Direct Measurement of the Zak phase in Topological Bloch Bands

TL;DR

This paper demonstrates a method to directly measure the Zak phase, a topological invariant, in cold atom systems within optical lattices, revealing topological differences between phases of a dimerized lattice.

Contribution

It introduces a novel experimental approach combining Bloch oscillations and Ramsey interferometry to measure the Zak phase in optical lattices.

Findings

Measured a Zak phase difference of approximately pi between two dimerized phases.

Confirmed that different dimerization patterns correspond to distinct topological classes.

Established a new method for probing topological properties in cold atom systems.

Abstract

Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the modern band theory of solids. Here we report on the direct measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase - the Berry phase acquired during an adiabatic motion of a particle across the Brillouin zone - which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized optical lattice, which models polyacetylene, we measure a difference of the Zak phase equal to phi_Zak=0.97(2)pi for the two possible polyacetylene phases with different dimerization. This indicates that the two dimerized phases belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands in optical lattices.