Coupled lasers can be exploited in both applied and fundamental research. It has been shown that a very large arrays of >1000 lasers with nearest-neighbor coupling rapidly “dissipates” into long-range phase ordering, identical to the ground state of a corresponding XY spin Hamiltonian [1]. Finding the ground state can be mapped to solve optimization problems that are NP-hard [2, 3]. When a system undergoes a transition, by spontaneous symmetry breaking, from a complex disordered phase state to a long-range phase ordered state, topological defects arise. Such topological defects may prevent the system from reaching a perfect ordered state. The underlying physical mechanism of their origin and control is becoming an increasingly important and fascinating field of research in various fields such as spin systems, cosmology and optics.

We investigated dissipative topological defects in a one-dimensional ring network of coupled lasers, and show how they are linked to the Kibble-Zurek (KZ) mechanism [4, 5]. These defects may be topologically protected, depending on the size and geometry of the system, preventing it from reaching a perfect ordered state. We experimentally found that the probability of topological defects increases with the system size, and also strongly depends on various laser parameters such as pump and coupling strengths. We confirmed that the formation of topological defects is governed by two competing time scales, namely phase locking time and synchronization time of the lasers amplitude fluctuations. More specifically, when the phase locking time is smaller than the synchronization time, the probability for topological defects formation is zero. Whereas, when the phase locking time exceeds the synchronization time, the probability for topological defects formation is finite.

The details of the experimental arrangement, procedures and results, as well as supporting theoretical results will be presented.

[1] M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, Phys. Rev. Lett. 110, 184102 (2013).

[2] A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, Nat. Photon. 8, 937 (2014).

[3] N. G. Berloff, K. Kalinin, M. Silva, W. Langbein, and P. G. Lagoudakis, arXiv:1607.06065 (2016).

[4] T. W. B. Kibble, J. Phys. A: Math. Gen. 9, 1387 (1976).

[5] W. H. Zurek, Nature 317, 505 (1985)