L\'evy Statistics for Random Single--Molecule Line Shapes in a Glass

TL;DR

This paper shows that the statistical fluctuations of single-molecule spectral lines in a glass at low temperature follow Le9vy statistics, confirming theoretical predictions and linking to the glass's long-range interactions.

Contribution

It experimentally verifies Le9vy statistics for single-molecule line shapes in a glass, supporting the standard tunneling model and long-range interaction theories.

Findings

Line shape fluctuations follow Le9vy statistics

Universal amplitude ratio consistent with tunneling model

Long-range interactions influence spectral behavior

Abstract

We demonstrate that the statistical behavior of random line shapes of single tetra-tert-butylterrylene chromophores embedded in an amorphous polyisobutylene matrix at T=2 K, is described by L\'evy statistics as predicted theoretically by Barkai, Silbey, and Zumofen [{\em Phys. Rev. Lett.} {\bf 84} 5339 (2000)]. This behavior is a manifestation of the long range interaction between two level systems in the glass and the single molecule. A universal amplitude ratio is investigated which shows that the standard tunneling model assumptions are compatible with the experimental data.