Gradient corrections to the local density approximation for trapped superfluid Fermi gases

Abstract

Two species superfluid Fermi gas is investigated on the BCS side up to the Feshbach resonance. Using the Greens's function technique gradient corrections are calculated to the generalized Thomas-Fermi theory including Cooper pairing. Their relative magnitude is found to be measured by the small parameter $(d/R_{TF}{)}^4$, where $d$ is the oscillator length of the trap potential and $R_{TF}$ is the radial extension of the density $n$ in the Thomas-Fermi approximation. In particular at the Feshbach resonance the universal %constant $A_{TF}$ has the %correction in the center $A=A_{TF}+A_2(d/R_{TF}{)}^4+\dot{.}.$ corrections to the local density approximation are calculated and a universal prefactor ${\kappa }_W=7/27$ is derived for the von Weizsäcker type correction ${\kappa }_W({\hslash }^2/2m)({\nabla }^2{n}^{1/2}/n^{1/2})$.

13 pages, 8 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Superfluid Bose-Fermi mixture from weak-coupling to unitarity
• Macroscopic Periodic Tunneling of Fermi Atoms in the BCS-BEC Crossover
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Expansion of a Fermi Cloud in the BCS-BEC Crossover
• Hydrodynamics of Bose and Fermi superfluids at zero temperature: the superfluid nonlinear Schrodinger equation