Superradiance and anomalous hyperfine splitting in inhomogeneous ensembles

TL;DR

This paper develops a Green function-based formalism to model collective light-matter interactions in inhomogeneous ensembles, revealing how hyperfine-induced inhomogeneities affect superradiance and spectral features in waveguide systems.

Contribution

The authors introduce a new formalism for analyzing collective effects in inhomogeneous ensembles, accounting for hyperfine-induced shifts and splittings in one-dimensional waveguides.

Findings

Inhomogeneous broadening effects can be suppressed when collective coupling is large.

The formalism provides a compact formula for the collective spectrum with deviations from uniform shifts.

Application to x-ray scattering demonstrates the model's relevance to real systems.

Abstract

Collective effects in the interaction of light with ensembles of identical scatterers play an important role in many fields of physics. However, often the term ``identical'' is not accurate due to the presence of hyperfine fields which induce inhomogeneous transition shifts and splittings. Here we develop a formalism based on the Green function method to model the linear response of such inhomogeneous ensembles in one-dimensional waveguides. We obtain a compact formula for the collective spectrum, which exhibits deviations from the uniform frequency shift and broadening expected of two level systems. In particular, if the coherent contribution to the collective coupling is large, the effect of inhomogeneous broadening can be suppressed, with the linewidth approaching that of the superradiant value. We apply this formalism to describe collective effects in x-ray scattering off thin-film waveguides for inhomogeneous hyperfine parameters.