Many body exchange effects close to the s-wave Feshbach resonance in two-component Fermi systems: is a triplet superfluid possible?

Abstract

We suggest that the exchange fluctuations close to a Feshbach resonance in a two-component Fermi gas can result in an effective p-wave attractive interaction. On the BCS side of a Feshbach resonance, the magnitude of this effective interaction is comparable to the s-wave interaction, therefore leading to a possible spin-triplet superfluid in the range of temperatures of actual experiments. We also show that the particle-hole exchange fluctuations introduce an effective scattering length which does not diverge, as the standard mean-field one does. Finally, using the effective interaction quantities we are able to model the molecular binding energy on the BEC side of the resonance.In the atomic Fermi gases such as 40 K and 6 Li, the use of Feshbach resonances has opened the possibility of exploring the very interesting limit for which the mean-field approximation predicts a smooth crossover from BEC to BCS pairing as one goes through the resonance. At low energies, the interatomic interaction is very well described by the s-wave scattering length, a s . Moreover, no direct interactions are possible in the triplet channel. In fact, higher-order expansions in the scattering length are suppressed at very low temperatures and the symmetry of the wave function, due to Pauli exclusion, does not allow s-wave scattering for fermionic atoms in the same spin channel.ô Although the scattering length in the two-body problem is diverging, it is instructive to consider the possibility of pairing in the higher-order scattering channels due to exchange fluctuations. It is also not clear whether atomic systems behave as Fermi liquids (FL), or how similar they are with high T c superconductors (HTSC) or any other strongly correlated systems.In this Letter, we want to show two things. Firstly, that it is possible to build a Fermi liquid theory (FLT) in the atomic Fermi gases, particularly in the *Corresponding author. Email: sergio.gaudio@roma1.infn.it ôFor the sake of clarity, throughout the paper, triplet pairing corresponds to pairing between particles in the same spin channel and s-wave to pairing in different spin channels.

Superfluid amplitude fluctuations aboveTcin a unitary Fermi gas

“…These numbers are independent of the density at unitarity so the thermodynamic scaling is just like what we found for the local model but with a smaller value for T s . We also found that when we use the s-p approximation 7,22 to construct the scattering amplitude from our Fermi liquid parameters we get better fits for some of our calculated properties. These include, T c and E b , where T c ≈ 0.14T F and E b ≈ −0.3E F .…”

“…By choosing F a 0 = 1.7 and plotting the sum of the classical and low temperature limit of the spin diffusion coefficient given by (Eq.20), we are able to present for the Fermi liquid parameter, F s 0 , and the thermodynamic scaling temperature, T s , as well as T c . In earlier publications 18,22 we used the momentum dependent induced interaction which generated Fermi liquid parameters with l > 0. In the unitary limit the induced interaction gives a small mass correction, about 15% above the bare mass, and it gives an F s 0 = −0.6.…”

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

“…The crossing-symmetric method [14][15][16] [18], paramagnetic metals [16], heavy-fermion systems [19], nuclear matter [20], and ultracold atomic Fermi gases [21]. It has been known [14,19,22,23] that a consistent Fermi-liquid theory cannot be formulated in terms of short-range effective interactions alone; collective excitations generated by these must be exchanged between quasiparticles.…”

“…The physics is described in terms of the Landau interaction parameters and scattering amplitudes to be discussed. In a previous study Gaudio et al [21] considered s-wave scattering by including ℓ = 0 density and spin fluctuation. We shall study s-and pwave scattering and include both ℓ = 0 density and spin fluctuations and ℓ = 1 current and spin-spin fluctuations.…”

Triplet Pair Correlations ins-Wave Superfluids as a Signature of the Fulde-Ferrell-Larkin-Ovchinnikov State

“…[25,26], corresponding to an interaction to kinetic energy ratio of −mg 1D / 2 = 1.6. It has been recently noted [27][28][29][30] that, in the normal (non-BCS condensed) phase, the intra-species interaction can be strongly modified (and in particular turned attractive) by the polarization of the medium. As a consequence, at sufficiently low temperatures, normal phases are unstable against the formation of intra-species p-wave superfluids.…”