Large Fluctuations in two-level systems with stimulated emission

TL;DR

This paper analyzes the large fluctuations in a system of two-level atoms under photon flux, using large deviation theory to understand rare emission events in large ensembles.

Contribution

It introduces a large deviation framework for modeling rare emission events in a system of many two-level atoms influenced by photon flux.

Findings

Characterization of the probability of large emission fluctuations

Asymptotic analysis of emission events as the number of atoms grows

Identification of conditions leading to large deviations in emission

Abstract

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 $N\to\infty$.