Floquet simulators for topological surface states in isolation

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.

17 pages (main text) + 10 pages (supplemental materials)

References in corpus (4)

• A 2D Quantum Walk Simulation of Two-Particle Dynamics
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Metallic phase of the quantum Hall effect in four-dimensional space

Cited by in corpus (2)

• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Geometry-independent tight-binding method for massless Dirac fermions in two dimensions