On the Preparation of Pure States in Resonant Microcavities

We consider the time evolution of the radiation field (R) and a two-level atom (A) in a resonant microcavity in terms of the Jaynes-Cummings model with an initial general pure quantum state for the radiation field. It is then shown, using the Cauchy-Schwarz inequality and also a Poisson resummation technique, that {\it perfect} coherence of the atom can in general never be achieved. The atom and the radiation field are, however, to a good approximation in a pure state $|\psi >_A\otimes|\psi >_R$ in the middle of what has been traditionally called the ``collapse region'', independent of the initial state of the atoms, provided that the initial pure state of the radiation field has a photon number probability distribution which is sufficiently peaked and phase differences that do not vary significantly around this peak. An approximative analytic expression for the quantity $\Tr[\rho^2_{A}(t)]$, where $\rho_{A}(t)$ is the reduced density matrix for the atom, is derived. We also show that under quite general circumstances an initial entangled pure state will be disentangled to the pure state $|\psi >_{A\otimes R}$.