We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state
(T=0) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the
s-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature
(T=Tc), and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near
Tc, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.
We consider the problem of spin-triplet
p-wave superfluid pairing with total spin projection
ms=0 in atomic Fermi gas across the Feshbach resonance. We allow for imbalanced populations and take into account the effects due to the presence of a harmonic trapping potential. Within the mean-field approximation for the one- and two-channel pairing models we show that the
p-wave superfluid state has the lowest energy up to some distance from the trap center, the distance depending on population imbalance and the side of the Feshbach resonance (BCS or BEC) the system is in. Beyond this, the system is in the normal state. Since the system, even in the presence of the harmonic trap, is invariant under O(3) space rotation, the superfluid cores which emerge in the trap are comprised of states that are degenerate with respect to the ``orbital ferromagnet'' state, ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$, as well as the ones in which all angular momentum components of the order parameter are nonzero, provided the modulus of the order parameter maintains a fixed magnitude.
We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions [2019 {\rm J. Phys. B: At. Mol. Opt. Phys.} {\bf 52}, 165004]. Using exact scattering solution of the potential, we derive two-body
T-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitarity regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitarity limits is found to be
0.42EF which is quite close to the recent result of the quantum Monte Carlo simulation [2018 {\rm Phys. Rev.A} {\bf 97}, 013601]. The chemical potential in the zero range limit also agrees well with that for the contact potential.
We define the three-body scattering hypervolume
DF for identical spin-polarized fermions in two dimensions by considering the wave function of three such fermions colliding at zero energy and zero orbital angular momentum. We derive the asymptotic expansions of such a wave function when three fermions are far apart or one pair and the third fermion are far apart, and
DF appears in the coefficients of such expansions. For weak-interaction potentials, we derive an approximate formula of
DF by using the Born expansion. We then study the shift of energy of three such fermions in a large periodic area due to
DF. This shift is proportional to
DF times the square of the area of the triangle formed by the momenta of the fermions. We also calculate the shifts of energy and of pressure of spin-polarized two-dimensional Fermi gases due to a nonzero
DF and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases in two dimensions.
Abstract We calculate Bardeen–Cooper–Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions (2019 J. Phys. B: At. Mol. Opt. Phys. 52 165004). Using exact scattering solution of the potential, we derive two-body T-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitary regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated in mean-field theory with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be 0.42E F which is quite close to the recent result of the quantum Monte-Carlo simulation (2018 Phys. Rev. A 97 013601). The chemical potential in the zero range limit also agrees well with that for the contact potential.