Coherence build up and laser thresholds from nanolasers to macroscopic lasers

TL;DR

This paper develops models for nanolasers and macroscopic lasers that predict a universal laser threshold, driven by photon correlation growth, with results aligning well with experimental observations and providing new insights into laser coherence buildup.

Contribution

The paper introduces a comprehensive model that includes both coherent and incoherent variables, predicting laser thresholds across different cavity sizes and emitter numbers, bridging nano- and macro-scale laser physics.

Findings

Laser threshold exists regardless of cavity size or emitter number.

Photon correlation growth drives the transition to stimulated emission.

Predictions match experimental coherence measurements.

Abstract

We detail the derivation of nanolaser models that include coherent and incoherent variables and predict the existence of a laser threshold, irrespective of cavity size and emitter number, for both single- and multi-electron systems. The growth in photon number in the lasing mode is driven by an increase in correlation between absorption and emission processes, leading to the onset of self-sustained stimulated emission (laser threshold), followed, in turn, by a correlation decrease and ending with the dominance of coherent emission. The first-order coherence $g^{(1)}$ steadily increases, as the pump grows towards the laser threshold value, and reaches unity at or beyond threshold. The transition toward coherent emission becomes increasingly sharp as the number of emitters and of the coupled electromagnetic cavity modes increase, continuously connecting, in the thermodynamic limit, the physics of nano- and macroscopic lasers at threshold. Our predictions are in remarkable agreement with experiments whose first-order coherence measurements have so far been explained only phenomenologically. A consistent evaluation of different threshold indicators provides a tool for a correct interpretation of experimental measurements at the onset of laser action.