this picture is modified due to the presence of the
environmental couplings. Analytical expressions for the experimental
conditional probabilities and the linear entropy are given. We conclude that
the phenomenon can still be observed provided the ratio between the damping
constant and the inter-cavities coupling does not exceed about a few percent.
This observation is favored for superpositions of states with large overlap.
