The two-level atom laser: analytical results and the laser transition

TL;DR

This paper provides an analytical study of the two-level atom laser, revealing the conditions for the laser transition and Poissonian statistics, and shows the broader relevance of these findings to laser models.

Contribution

It introduces an analytical continued fraction solution for the two-level atom laser and links the laser transition to a specific scaling limit, extending the understanding to similar models.

Findings

Sharp transition to Poissonian statistics under specific scaling limits

Analytical continued fraction expression for steady-state solutions

Connection of laser transition conditions to a general scaling regime

Abstract

The problem of the two-level atom laser is studied analytically. The steady-state solution is expressed as a continued fraction, and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected with the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g \to 0$, such that $g^2/\kappa$ stays finite and $g^2/\kappa > 2 \gamma$, where $\gamma$ is the rate of atomic losses. The same scaling procedure is also shown to describe a similar change to Poisson distribution in the Scully-Lamb laser model too, suggesting that the low-$\kappa$, low-$g$ asymptotics is of a more general significance for the laser transition.