Topological charge pumping with subwavelength Raman lattices

TL;DR

This paper introduces a new topological charge pump using subwavelength Raman lattices with coupled Rice--Mele chains, demonstrating fractional displacement per cycle through analytical and numerical methods.

Contribution

It presents a novel topological charge pump based on coupled subwavelength Rice--Mele chains created by detuning modulation in Raman lattices, revealing fractional displacement phenomena.

Findings

Topological charge pump with fractional displacement per cycle.

Analytical description using Chern numbers.

Numerical identification of edge states.

Abstract

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.