Bosonic Hofstadter butterflies in synthetic antiferromagnetic patterns

TL;DR

This paper theoretically investigates bosonic Hofstadter butterflies in synthetic antiferromagnetic patterns, revealing fractal spectra in artificial structures and proposing experimental realizations with microring resonators.

Contribution

It introduces a novel tight-binding model for bosonic Hofstadter butterflies in synthetic antiferromagnetic lattices, including next-nearest neighbor tunneling effects.

Findings

Fractal Hofstadter spectra can form even with zero gauge flux.

The model applies to square and honeycomb lattices.

Experimental setups with microring resonators are feasible.

Abstract

The emergence of Hofstadter butterflies for bosons in synthetic-gauge-field antiferromagnetic patterns is theoretically studied. We report on a specific tight-binding model of artificial antiferromagnetic structures incorporating both nearest and next-to-nearest neighbour tunnelings and allowing for the formation of the fractal spectra even with the vanishing gauge field flux through the lattice. The model is applied to square and honeycomb lattices. Possible experimental realization is suggested for the lattices of microring resonators connected by waveguides. Finally, the structure of the butterflies is analyzed for different points in the magnetic Brillouin zone for both the ferromagnetic and antiferromagnetic patterns.