Flux lattices reformulated

TL;DR

This paper provides a theoretical framework for understanding and designing optical flux lattices in ultra-cold atoms, analyzing geometric potentials, gauge singularities, and topological properties with a practical laser configuration.

Contribution

It introduces a detailed theoretical analysis of flux lattices, including gauge singularities and topological characteristics, with a realistic laser setup for experimental realization.

Findings

Explicit laser configuration for flux lattice creation

Identification of phase-difference impact on magnetic flux

Calculation of Chern number indicating topological bands

Abstract

We theoretically explore the optical flux lattices produced for ultra-cold atoms subject to laser fields where both the atom-light coupling and the effective detuning are spatially periodic. We analyze the geometric vector potential and the magnetic flux it generates, as well as the accompanying geometric scalar potential. We show how to understand the gauge-dependent Aharonov-Bohm singularities in the vector potential, and calculate the continuous magnetic flux through the elementary cell in terms of these singularities. The analysis is illustrated with a square optical flux lattice. We conclude with an explicit laser configuration yielding such a lattice using a set of five properly chosen beams with two counterpropagating pairs (one along the x axes and the other y axes), together with a single beam along the z axis. We show that this lattice is not phase-stable, and identify the one phase-difference that affects the magnetic flux. Thus armed with realistic laser setup, we directly compute the Chern number of the lowest Bloch band to identify the region where the non- zero magnetic flux produces a topologically non-trivial band structure.