Replica symmetry breaking in random lasers: experimental measurement of the overlap distribution

TL;DR

This paper reports the first experimental measurement of the overlap distribution in random lasers, validating the Parisi order parameter concept in complex disordered optical systems.

Contribution

It introduces a new experimental protocol to measure the overlap distribution in random lasers, linking theoretical replica symmetry breaking to observable optical phenomena.

Findings

Successful measurement of the overlap distribution in a random laser

Identification of a connection between overlap distribution and laser intensity fluctuations

Discussion of the role of spatial heterogeneities and turbulence in random media

Abstract

In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi order parameter, we focus on the systems where the measurement has been possible for the first time: random lasers. Starting from first principles of light-matter interaction we sketch the main steps leading to the construction of the statistical mechanical model for the dynamics of light modes in a random laser, a spherical multi-p-spin model with complex spins. A new overlap is introduced, the intensity fluctuation overlap, whose probability distribution, under specific assumptions, is equivalent to the Parisi overlap distribution. The experimental protocol for measuring this overlap is based on the possibility of experimentally realizing real replicas. After a description of the first experiment on the random laser made of T5CO$_x$ grains we review and discuss various experiments measuring the overlap distribution, as well as the possible connection with Levy-like distribution of the intensity of the light modes around the laser threshold, the connection with turbulence in fiber lasers and the role of spatial etherogeneities of light modes in random media.