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arXiv:cond-mat/0505306 · Bulletin of the American Physical Society

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

S. Gaudio, Jason Jackiewicz, Kevin S. Bedell

Published May 11, 2005• 0 citations
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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.

DOI
10.48550/arxiv.cond-mat/0505306

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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.
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.
Many-body effects may influence properties, such as scattering parameters, nature of pairing, etc., close to a Feshbach resonance in the fermion BEC-BCS crossover problem. We study effects such as these using a tractable crossing-symmetric approach. This method allow us to include quantum fluctuations, such as density, current, spin, spin-current, and the higher-order fluctuations in a self-consistent fashion. The underlying fermion interaction is reflected in the ``driving'' term. We perform calculations here on both Bose-Einstein condensate (BEC) and BCS sides and taking the driving term to be finite range and of arbitrary strength. These are related to two-body singlet and triplet scattering parameters and can be connected with experimental sss- and ppp-wave Feshbach resonances. We include the $\ensuremath{\ell}=0$ density and spin fluctuations as well as $\ensuremath{\ell}=1$ current and spin-current fluctuations. We calculate renormalized scattering amplitudes, pairing amplitudes, nature of pairing, etc., on both the BEC and BCS sides. We then compare our results qualitatively with experiments.
We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length, aF,a_{F},aF​, and the effective range parameter, re.r_{\mathrm{e}}.re​. In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances. By matching two-body scattering properties near a Feshbach resonance to a simple renormalized model potential, a broad resonance is characterized by a small effective range and the gas displays a universal BCS-BEC crossover behavior. On the other hand, for a narrow resonance thermodynamic quantities depend the effective range which may be large and negative at resonance. For increasing values of −re-r_{\mathrm{e}}−re​ we find the transition temperature to be suppressed in the crossover region. We furthermore argue for existence of a lower bound of TcT_{c}Tc​ at fixed coupling for increasing −re-r_{\mathrm{e}}−re​ in the crossover region.
We investigate the effective interaction between Cooper-pair molecules in the st rong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analy sis of fluctuations in a single-channel model. We show that a physical cutoff en ergy ωcω_cωc​ originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work t hus clarifies recent results by showing that aM=2aFa_{\rm M}=2a_{\rm F}aM​=2aF​ is a {\it ba re} molecular scattering length while aM=(0.6∼0.75)aFa_{\rm M}=(0.6\sim0.75) a_{\rm F}aM​=(0.6∼0.75)aF​ is the low energy molecular scattering length renormalized to include high-energy scat tering up to ωcω_cωc​ (here aFa_{\rm F}aF​ is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that aMa_{\rm M}aM​ is strongly dependent on temperature, vanishing at TcT_{\rm c}Tc​, consistent with the earlier Bose gas results of Bijlsma and Stoof.
We consider the problem of spin-triplet ppp-wave superfluid pairing with total spin projection ms=0{m}_{s}=0ms​=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 ppp-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 investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasimolecules with finite orbital angular momenta Lz=+/-1,0, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper pairs and molecules which are not Bose condensed.