Home

Measuring maximal eigenvalue distribution of Wishart random matrices with coupled lasers


  Moti Fridman [1]  ,  Rami Pugatch [1]  ,  Micha Nixon [1]  ,  Asher Friesem [1]  ,  Nir Davidson [1]  
 [1] Weizmann Institute of Science, Department of Physics of Complex Systems, Rohovot Israel

We determined the probability distribution of the combined output power from 25 coupled fiber lasers and

show that it agrees well with the Tracy-Widom and Majumdar-Vergassola 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 distribution is correct.