Topological charge pumping with subwavelength Raman lattices

Recent experiments demonstrated deeply subwavelength lattices using atoms with N internal states Raman coupled with lasers of wavelength lambda. The resulting unit cell was lambda/2N in extent, an N-fold reduction compared to the usual lambda/2 periodicity of an optical lattice. For resonant Raman coupling, this lattice consists of N independent sinusoidal potentials (with period lambda/2) displaced by lambda/2N from each other. We show that detuning from Raman resonance induces tunneling between these potentials. Temporally modulating the detuning couples the s and p bands of the potentials, creating a pair of coupled subwavelength Rice-Mele chains. This operates as a topological charge pump that counterintuitively can give half the displacement per pump cycle of each individual Rice-Mele chain separately. We analytically describe this behavior in terms of infinite-system Chern numbers and numerically identify the associated finite-system edge states.

Automated summary

Recent experiments have shown the realization of deeply subwavelength lattices using atoms with multiple internal states coupled with lasers. These lattices have smaller unit cells compared to traditional optical lattices, and detuning from resonance induces tunneling between the potentials. By modulating the detuning, coupled subwavelength Rice-Mele chains can be created, which operate as a topological charge pump. This behavior is described analytically using infinite-system Chern numbers and numerically identified finite-system edge states.