Effects of Decoherence on Entangled Atomic Wave Functions in Microcavities

We consider an experimental set-up where two-level atoms are streamed through a microcavity in such a manner that at most one atom is present inside the cavity at any instant of time. The interaction of a single atom with the cavity photons leaves an imprint on the steady-state cavity density operator. The wave function of the next atom that passes through the cavity gets entangled with the cavity photons and subsequent secondary correlations develop between two or more atoms in this way. After leaving the cavity the atoms pass through an electromagnetic field that is tuned to give a π/2 pulse to the atoms with varied phase for different atoms. The atoms are then detected in either of their upper or lower states. The secondary correlations between two or more subsequent atoms can be exploited to formulate Bell-type inequalities for their detection probabilities. We investigate the effects of decoherence on atomic entanglement brought about by both atomic decay and cavity dissipation through interaction with their respective reservoirs. We show by using realistic models for the micromaser as well as the microlaser that effects of decoherence on the Bell sum can be experimentally monitored and observed in a controlled fashion.