Superfluid pairing in a quasi-2D gas of fermionic atoms

During the last decade, several groups have successfully created quasi-2D quantum-degenerate gases of fermionic atoms. These are of interest, since 2 is the limiting dimensionality of the Mermin-Wagner theorem and so the superfluidity is fundamentally different to that in 3D. In addition, these simple systems could provide insight into the much more complicated high-Tc superconductors. We consider a population balanced two-component Fermi gas, strongly confined in one direction by a harmonic oscillator potential. The dimensionality of the system depends on the ratio of the Fermi energy to the confinement energy. At low temperatures, only atoms with opposite "spins" interact at short range. These interactions can be tuned via the Feshbach resonance mechanism. For relatively weak interactions, atoms form large Bardeen-Cooper-Schrieffer (BCS)-type pairs. However, as the interaction strength increases, the pairs become smaller and turn into composite bosons, which undergo Bose-Einstein condensation (BEC). We study the evolution of pairing in the BCS-BEC crossover within a mean field approximation. The equations for the two band problem can be solved analytically to give the first order correction to the exactly 2D mean field expressions. It is also possible to extrapolate to infinitely many harmonic oscillator bands numerically. For large enough interaction strengths and Fermi energies, these higher bands contribute significantly. We believe that recent radio frequency spectroscopy experiments have already seen evidence of this.