Programmable All-Optical Spin Simulator with Artificial Gauge Fields

The coupling of lasers plays an important role in a variety of research activities, from generating high-power lasers to investigating out-of-equilibrium coupled systems. This Letter presents our investigations of Hermitian coupling in arrays of lasers, where it is possible to control both the amplitude and phase of the coupling and generate artificial gauge fields. The Hermitian coupling is demonstrated in three laser array geometries: a square array of 100 lasers with controlled laser coupling for obtaining continuous control over the phase-locked state, a triangular array of 130 lasers with controlled chirality of the lasers, and a ring array of eight lasers with a controlled topological charge. In the square array, we implemented arbitrary laser coupling with a precision of 2π/120 radians, enabling the attainment of arbitrary phase-locking states. 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. The results pave the way for exploring spin systems with programmable coupling in an all-optical spin simulator.