Seeing topological edge and bulk currents in time-of-flight images

TL;DR

This paper introduces a method to directly observe topological edge and bulk currents in optical lattices implementing the Haldane model using time-of-flight imaging, demonstrating their robustness against experimental variations.

Contribution

It presents a novel methodology for directly measuring topological currents in optical lattices, including both edge and bulk currents, via time-of-flight images.

Findings

Edge and bulk currents are observable in optical lattices implementing the Haldane model.

These currents are resilient to trapping potential, temperature, and disorder.

Time-of-flight imaging can effectively capture the properties of these topological currents.

Abstract

Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions.