Optical spin model simulators from momentum space modulation

Photonic solvers capable of finding the ground states of various spin Hamiltonians can be employed to investigate numerous interactive physical systems and combinatorial optimization problems. We introduce a novel photonic solver that leverages spin Hamiltonians within the framework of Modulated Momenta of Light. We establish a real-and-momentum space correspondence for spin Hamiltonians using spatial light transport. The real-space spin interaction is determined by modulating the momentum-space flow of light. This principle, formulated as a generalized Plancherel theorem, enables us to construct a straightforward optical simulator capable of finding ground states for displacement-dependent spin interactions. In our experiments, we apply this principle to unveil the exotic magnetic phase diagram of iron chalcogenides, a family of iron-based superconductors, and we also observe vortex-mediated Berezinskii-Kosterlitz-Thouless dynamics. The precision achieved by momentum modulation in controlling spin interactions holds promise for exploring novel physical effects and solving complex optimization problems.