Regular Article

Synthetic mean-field interactions in photonic lattices^★

¹ SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
² Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
³ Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany

^a e-mail: p.ohberg@hw.ac.uk

Received: 24 October 2019
Received in final form: 5 February 2020
Published online: 1 May 2020

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.