Non-equilibrium states of a photon cavity pumped by an atomic beam

TL;DR

This paper analyzes the dynamics of a photon cavity pumped by an atomic beam, showing how photon number evolves in ideal and leaky conditions, and characterizing the resulting non-equilibrium states.

Contribution

It provides explicit formulas for photon number evolution, characterizes the limiting non-equilibrium state, and computes energy flux and entropy production.

Findings

Photon number increases indefinitely in an ideal cavity without leakage.

In a leaky cavity, the photon number stabilizes to a steady state.

The steady state is independent of initial conditions and characterized explicitly.

Abstract

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.