Simultaneous stochastic effects of a thermal reservoir and an electromagnetic field on the optical susceptibility of a two-level system

In this paper we derive analytical expressions for the optical susceptibility of a two-level system immersed in a thermal bath and interacting with an external electromagnetic field, where both of them are considered as noise sources. The dynamics of the system is described by a set of optical stochastic Bloch equations. The noise sources are modeled as Ornstein-Uhlenbeck processes. The optical stochastic Bloch equations are perturbatively solved up to second order in the external field. We found that each noise affects the dynamics in a different manner. Thus, at first order, the bath modifies the transverse relaxation time, whereas the effect of a random field can only be appreciated if the expansion is calculated up to second order, where correlations begin to be important.