Simulation of Hopfield-like Hamiltonians using time-multiplexed photonic networks

Abstract: We propose a time-multiplexed photonic network architecture based on coupled ring resonators, capable of accurately emulating specific Hamiltonian dynamics. We show that, in the Suzuki-Trotter limit, the resulting stroboscopic evolution reproduces the characteristic dynamics of the bosonized Hopfield model. Furthermore, by incorporating a nonlinear element within the main resonator loop, we outline a scalable route toward optical simulation of both mean-field and quantum nonlinear dynamics associated with the Tavis-Cummings model. Our results establish time-multiplexed resonator networks as a versatile photonic framework for simulating interacting light-matter Hamiltonians and collective many-body phenomena.