Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices

TL;DR

This paper introduces a method using semiclassical dynamics and a time-reversal protocol to map Berry curvature in optical lattices, enabling the study of topological properties in ultracold gases.

Contribution

It presents a novel experimental protocol for measuring Berry curvature in optical lattices via wave packet dynamics and compares positive and negative forces for clarity.

Findings

Proposes a time-reversal protocol to measure Berry curvature.

Demonstrates the method on specific lattice systems with nonzero Chern number.

Discusses experimental implementation and observation of topological effects.

Abstract

We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a "time-reversal" protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice, and two "optical flux" lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.