Topological quantum walk in synthetic non-Abelian gauge fields

TL;DR

This paper introduces a method to implement synthetic non-Abelian gauge fields in photonic quantum walks, enabling control over topological invariants and simulation of entanglement in Floquet systems.

Contribution

It provides a novel photonic setup for realizing non-Abelian gauge fields in quantum walks, expanding the capabilities for topological and entanglement studies.

Findings

SU(2) gauge fields induce Peierls substitution in momentum and quasienergy

Photonic protocols for topological invariants are controllable via gauge fields

Non-Abelian gauge fields facilitate simulation of entanglement with polarization and spatial modes

Abstract

We theoretically introduce synthetic non-Abelian gauge fields for topological quantum walks. The photonic mesh lattice configuration is generalized with polarization multiplexing to achieve a four-dimensional Hilbert space, based on which we provide photonic building blocks for realizing various quantum walks in non-Abelian gauge fields. It is found that SU(2) gauge fields can lead to Peierls substitution in both momenta and quasienergy. In one and two dimensions, we describe detailed photonic setups to realize topological quantum walk protocols whose Floquet winding numbers and Rudner-Lindner-Berg-Levin invariants can be effectively controlled by the gauge fields. Finally, we show how non-Abelian gauge fields facilitate convenient simulation of entanglement in conjunction with polarization-dependent and spatial-mode-dependent coin operations. Our results shed light on the study of synthetic non-Abelian gauge fields in photonic Floquet systems.