Polytropic equilibrium and normal modes in cold atomic traps

TL;DR

This paper models the equilibrium and collective modes of cold atomic traps considering long-range interactions caused by light scattering, bridging temperature and multiple-scattering dominated regimes.

Contribution

It introduces a generalized Lane-Emden equation to describe polytropic equilibrium in magneto-optical traps with long-range interactions.

Findings

Derived a model for equilibrium states considering long-range interactions.

Calculated the normal collective modes of the system.

Described the transition between temperature-dominated and scattering-dominated regimes.

Abstract

The compressibility limit of a cold gas confined in a magneto-optical trap due to multiple scattering of light is a long-standing problem. This scattering mechanism induces long-range interactions in the system, which is responsible for the occurrence of plasma-like phenomena. In the present paper, we investigate the importance of the long-range character of the mediated atom-atom interaction in the equilibrium and dynamical features of a magneto-optical trap. Making use of a hydrodynamical formulation, we derive a generalized Lane-Emden equation modeling the polytropic equilibirum of a magneto-optical trap, allowing us to describe the cross-over between the two limiting cases: temperature dominated and multiple-scattering dominated traps. The normal collective modes of the system are also computed.