COLLAPSE AND REVIVAL OF ULTRACOLD ATOMS IN A MICROWAVE CAVITY AND OF PHOTONS IN PARAMETRIC DOWN-CONVERSION

We present a 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 that 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 behavior, of not only the mean valu e but also the variance of the number of excited atoms is derived and solved analytically. For different initial states the mean number of e xcited atoms exhibits periodically reappearing dips, with an accompany ing peak in the variance, or fractional collapses and revivals. Closed expressions for the period and the revival time are obtained. [S1050- 2947(98)03702-0].