Probing the Ginzburg-Landau Potential for Lasers Using Higher-order Photon Correlations

TL;DR

This paper investigates the applicability of the Ginzburg-Landau theory to laser systems using higher-order photon correlations, revealing conditions under which the theory holds or breaks down, especially in relation to photon and carrier lifetimes.

Contribution

It provides a theoretical analysis of the Ginzburg-Landau potential for lasers, using stochastic rate equations and photon correlations to test the theory's validity across different parameters.

Findings

GL theory applies to low-β lasers with comparable photon and carrier lifetimes

Photon-carrier relaxation oscillations cause breakdown of GL theory

Higher-order photon correlations can verify GL theory applicability

Abstract

Lasing transition is known to be analogous to the second-order phase transition. Furthermore, for some cases, it is possible to define the Ginzburg-Landau (GL) potential, and the GL theory predicts the photon statistical properties of lasers. However, the GL potential for lasers is surprising, because lasers are operating far from equilibrium. In this paper, we theoretically examine the validity of the GL theory for lasers in terms of various parameters, particularly, the ratio between photon and carrier lifetimes. For this purpose, we use stochastic rate equations and higher-order photon correlation functions. With higher-order photon correlation measurements, we can check whether or not laser dynamics are described by the GL theory. We demonstrate that, for low-$\beta$ lasers, the GL theory is applicable even when the photon lifetime is comparable to the carrier lifetime and that photon-carrier relaxation oscillation is the fundamental origin of the breakdown of the GL theory, which can be understood in the framework of center manifold reduction.