Dipole-dipole interactions mediated by a photonic flat band

TL;DR

This paper investigates how flat bands in photonic systems mediate unique, exponentially decaying dipole-dipole interactions between emitters, with a localization length that saturates near the flat band energy, revealing universal scaling laws.

Contribution

It introduces a theoretical framework for understanding photon-mediated interactions in flat band systems, highlighting the saturation of localization length and universal scaling laws for CLS overlaps.

Findings

Interaction strength decays exponentially with distance.

Localization length saturates near the flat band energy.

Universal scaling law for CLS overlap and localization length.

Abstract

Flat bands (FBs) are energy bands with zero group velocity, which in electronic systems were shown to favor strongly correlated phenomena. Indeed, a FB can be spanned with a basis of strictly localized states, the so called "compact localized states" (CLSs), which are yet generally non-orthogonal. Here, we study emergent dipole-dipole interactions between emitters dispersively coupled to the photonic analogue of a FB, a setup within reach in state-of the-art experimental platforms. We show that the strength of such photon-mediated interactions decays exponentially with distance with a characteristic localization length which, unlike typical behaviours with standard bands, saturates to a finite value as the emitter's energy approaches the FB. Remarkably, we find that the localization length grows with the overlap between CLSs according to an analytically-derived universal scaling law valid for a large class of FBs both in 1D and 2D. Using giant atoms (non-local atom-field coupling) allows to tailor interaction potentials having the same shape of a CLS or a superposition of a few of these.