Spin Hamiltonians in the Modulated Momenta of Light

Abstract: Photonic solvers that are able to find the ground states of different spin Hamiltonians can be used to study many interactive physical systems and combinatorial optimization problems. Here, we establish a real-and-momentum space correspondence of spin Hamiltonians by spatial light transport. The real-space spin interaction is determined by modulating the momentum-space flow of light. This principle is formulated as a generalized Plancherel theorem, allowing us to implement a simple optical simulator that can find the ground states for any displacement-dependent spin interactions. Particularly, we use this principle to reveal the exotic magnetic phase diagram from a J1-J2-J3 model, and we also observe the vortex-mediated Berezinskii-Kosterlitz-Thouless dynamics from the XY model. These experiments exhibit high calculation precision by subtly controlling spin interactions from the momentum space of light, offering a promising scheme to explore novel physical effects.