Polytropic equilibrium and normal modes in cold atomic traps

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 are 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 equilibrium of a magneto-optical trap, allowing us to describe the crossover between the two limiting cases: temperature-dominated and multiple-scattering-dominated traps. The normal collective modes of the system are also computed.