Floquet Simulators for Topological Surface States in Isolation

With recent advances in time-resolved device control, the dynamical engineering of novel quantum phases is becoming reality. One of the striking new options is the dynamical generation of space-synthetic dimensions, transcending the confines of static crystalline solid-state physics. We apply this principle to propose protocols allowing for the engineered realization of topological surface states in isolation. As a concrete example, we consider 3D topological surface states of a 4D quantum Hall insulator via a (1+2_{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_{syn})-dimensional surface of the common 3D topological insulator.