A scaling-limit approach to the theory of laser transition

TL;DR

This paper introduces a scaling-limit framework to rigorously define the laser transition, demonstrating that under specific asymptotic conditions, photon output becomes large and Poissonian, with numerical validation for two- and three-level emitters.

Contribution

It formulates a novel scaling-limit approach to characterize the laser transition analytically and numerically, connecting physical parameters to the emergence of lasing behavior.

Findings

Photon output becomes large above threshold in the scaling limit.

Photon statistics become strictly Poissonian in the asymptotic regime.

Numerical examples confirm the analytical predictions for different emitter types.

Abstract

The conditions for the appearance of a sharp laser transition are formulated in terms of a scaling limit, involving vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g \to 0$, such that $g^2/\kappa$ stays finite. It is shown analytically that in this asymptotic parameter domain, and for pump rates above the threshold value, the photon output becomes large in a sense that is specified, and the photon statistics becomes strictly Poissonian. Numerical examples for the case of a two-level and a three-level emitter are presented and discussed in relation to the analytic result.