The Peierls substitution in an engineered lattice potential

TL;DR

This paper demonstrates how to engineer a one-dimensional lattice with ultracold atoms where the tunneling matrix element is complex, effectively implementing the Peierls substitution and opening pathways to simulate quantum Hall physics.

Contribution

It introduces a novel method to realize complex tunneling in a lattice using Zeeman-shifts, Raman coupling, and radiofrequency fields, enabling control over tunneling phase and amplitude.

Findings

Successfully controlled tunneling phase and amplitude.

Realized Peierls substitution in ultracold atoms.

Potential to simulate quantum Hall effects.

Abstract

Artificial gauge fields open new possibilities to realize quantum many-body systems with ultracold atoms, by engineering Hamiltonians usually associated with electronic systems. In the presence of a periodic potential, artificial gauge fields may bring ultracold atoms closer to the quantum Hall regime. Here, we describe a one-dimensional lattice derived purely from effective Zeeman-shifts resulting from a combination of Raman coupling and radiofrequency magnetic fields. In this lattice, the tunneling matrix element is generally complex. We control both the amplitude and the phase of this tunneling parameter, experimentally realizing the Peierls substitution for ultracold neutral atoms.