Quantum walks in synthetic gauge fields with three-dimensional integrated photonics

There is great interest in designing photonic devices capable of disorder-resistant transport and informationprocessing. In this work we propose to exploit three-dimensional integrated photonic circuits in order to realizetwo-dimensional discrete-time quantum walks in a background synthetic gauge field. The gauge fields aregenerated by introducing the appropriate phase shifts between waveguides. Polarization-independent phase shiftslead to an Abelian or magnetic field, a case we describe in detail. We find that, in the disordered case, themagnetic field enhances transport due to the presence of topologically protected chiral edge states that do notlocalize. Polarization-dependent phase shifts lead to effective non-Abelian gauge fields, which could be adoptedto realize Rashba-like quantum walks with spin-orbit coupling. Our work introduces a flexible platform for theexperimental study of multiparticle quantum walks in the presence of synthetic gauge fields, which paves theway towards topologically robust transport of many-body states of photons