Measuring maximal eigenvalue distribution of Wishart random matrices with coupled lasers

TL;DR

This study experimentally links the distribution of combined fiber laser output power to the largest eigenvalue distributions of Wishart random matrices, validating theoretical predictions with extensive measurements.

Contribution

It provides the first experimental verification that the output power distribution of coupled lasers follows Tracy-Widom and related Wishart eigenvalue distributions.

Findings

Distribution matches Tracy-Widom for small deviations

Distribution follows Majumdar-Vergassola for large deviations

Extensive measurements confirm theoretical predictions

Abstract

We determined the probability distribution of the combined output power from twenty five coupled fiber lasers and show that it agrees well with the Tracy-Widom, Majumdar-Vergassola and Vivo-Majumdar-Bohigas distributions of the largest eigenvalue of Wishart random matrices with no fitting parameters. This was achieved with $500,000$ measurements of the combined output power from the fiber lasers, that continuously changes with variations of the fiber lasers lengths. We show experimentally that for small deviations of the combined output power over its mean value the Tracy-Widom distribution is correct, while for large deviations the Majumdar-Vergassola and Vivo-Majumdar-Bohigas distributions are correct.