Synthetic mean-field interactions in photonic lattices

TL;DR

This paper introduces a versatile method to simulate mean-field interactions in photonic lattices using external optical components, enabling the study of complex interacting phenomena like self-trapping and Bloch oscillation decay.

Contribution

It presents a novel technique employing Suzuki-Trotter decomposition to realize mean-field interactions in photonic lattices, expanding their simulation capabilities.

Findings

Demonstrates the feasibility of emulating non-decaying interactions

Proposes an experimental scheme for observing self-trapping

Shows potential to study Bloch oscillation decay

Abstract

Photonic lattices are usually considered to be limited by their lack of methods to include interactions. We address this issue by introducing mean-field interactions through optical components which are external to the photonic lattice. The proposed technique to realise mean-field interacting photonic lattices relies on a Suzuki-Trotter decomposition of the unitary evolution for the full Hamiltonian. The technique realises the dynamics in an analogous way to that of a step-wise numerical implementation of quantum dynamics, in the spirit of digital quantum simulation. It is a very versatile technique which allows for the emulation of interactions that do not only depend on inter-particle separations or do not decay with particle separation. We detail the proposed experimental scheme and consider two examples of interacting phenomena, self-trapping and the decay of Bloch oscillations, that are observable with the proposed technique.