Programmable all optical spin simulator with artificial gauge fields

The interconnection of lasers is pivotal across various research domains, from generating high-power lasers to studying out-of-equilibrium coupled systems. This paper explores our investigation into Hermitian coupling between lasers in an array, with the aim of achieving arbitrary coupling and creating artificial gauge fields that can break time-reversal symmetry. For that, we investigated Hermitian coupling within three laser array geometries: a square array of 100 lasers, a triangular array of 130 lasers, and a ring array of 8 lasers. In the square array, we implemented arbitrary laser coupling with a precision of $2\pi/120$ radians, enabling the attainment of any desired phase-locking state. In the triangular array, we controlled the chirality of the lasers with 99% purity. In the ring array, the introduction of an artificial gauge field revealed discrete quantized first-order transitions between distinct topological phase-locking states. This arbitrary coupling, with control over both the strength and phase, paves the way for exploring spin systems and configurations characterized by exotic, non-conventional coupling.