Equation of state of a laser cooled gas

TL;DR

This paper experimentally determines the equation of state of a laser cooled gas using a modified Lane-Emden formalism, revealing detailed insights into atomic profiles and collective interactions in large magneto optical traps.

Contribution

It introduces a novel application of the Lane-Emden formalism to laser cooled gases, incorporating multiple scattering effects into a generalized model and validating it experimentally.

Findings

Excellent agreement between model and experiment.

Ability to infer the system's equation of state from ideal gas to correlated phases.

Mapping multiple scattering effects onto controllable experimental variables.

Abstract

We experimentally determine the equation of state of a laser cooled gas. By employing the Lane-Emden formalism, widely used in astrophysics, we derive the equilibrium atomic profiles in large magneto optical traps where the thermodynamic effects are cast in a polytropic equation of state. The effects of multiple scattering of light are included, which results in a generalized Lane-Emden equation for the atomic profiles. A detailed experimental investigation reveals an excellent agreement with the model, with a two-fold significance. In one hand, we can infer on the details of the equation of state of the system, from an ideal gas to a correlated phase due to an effective electrical charge for the atoms, which is accurately described by a microscopical description of the effective electrostatic interaction. On the other hand, we are able map the effects of multiple scattering onto directly controllable experimental variables, which paves the way to subsequent experimental investigations of this collective interaction.