Large Fluctuations in Two-Level Systems With Stimulated Emission

Abstract

We consider a system of N identical independent Markov processes, each taking values 0 or 1. The system describes the stochastic dynamics of an ensemble of two-level atoms. The atoms are exposed to a photon flux. Under the photon flux action, each atom changes its state with some rates either from its ground state (state 0) to the excited state (state 1) or from the excited state to the ground state (stimulated emission). The atom can also spontaneously change its state from the excited to the ground state. We study rare events where a large cumulative emission occurs during a fixed time interval [0, T]. For this, we apply the large-deviation theory, which allows an asymptotic analysis as N → ∞.