The Backward Lévy

Photons in a hot atomic vapor don’t diffuse normally. They perform Lévy flights — anomalously long steps where a photon, absorbed and re-emitted at a slightly different frequency, can travel far before the next interaction. The step-size distribution has heavy tails (power-law with Lévy parameter α), producing superdiffusion that spreads faster than any Gaussian process.

This paper measures the Lévy parameter through backward-scattered fluorescence for the first time, revealing a structural asymmetry between forward and backward scattering.

Both forward transmission and backward reflection measurements yield α = 1 — the same Lévy exponent, confirming the superdiffusive character. But the backward signal contains a non-negligible fraction of single-scattering events even at high atomic densities, where forward-scattered photons are dominated by multiple scattering. The backward direction preferentially samples photons that scattered only once and reversed direction, while the forward direction filters for photons that scattered many times and maintained their general heading.

This asymmetry means the backward fluorescence signal is contaminated by ballistic photons that never performed a Lévy walk at all — they just bounced once and came back. At high density, where the mean free path is short, the single-scattering contamination in the backward signal persists because backward collection geometrically favors the first scattering event.

The Lévy parameter is the same in both directions, but the populations contributing to it are different. Forward probes the many-scattering tail. Backward probes the few-scattering core. Same exponent, different physics.