Floquet simulators for topological surface states in isolation

TL;DR

This paper introduces dynamical protocols using synthetic dimensions to realize isolated topological surface states, enabling exploration of higher-dimensional topological phases without bulk support, with potential implementation in quantum optical devices.

Contribution

It proposes a novel method to engineer topological surface states via incommensurate driving frequencies, eliminating the need for a supporting bulk phase.

Findings

Analytical calculations show no 4d bulk phase needed for 3d surface states.

Numerical simulations validate the proposed protocols.

Blueprint provided for realization with existing quantum optical technology.

Abstract

We propose dynamical protocols allowing for the engineered realization of topological surface states in isolation. Our approach builds on the concept of synthetic dimensions generated by driving systems with incommensurate frequencies. As a concrete example, we consider 3d topological surface states of a 4d quantum Hall insulator via a $(1+2_\mathrm{syn})$-dimensional protocol. We present first principle analytical calculations demonstrating that no supporting 4d bulk phase is required for a 3d topological surface phase. We back the analytical approach by numerical simulations and present a detailed blueprint for the realization of the synthetic surface phase with existing quantum linear optical network device technology. We then discuss generalizations, including a proposal for a quantum simulator of the $(1+1_\mathrm{syn})$ dimensional surface of the common 3d topological insulator.