Photonic Ising machines are inherently limited to all-to-all spin interactions, restricting their ability to model complex physical systems. To address this, researchers developed an optical spin model simulator that enables distance-dependent spin interactions by modulating light in momentum space. Using a laser beam and a phase-only spatial light modulator, the system reproduces complex magnetic states and topological phase transitions, enabling new possibilities for simulating spins and topological effects in physics and materials science.

Understanding complex physical systems, such as magnetic phase transitions in materials to neural networks and financial markets, can often be described using spin models (such as Ising model). These models are based on a Hamiltonian, a mathematical formula that describes how each spin interacts with others based on their spatial displacement. These interactions are expressed as a function J(r) , where r represents the distance between spin i and j.

Spatial photonic Ising machines (SPIMs) have emerged as platforms for simulating spin Hamiltonians using light. These optical devices use free-space light propagation to perform parallel computations with high speed and low energy consumption. However, these systems are inherently limited to all-to-all interactions due to the nature of light’s momentum, restricting their ability to model general spin Hamiltonians with more complex, distance-dependent interactions.

A study in Advanced Photonics, an open-access journal published by SPIE, has overcome this limitation by modulating the momentum space of light, enabling arbitrary displacement-dependent spin interactions J(r) in a simple optical platform.

Key to this breakthrough is the generalized Plancherel theorem, which links the spin Hamiltonian to the light diffraction pattern, which can be represented as a Fourier transform. By shaping the light's properties in momentum space with a custom function V(k), the researchers can implement any desired spin interaction J(r) at different distances.

Using this principle, the researchers constructed an optical spin model simulator that consists of a 532-nm laser beam phase-modulated by a spatial light modulator (SLM), which creates a lattice of optical phases representing spins. The beam then passes through a lens, transforming the pattern into its momentum-space intensity I(k), which is captured by a CMOS camera. The energy of the current spin configuration is calculated by measuring the total intensity of I(k)·V(k) over the entire momentum space k. A computer algorithm then slightly changes the spin directions to find lower-energy configurations, driving the system towards minimizing energy.

To validate their approach, the team conducted two experiments. First, they simulated the complex magnetic ground states observed in iron chalcogenides by tuning nearest-neighbor, next-to-nearest-neighbor, and third nearest-neighbor interaction strengths. Using optical annealing, they successfully reproduced theoretical predictions, including antiferromagnetic, double-stripe, and staggered-dimer patterns. These patterns are important ground-state candidates for iron-based superconductors.

Second, by extending spins as quasi-continuous variables, the team observed the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, a signature of two-dimensional topological phase transitions, by capturing the spontaneous formation of vortices within the optical spin array.

Unlike previous SPIMs, which require additional computational steps, the proposed optical simulator can simulate a wide variety of spin interactions while using only simple equipment, with modifications to the momentum pattern V(k).

This capability could help researchers explore new types of spin models in physics, including those that are difficult to simulate on traditional computers. Moreover, the architecture of the spin model simulator is compatible with intracavity optical systems. In these setups, the interaction function V(k) can be implemented using spatial light modulators (SLMs) or advanced metasurfaces placed in the momentum plane of an optical cavity.

These findings could potentially transform how we tackle complex physics and optimization-related challenges!

Simplified experimental setup of the optical spin modulator. This cutting-edge optical simulator uses light's properties to efficiently visualize the complex magnetic states and BKT transition.

The research was published in “Juan Feng, Zengya Li, Luqi Yuan, Erez Hasman, Bo Wang, Xianfeng Chen (2025). Spin Hamiltonian in the modulated momenta of light. Adv. Photonics, 7(4), 046001-046001.”

Link: https://doi.org/10.1117/1.AP.7.4.046001