Synthetic mean-field interactions in photonic lattices

Callum W Duncan,Michael J Hartmann,Patrik Öhberg,Robert R Thomson

doi:10.1140/epjd/e2020-100521-0

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.Graphical abstract

Highlights

Over recent years, photonic lattices have emerged as a fruitful platform for the investigation of states of matter [1,2,3,4,5,6,7]
Photonic lattices consist of periodic arrays of waveguides in either one or two dimensions, which are fabricated inside a glass substrate along its full length
An advantage of photonic lattices is that the fabrication process allows for the dynamical control of the parameters of the tight-binding model

Summary

Introduction

Photonic lattices have emerged as a fruitful platform for the investigation of states of matter [1,2,3,4,5,6,7]. The optical state in the photonic lattice behaves as if it was a single particle state in a tight-binding model, with a tunnelling and site-dependent potential. One method to induce interactions in photonic lattice systems is through non-linearities of the propagating material [13,14,15] An example of this is the Kerr effect which results in a variation of the material’s refractive index which is dependent on the intensity of the light. The state recycling technique of reference [6] allows multiple passes of the optical state through a single photonic lattice by the use of standard optical components This set-up, in effect, applies the unitary evolution under the general Hamiltonian in equation (2) multiple times. It allows for the observation of the state in between each unitary evolution using an array of single photon detectors where after each round trip a small fraction of the

Introducing interactions

Proposed realisation

Josephson effect

Bloch oscillations

Non-symmetric interactions

Conclusions