Resonance superfluidity: Renormalization of resonance scattering theory

Abstract

We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-T c behavior of the system, and predicts a value of T c that is a significant fraction of the Fermi temperature. It is shown that this mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory, we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic 6 Li.

Resonant dynamics in boson-fermion mixtures

“…The corresponding masses of these atoms and molecules, and the trapping potentials confining them are indexed by f, b and m to indicate fermionic atoms, bosons and molecules, respectively. In the last term we stress that the parameter ν bare appearing in the Hamiltonian (3) is the bare molecular binding energy [10]. The true binding energy ν (B) given in (2) differs from this quantity due to virtual dissociations of the molecules.…”

“…The two terms appearing in |ψ(t) , expression (15) give rise to the corresponding two terms in f (t), expression (10), and in m(t), expression (11). The first term (the first line in expressions (10), (11)) is related to the bound state and the second term (containing the integration over ω) is related to the excited states.…”

“…A good description of the scattering physics near a Feshbach resonance can be obtained by explicitly introducing molecules [9,10]. These molecular states are the bound states of an interatomic potential in a closed channel and their energy relative to the threshold is given by…”

“…In evaluating the integral in (8), we have used the relation between the real and bare molecular binding energy, ν and ν bare , for a momentum cutoff K [10]: ν = ν bare − Kg 2 m m r /(π ) 2 .…”

Medium effects close tos- andp-wave Feshbach resonances in atomic Fermi gases

“…In the vicinity of a Feshbach resonance, the s-wave scattering length a(B) is described approximately by [28] …”