Observing Dissipative Topological Defects with Coupled Lasers

Abstract

Topological defects have been observed and studied in a wide range of systems, such as cosmology, spin systems, cold atoms, and optics, as they are quenched across a phase transition into an ordered state. These defects limit the coherence of the system and its ability to approach a fully ordered state, so revealing their origin and control is becoming an increasingly important field of research. We observe dissipative topological defects in a one-dimensional ring of phased-locked lasers, and show how their formation is related to the Kibble-Zurek mechanism and is governed in a universal manner by two competing time scales. The ratio between these two time scales depends on the system parameters, and thus offers the possibility of enabling the system to dissipate to a fully ordered, defect-free state that can be exploited for solving hard computational problems in various fields.

Dynamics of dissipative topological defects in coupled phase oscillators

“…The Kuramoto model describes the temporal evolution of the phase of coupled oscillators [25,26]. It was successfully applied in many areas such as neural networks, complex systems, chemical and biological oscillators [24,25] and recently in coupled lasers for observing topological defects [18,27]. The model is valid when all oscillators are nearly identical and the coupling between them is weak.…”

“…a chain with periodic boundary conditions. The detuning between the oscillators is randomly initialized in the range of [0 to Ω max ≈ τ −1 For a ring array geometry, the defect number D is globally defined for the whole array as [18,22]:…”

“…Recently, dissipative topological defects were numerically and experimentally investigated using a onedimensional ring array of phased-locked lasers, where their formation was shown to be related to the KZM in a universal manner by two competing time scales [18]. The ratio between these two time scales depends on the system parameters, with which it is possible to enable the system to dissipate to a fully ordered, defect-free state that can be exploited for solving computational prob- * Corresponding author: sim.mahler@gmail.com lems in various fields [19].…”

Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism

“…The KZ picture predicts a scaling law of the density of defects n during a linear quench across a phase transition, as a function of the quench rate (or the total quench time τ Q ) 1,2 . It is based on the assumption that at quasiequilibrium the system has a response timescale τ R (t) arXiv:1807.10611v2 [quant-ph] 16 May 2019 which scales as τ R ∝ |h − h c | −νz with the distance from the critical point h c of the driving parameter…”

Improved Phase Locking of Laser Arrays with Nonlinear Coupling

“…Accordingly, the total brightness of the lasers is high and allows focusing of all the lasers to a sharp spot [3][4][5]. Phase locking of lasers has been incorporated in many investigations, including simulating spin systems [6][7][8], finding the ground-state solution of complex landscapes [6,9], observing dissipative topological defects [10,11] and solving hard computational problems [9,12].Phase locking of laser arrays can be achieved with dissipative coupling that leads to a stable state of minimal loss, which is the phase locked state [6,10,11]. Dissipative coupling involves mode competition whereby modes of different losses compete for the same gain [2,6,9,13].…”