Collective oscillations of ultracold matter

We consider the collective oscillations of an ultracold atomic cloud by using a wave kinetic description which retains phonon recoil effects. We derive an exact quantum-wave dispersion relation for hybrid plasma-acoustic oscillations and the associated atomic Landau damping. The quasilinear kinetic theory is also extended into the quantum regime, leading to a Boltzmann type of equation for the atoms in a collective force field. Comparison with our previous quasiclassical results is considered. Diffusion in velocity space due to density fluctuations is discussed in detail. This will us allow to establish an additional temperature limit, different from the usual Doppler limit, below which the laser cooling process is prevented by the density fluctuations. This work could also be useful to describe low-frequency Doppler instabilities, as well as collective phonon laser processes.