Motional Broadening in Ensembles With Heavy-Tail Frequency Distribution

TL;DR

This paper demonstrates that ensembles with heavy-tail frequency distributions can experience motional broadening, contrasting with the traditional motional narrowing, and provides conditions and formulas for this phenomenon.

Contribution

It establishes the conditions for motional broadening in ensembles with heavy-tailed distributions and derives the resulting lineshape and width.

Findings

Motional broadening occurs with heavy-tail distributions.

The lineshape is Lorentzian in the motional-broadened regime.

Motional broadening persists despite physical cutoffs.

Abstract

We show that the spectrum of an ensemble of two-level systems can be broadened through `resetting' discrete fluctuations, in contrast to the well-known motional-narrowing effect. We establish that the condition for the onset of motional broadening is that the ensemble frequency distribution has heavy tails with a diverging first moment. We find that the asymptotic motional-broadened lineshape is a Lorentzian, and derive an expression for its width. We explain why motional broadening persists up to some fluctuation rate, even when there is a physical upper cutoff to the frequency distribution.