Superfluid Fermi Gases with Large Scattering Length

Abstract

We report quantum Monte Carlo calculations of superfluid Fermi gases with short-range two-body attractive interactions with infinite scattering length. The energy of such gases is estimated to be (0.44 ± 0.01) times that of the noninteracting gas, and their pairing gap is approximately twice the energy per particle. PACS: 03.75.Fi, 05.30.Fk, 21.65.+F In dilute Fermi gases the pair interactions have a range much smaller than the interparticle spacing. However, when the two-particle scattering length is large, these short range interactions can modify the gas properties significantly. A well known example is low density neutron matter which may occur in the inner crust of neutron stars [1]. The two-neutron interaction has a range of ∼ 2 fm, but the scattering length is large, −18 fm, so that even at densities as small as one percent of the nuclear density the parameter ak F has magnitude much larger than one. Bertsch proposed in 1998 that solution of the idealized problem of a dilute Fermi gas in the limit ak F → −∞ could give useful insights into the properties of low density neutron gas.Cold dilute gases of 6 Li atoms have been produced in atom traps. The interaction between these atoms can be tuned using a known Feshbach resonance; and the estimated value of ak F in the recent experiment [2] is ∼ −7.4. As the interaction strength is increased beyond that for a = −∞, we get bosonic two-fermion bound states. In this sense a dilute Fermi gas with large a is in between weak coupling BCS superfluid and dilute Bose gases with Bose-Einstein condensation [3]. Attempts to produce Bose gases in the limit, a/r 0 → ∞ using Feshbach resonances [4,5], are in progress, and their energy has been recently estimated using variational methods [6].In the a → −∞ limit k 2 F /m is the only energy scale, and the ground state energy of the interacting dilute Fermi gas is proportional to the noninteracting Fermi gas energy:Baker [7] and Heiselberg [8] have attempted to obtain the value of the constant ξ from expansions of the Fermi gas energy in powers of ak F . Heiselberg obtained ξ = 0.326, while Baker's values are ξ = 0.326 and 0.568. Fermi gases with attractive pair interaction become superfluid at low temperature. The BCS expressions in terms of the scattering length were given by Leggett [9], and they were used to study the properties of superfluid dilute Fermi gases, as a function of ak F , by Engelbrecht, Randeria and Sá de Melo [10]. For ak F = −∞ they obtain an upperbound, ξ = 0.59, using the BCS wave function. These gases are also estimated to have large gaps comparable to the ground state energy per particle.Here we report studies of Fermi gases with quantum Monte Carlo methods using the model potential:The zero energy solution of the two-body Schrödinger equation with this potential is tanh(µr)/r and corresponds to a = −∞. The effective range is 2/µ, and in order to ensure that the gas is dilute we use µr 0 > 10, where r 0 is the unit radius; ρr 3 0 = 3/4π. All the results presented here are for µr 0 = 12; however some ...

Many body methods and effective field theory

“…In order to test this idea we have calculated particle ladders for arbitrary D. We find that if the coupling constant is scaled appropriately then all particle ladders are indeed of the same order in 1/D. We also find that the universal parameter ξ is given by ξ = 1/2, in surprisingly good agreement with the Green function Monte Carlo result ξ = 0.44 [32]. We also verified that the contribution from the pairing energy is suppressed by 1/D.…”

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

“…This may easily be seen from the fact that at early times, where few interactions have occurred, the correlation function falls off exponentially like that of free fermions with a Z-factor near unity. A better approach is to incorporate pairing correlations into the interpolating field by constructing sources and sinks out of two-fermion wave functions [32]. In practice, such an approach may only be carried out at the sink, however, because our numerical approach requires that sources be separable functions; this is none-the-less adequate to achieve far superior overlap with the ground state.…”

Occupation-number-based energy functional for nuclear masses

“…(22) to be the best choice for lowering our least-squares deviation. Equations (25) and (26) were determined similarly, from very large sets of possible terms. In this way we successfully lowered the functional's least-squares error to a meaningful χ = 1.31 MeV with 17 fit parameters.…”

“…Furnstahl and colleagues [22][23][24] derived energy-density functionals for dilute Fermi gases with short-ranged interactions. For Fermi gases in the unitary regime, simple scaling arguments suggest the form of the energy-density functional [25][26][27][28]. We similarly use scaling arguments in the development of our functional.…”