We study the possibility to enhance the phase-space density of noninteracting 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 particle motion is more reliable than semiclassical 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 of the position-momentum phase-space density can only increase by a factor $M$ for $M$-level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase-space density in the same internal state.

• Received 14 June 2018

DOI:https://doi.org/10.1103/PhysRevA.98.063432