BCS-BEC crossover in a quasi-two-dimensional Fermi superfluid

We study the crossover from the Bardeen-Cooper-Shrieffer regime to the Bose-Einstein-condensation regime in an anisotropic trapped quantum gas of ultracold fermionic atoms. Using an effective two-dimensional Hamiltonian with renormalized interactions between atoms and dressed molecules, we extend the Gaussian pair fluctuation theory to quasi-two-dimensional systems. The equation of state, pair size and sound velocity as well as the convexity parameters of the Goldstone mode are investigated to show how Fermi superfluidity is affected by reduced dimensionality and Gaussian fluctuations at zero temperature in a wide range of crossover. We compare our results with the recent experiment of Li-6 atomic gases and find good agreements.