On a quantum-mechanical model for a Maser II

A model very similar to the one we have previously studied1) and closely related to a model of Lamb and Scully2) is considered. Atoms described as two-level systems, initially in an incoherent superposition of the two levels, interact successively with a one-mode electromagnetic field during a time T. In contrast to our previous model T now varies from atom to atom according to a probability law. If the atoms are initially in the upper state with probability γ < 12 then we show that almost always the field converges to a thermal state with a relaxation time bounded by (12− γ)-2 times a constant independent of γ. For γ > 12 we prove that the photon number distribution almost always is asymptotically concentrated around k(γ − 12) with a width bounded by √k ln k(γ − 12), where k is the number of atoms that have interacted with the field. Furthermore, the off-diagonal elements of the density matrix for the field (off-diagonal with respect to the photon number eigen basis) converge again exponentially to zero.