Low- and high-β lasers in the class-A limit: photon statistics, linewidth, and the laser-phase transition analogy

Nanocavity lasers are commonly characterized by the spontaneous coupling coefficient beta that represents the fraction of photons emitted into the lasing mode. While beta is conventionally discussed in semiconductor lasers where the photon lifetime is much shorter than the carrier lifetime (class-B lasers), little is known about beta in atomic lasers where the photon lifetime is much longer than the other lifetimes and only the photon degree of freedom exists (class-A lasers). We investigate the impact of the spontaneous coupling coefficient beta on lasing properties in the class-A limit by extending the well-known Scully-Lamb master equation. We demonstrate that in the class-A limit all the photon statistics are uniquely characterized by beta and that the laser phase transition-like analogy becomes transparent. In fact, beta perfectly represents the system size in phase transition. Finally, we investigate the laserphase transition analogy from the standpoint of a quantum dissipative system. Calculating a Liouvillian gap, we clarify the relation between beta and the continuous phase symmetry breaking. (C) 2021 Optical Society of America

Automated summary

In this study, the impact of the spontaneous coupling coefficient beta on lasing properties in class-A limit is investigated, revealing that in this scenario all photon statistics are uniquely characterized by beta. The analogy of laser phase transition becomes transparent in the class-A limit.