Processos estocásticos na interação da luz com a matéria

Abstract

We study and characterize the dynamics of population inversion in the Jaynes-Cummings model. Initially we analyze the less studied case of stochastic phase fluctuations in the atomfield coupling coefficient where the fluctuations are modelled by a random phase telegraph process. We have obtained an equation for the density operator and for the population inversion averaged over the distribution of fluctuations. We present analytical expressions for non-pertuvative quantum effects such as revivals in the inversion for an initial coherent state of the field that was calculated using the Poisson summation and the steepest descent method. The expression found for each revival allow us to estimate their time of occurrence, the oscillation frequency, the width and the time intervals between two consecutive revivals. The same analysis is performed for an ideal atom-field interacting system and for the dissipative one. In the end, we compare the effects on the population inversion due to different processes. We pay particular attention to how quantum effects disappear with the decrease of time intervals between jumps in the atom-field coupling parameter or the increase of the dissipation rate for the field, and the result seems to be completely classical. We show that the details of obtaining the classical limit can be very different for each different process