Testing the limits of the Maxwell distribution of velocities for atoms flying nearly parallel to the walls of a thin cell

TL;DR

This study experimentally probes the velocity distribution of atoms moving nearly parallel to the walls in a thin vapor cell, testing the validity of the Maxwell-Boltzmann law in this constrained geometry.

Contribution

It introduces a novel pump-probe experimental method to analyze atomic velocity distributions parallel to cell surfaces in thin vapor cells.

Findings

No deviation from Maxwell-Boltzmann law for slow atoms with velocities 5-20 m/s.

Effective probing of atomic velocities nearly parallel to the surface.

Method demonstrates potential to explore surface effects on atomic velocity distributions.

Abstract

For a gas at thermal equilibrium, it is usually assumed that the velocity distribution follows an isotropic 3-dimensional Maxwell-Boltzmann (M-B) law. This assumption classically implies the assumption of a "cos theta" law for the flux of atoms leaving the surface, although such a law has no grounds in surface physics. In a variety of recently developed sub-Doppler laser spectroscopy techniques for gases one-dimensionally confined in a thin cell, the specific contribution of atoms moving nearly parallel to the boundary of the vapor container becomes essential. We report here on the implementation of an experiment to probe effectively the distribution of atomic velocities parallel to the windows for a thin (60 microns) Cs vapor cell. The principle of the set-up relies on a spatially separated pump-probe experiment, where the variations of the signal amplitude with the pump-probe separation provide the information on the velocity distribution. The experiment is performed in a sapphire cell on the Cs resonance line, which benefits of a long-lived hyperfine optical pumping. Presently, we can analyze specifically the density of atoms with slow normal velocities ~ 5-20 m/s, already corresponding to unusual grazing flight theta at ~85{\deg}-88.5{\deg} from the normal to the surface and no deviation from the M-B law is found within the limits of our elementary set-up. Finally we suggest tracks to explore more parallel velocities, when surface details -roughness or structure- and the atom-surface interaction should play a key role to restrict the applicability of a M-B-type distribution.