Phase space density limitation in laser cooling without spontaneous emission

We study the possibility to enhance the phase space density of non-interacting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the atomic motion is more reliable than semi-classical description which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position - momentum phase space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum phase space density, can only be improved by a factor M for M-level atoms. This bound comes from a transfer between the external and internal degrees of freedom. To circumvent this limit, one can use non-coherent light fields, informational feedback cooling schemes, involve collectives states between fields and atoms, or allow a single spontaneous emission even