Singular band Induced by Long-Range Interaction Enables Unsplit Spreading of Localized Excitations

TL;DR

This paper shows that long-range interactions cause singularities in band structures, enabling localized excitations to spread without splitting, which can serve as an experimental signature.

Contribution

It reveals that band singularities induced by long-range interactions enable unsplit spreading of localized excitations in lattice models.

Findings

Singular band features are necessary for unsplit spreading.

Unsplitted spreading observed in 1D and 2D atomic array models.

Band singularities serve as an experimental signature.

Abstract

In conventional lattice models, the dispersion relation $\omega(k)$ is assumed to be a smooth function which is periodic over the first Brillouin Zone. However, in subwavelength atom arrays the dispersion of the light-mediated long-range interaction is singular at the light cone. This observation prompts us to ask what effect arises from such band singularity. Here we demonstrate that, due to the topology of smooth functions defined over the periodic Brillouin zone, smoothness implies the splitting of an initially localized excitation into counter-propagating wave packets. Consequently, unsplit spreading can occur only when $\omega(k)$ develops singular features, precisely what long-range interactions enable. We identify unsplit spreading in 1D toy tight-bounding models and the realistic models of 1D and 2D subwavelength atomic arrays. Our work establishes unsplit spreading as an experimentally accessible, smoking-gun signature of singular band structure.