Superfluid transition in quasi-two-dimensional Fermi gases

Abstract

We show that atomic Fermi gases in quasi2D geometries are promising for achieving superfluidity. In the regime of BCS pairing for weak attraction, we calculate the critical temperature Tc and analyze possibilities of increasing the ratio of Tc to the Fermi energy. In the opposite limit, where a strong coupling leads to the formation of weakly bound quasi2D dimers, we find that their Bose-Einstein condensate will be stable on a long time scale. 03.75.Fi,05.30.Fk Recent progress in trapping and cooling of Fermi isotopes of K [1,2] and Li [3,4,5,6] has shown the ability to go far below the temperature of quantum degeneracy and to manipulate independently the trapping geometry, density, temperature and interparticle interaction. The Duke experiment [7] presents intriguing results on the possibility of achieving a superfluid phase transition in the two-component Fermi gas of 6 Li.Two-dimensional Fermi gases have striking features not encountered in 3D. In the superfluid state, thermal fluctuations of the phase of the order parameter strongly modify the phase coherence properties. The interaction strength depends logarithmically on the relative energy of the colliding atoms. For degenerate Fermi gases this energy is of the order of the Fermi energy ε F which is proportional to the 2D density n. Accordingly, the exponential dependence of the BCS transition temperature on the interaction strength transforms into a power law dependence on the density: T c ∝ n 1/2 [13,14]. This suggests a unique possibility to cross the critical point by adiabatically expanding a degenerate Fermi gas. Since the ratio T /ε F remains unchanged, the temperature scales as n and decreases with density faster than T c .Experimentally it is possible to achieve the quasi2D regime by confining the atoms in one direction so tightly that the corresponding level spacing exceeds the Fermi energy. Under this condition the degenerate Fermi gas is kinematically two-dimensional. Thus far, this regime has been reached for Cs atoms [8,9,10] and for Bose-Einstein condensates of Na [11] and Rb [12].In the quasi2D regime the mean-field interaction between particles exhibits a similar logarithmic dependence on the particle energy as in the purely 2D case [15]. The amplitude of the s-wave scattering turns out to be sensitive to the strength of the tight confinement [15]. This opens new handles on manipulations of the interparticle interaction and superfluid pairing.In this Rapid Communication we show that atomic Fermi gases in quasi2D geometries can become strong competitors of 3D gases in achieving superfluidity. The ability to increase the interparticle interaction by tuning the trap frequencies gives an opportunity to realize a transition from the standard BCS pairing in the case of weak attraction to the limit of strong interactions and pairing in coordinate space. In the latter case one eventually gets a dilute system of weakly bound quasi2D dimers of fermionic atoms, which can undergo Bose-Einstein condensation. For the BCS case, we calculate the critic...

Observation of Pair Condensation in the Quasi-2D BEC-BCS Crossover

“…Each data point is the average of about 30 measurements. The dashed white line is the theoretical prediction for the BKT transition temperature given in [40].…”

Finite-temperature phase diagram of quasi-two-dimensional imbalanced Fermi gases beyond mean field

“…As in [14][15][16][17][18][19], we consider only pairing between atoms with equal and opposite momenta.…”

Fermions in Two Dimensions: Scattering and Many-Body Properties

“…703 − 2η (for the dimer scattering length a d ≈ 0.557a 2D [50]) and d = log π + 2γ + 0.5. The BCS form is given by:…”