Quantum correlations, mixed states and bistability at the onset of lasing

TL;DR

This paper presents a quantum model of a single-mode laser revealing quantum bistability and non-classical states at the lasing threshold, contrasting with semi-classical predictions and highlighting finite-size effects.

Contribution

It introduces a comprehensive quantum model including photon-electron correlations, showing bistability and non-classical states at the onset of lasing, which are absent in semi-classical models.

Findings

Lasing occurs with quantum bistability between non-lasing and non-classical states.

Coherent emission emerges through a saddle-node bifurcation with finite amplitude.

Lasing threshold approaches semi-classical prediction in large systems, but requires finite perturbations.

Abstract

We derive a model for a single mode laser that includes all two particle quantum correlations between photons and electrons. In contrast to the predictions of semi-classical models, we find that lasing takes place in the presence of quantum bistability between a non-lasing and a non-classical coherent state. The coherent state is characterized by a central frequency and a finite linewidth and emerges with finite amplitude from a saddle-node bifurcation together with an unstable coherent state. Hence coherent emission in nanolasers originates through a mixing of lasing and non-lasing states. In the limit of a macrolaser with a large number of emitters and non-resonant modes, the laser threshold approaches the prediction of the semi-classical theory, but with the important difference that lasing can be achieved only in the presence of finite size perturbations.