Spin Hamiltonians in the Modulated Momenta of Light

TL;DR

This paper introduces an optical method to simulate and analyze spin Hamiltonians by manipulating light's momentum space, enabling the study of complex magnetic phases and dynamic phenomena with high precision.

Contribution

It establishes a novel real-and-momentum space correspondence for spin Hamiltonians using spatial light transport, forming a generalized Plancherel theorem for optical simulation.

Findings

Revealed the magnetic phase diagram of a J1-J2-J3 model.

Observed vortex-mediated Berezinskii-Kosterlitz-Thouless dynamics.

Demonstrated high-precision control of spin interactions via light momentum space.

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.