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[Submitted on 11 Oct 2022]

Overview: Recent experiments have demonstrated deep sub-wavelength lattices using atoms with Raman-coupled $N$ internal states with a laser of wavelength $\lambda$. The resulting unit cell was $\lambda/2N$ in extent, a $N$ reduction compared to the usual $\lambda/2$ periodicity of the optical lattice. For resonant Raman coupling, this lattice consists of $N$ independent sinusoidal potentials (period $\lambda/2$) displaced from each other by $\lambda/2N$. We show that detuning from the Raman resonance induces tunneling between these potentials. Periodically modulating the detuning couples the $s and$p bands of the potential, creating a pair of coupled subwavelength Rice-Mellet chains. This works as a novel topological charge pump that, counter-intuitively, can independently give half the capacity for each pump cycle of the individual Rhys-Melle chain. We analytically describe this behavior in terms of an infinite-system Chern number and numerically identify the associated finite-system edge states.