  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.
Periodically 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 novel topological charge pump that counter-intuitively 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.
