Mean-field analysis of dimensional crossover from two dimensions to three dimensions in a weakly interacting Fermi gas

We investigate theoretically the transition from two to three dimensions in a weakly interacting ultracold Fermi gas. This transition was recently observed by Dyke et al. [Phys. Rev. Lett. 106, 105304 (2011)] in a cloud of fermionic Li-6 atoms trapped in an oblate harmonic potential. We calculate the density distribution and cloud size of the Fermi cloud by numerically solving three-dimensional Hartree-Fock mean-field equations. Local density approximation is used to ease the calculations in the weakly confined radial direction. Our theoretical results are shown to be in good agreement with the experimental measurements.