Lévy Statistics for Random Single-Molecule Line Shapes in a Glass

We demonstrate that the statistical behavior of random line shapes of single tetra-tert-butylterrylene chromophores embedded in an amorphous polyisobutylene matrix at $T=2\mathrm{K}$ is described by Lévy statistics as predicted theoretically by Barkai, Silbey, and Zumofen [ Phys. Rev. Lett. 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.