  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
