Dynamics of topological defects play an important role in various fields such as atomic and molecular physics, condensed matter, cosmology and optics.  We numerically investigated the dynamics of defects in a dissipative system of coupled lasers, arranged in one and two-dimensional arrays, which are approximated as coupled Kuramoto phase oscillators [1,2].  The results reveal an analogy to the Kibble-Zurek mechanism, where the dynamics of defects is governed by two competing time scales, and density of defects scales with the cooling rate [2]. 

We found that in the steady-state regime the density of defects scales with the coupling rate, analogous to cooling mechanism in spins.  At a fixed coupling rate, the dynamics of defects exhibit two time scale regimes.  In the short time scale regime, the number of defects rapidly decreases with increasing coupling rate, whereas in the longer time scale regime, the number of defects decrease slowly with increasing coupling rate.  In the steady-state regime, the inversion of defects scaling with coupling rate shows an analogy to the Kibble-Zurek mechanism [1,2]. The laser arrays arrangement and numerical results will be presented.

[1] Vishwa Pal, Chene Tradonsky, Ronen Chriki, Asher A. Friesem, and Nir Davidson. “Observing Dissipative Topological Defects with Coupled Lasers“. Phys. Rev. Lett. 119, 013902 – Published 7 July 2017.
[2] Simon Mahler, Vishwa Pal, Chene Tradonsky, Ronen Chriki, Asher A. Friesem and Nir Davidson. “Disorder-induced ordering and dynamics of dissipative defects in coupled phase oscillators”, to be submitted.