Large fluctuations in two-level systems with stimulated emission

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 $N\to\infty$.