Four-Dimensional Quantum Hall Effect with Ultracold Atoms

TL;DR

This paper proposes a feasible method to observe the four-dimensional quantum Hall effect using ultracold atoms in optical lattices, enabling exploration of higher-dimensional topological phases through synthetic dimensions.

Contribution

It introduces a realistic experimental scheme to detect 4D quantum Hall effects with ultracold atoms, connecting topological invariants to measurable responses.

Findings

Identification of quantized current responses related to 4D topology

Proposed protocols for measuring the second Chern number

Feasibility of simulating 4D topological phases with current technology

Abstract

We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semi-classical analysis, we identify the linear and non-linear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological 2nd Chern number. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.