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