An Aharonov-Bohm interferometer for determining Bloch band topology

TL;DR

This paper introduces an atomic interferometer that measures Berry flux in momentum space, enabling direct detection of Berry curvature distribution and topological features in energy bands, with implications for quantum computing.

Contribution

It presents a novel atomic interferometer setup for measuring Berry flux in momentum space, providing high-resolution characterization of topological band structures.

Findings

Detected singular π Berry flux at Dirac points

Enabled determination of Berry curvature distribution

Established a framework for topological band characterization

Abstract

The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an Aharonov-Bohm interferometer that measures the magnetic flux penetrating a given area in real space, we realize an atomic interferometer to measure Berry flux in momentum space. We demonstrate the interferometer for a graphene-type hexagonal lattice, where it has allowed us to directly detect the singular $\pi$ Berry flux localized at each Dirac point. We show that the interferometer enables one to determine the distribution of Berry curvature with high momentum resolution. Our work forms the basis for a general framework to fully characterize topological band structures and can also facilitate holonomic quantum computing through controlled exploitation of the geometry of Hilbert space.