  We present a new theoretical method to study a trapped gas of bosonic
two-level atoms interacting with a single mode of a microwave cavity. This
interaction is described by a trilinear Hamiltonian which is formally
completely equivalent to the one describing parametric down-conversion in
quantum optics. A system of differential equations describing the evolution,
including the long-time behaviour, of not only the mean value but also the
variance of the number of excited atoms is derived and solved analytically. For
different initial states the mean number of excited atoms exhibits periodically
reappearing dips, with an accompanying peak in the variance, or fractional
collapses and revivals. Closed expressions for the period and the revival time
are obtained.
