The cooling rate for cavity mediated laser cooling scales as the Lamb-Dicke
parameter eta squared. A proper analysis of the cooling process hence needs to
take terms up to eta^2 in the system dynamics into account. In this paper, we
present such an analysis for a standard scenario of cavity mediated laser
cooling with eta << 1. Our results confirm that there are many similarities
between ordinary and cavity mediated laser cooling. However, for a weakly
confined particle inside a strongly coupled cavity, which is the most
interesting case for the cooling of molecules, numerical results indicate that
even more detailed calculations are needed to model the cooling process
accurately.Comment: 15 pages, 10 figures, minor corrections, PRA (in press
