Collective Oscillations in ultracold trapped gases

An ultracold gas is considered as the coldest matter in the Universe. Thanks to its very low temperature, the quantum effects become very evident, by making the distinction between bosons and fermions more and more important. As a consequence of the quantum nature, many completely new and amazing physical properties appear which are not present in normal matter. Among them, I will focus on a macroscopic phenomenon of this kind of gases: the collective oscillations whose importance lies in considering them as an useful test to probe the superfluidity (absence of the viscosity) present in an ultracold gas. I have studied collective oscillations in the theoretical framework of the Hydrodynamic Theory and I will show the power of this very general approach in the study of ultracold gases for both quantum statistics, all dimensions and different geometrical regimes.

Collective Oscillations for harmonically trapped Fermi and Bose atomic ultracold quantum gases

The observation of collective oscillations for an harmonically trapped ultracold gas is a very useful tool to characterize the properties of its superfluid state. A general overview of the meaning of superfluidity for fermions within the Bardeen-Cooper-Schrieffer (BCS) theory and its analogies with the Bose-Einstein Condensation (BEC) for bosons will be discussed. These two phenomenons belong to the low-energy Physics world where the quantum effects are strongly increased and we can divide the particles, and in particular the atomic gases, between two statistics: Fermi-Dirac and Bose-Einstein. A very important theoretical tool to describe the condensate is the Gross-Pitaevskii (GP) equation, which, written in its generalized form, sketch out Fermi as well Bose quantum gases. Hydrodynamic equations, which embodies the superfluid nature of the gas, can be derived from the GP equation and from them, the wave equation, whose solutions are the collective frequencies, is deduced.

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