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arXiv:cond-mat/0306302

A dilute atomic Fermi system with a large positive scattering length

Aurel Bulgac, Paulo F. Bedaque, A. C. Fonseca

Published Jun 11, 2003• 4 citations
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Abstract

We show that a dilute atomic Fermi system at sufficiently low temperatures, can display fermionic superfluidity, even in the case of a repulsive atom-atom interaction, when the scattering length is positive. The attraction leading to the formation of Cooper pairs is provided by the exchange of Bogoliubov phonons if a fraction of the atoms form a BEC of weakly bound molecules.

DOI
10.48550/arxiv.cond-mat/0306302

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We show that a dilute atomic Fermi system at sufficiently low temperatures, can display fermionic superfluidity, even in the case of a repulsive atom-atom interaction, when the scattering length is positive. The attraction leading to the formation of Cooper pairs is provided by the exchange of Bogoliubov phonons if a fraction of the atoms form a BEC of weakly bound molecules.
We study the system of a dilute gas of fermions in 3-dimensions, with attractive interactions tuned to the unitarity point, using the non-perturbative Restricted Path Integral Monte Carlo (R-PIMC) method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state Quantum Monte Carlo calculations. We identify the temperature T � � 0.70ǫF below which pairing correlations develop, and estimate the critical temperature for the superfluid transition Tc � 0.25ǫF from a finite size scaling analysis of the superfluid density. PACS numbers: The recent experiments, starting with generating a degenerate gas of cold atoms[3], the use of Feshbach resonance to tune the effective interaction between the fermions[4, 5], the measurements of the gap to identify a pairing scale[6] and the measurements of vortices[7] to identify the superfluid state, have all given an impetus to the study of superfluidity in the BCS-BEC crossover regime. The nature of superconductivity or superfluidity in a many-particle system with an increasing pairing attraction was shown [1, 2] to interpolate smoothly between the BCS regime for weak attraction between the fermions, and the Bose-Einstein condensation (BEC) regime for strong coupling. In the weak coupling regime, the Cooper pair size is much larger than the interparticle spacing, and the simultaneous pairing and condensation of fermions is well described by the BCS theory. In the strong coupling regime, fermions form strongly bound bosonic molecules at a pairing temperature scale T ∗ that is considerably higher than the BEC temperature Tc. In a two species system of fermions with an attractive interaction between them, the unitary point is defined by the divergence of the zero energy s-channel scattering length, as, for two particles in free space. The unitary point is interesting since it describes a strongly correlated system with universal properties[8]. In general, there are two length scales that define the system: the interparticle spacing ∝ n −1/3 , and the scattering length as which contains information about the interaction potential. At the unitary point however, since as diverges, all the properties of the system are described by a single length scale k −1
We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length a. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length a from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature T/T(F) approximately 10(-2). The corresponding critical final value of k(F)/a/, which leads to the BCS transition, is found to be about one-half, where k(F) is the Fermi momentum.
After the experimental realization of Bose-Einstein condensation in dilute gases of alkali atoms, experimentalists started to trap the fermionic isotopes. The degenerate state for fermions was reported in 1999. The main objective of these experiments is to obtain superfluidity of fermionic gases. When there are attractive interactions between the fermions, the Fermi sea becomes unstable with respect to the formation of atomic Cooper pairs and the system becomes a superfluid. It turns out that the existing experimental cooling techniques allow minimum temperatures for fermions of the order of the Fermi temperature. Using Feshbach resonances induced by magnetic fields enhances the effective interactions between the atoms leading to superfluid transition temperatures of the order of the Fermi energy. This is a completely new regime of fermionic superfluidity far from the BCS superconductors, He and even high- superconductors. The achievement of superfluidity on gases
We investigate the Bose-Einstein condensation of fermionic pairs in three different superfluid systems: ultracold and dilute atomic gases, bulk neutron matter, and neutron stars. In the case of dilute gases made of fermionic atoms the average distance between atoms is much larger than the effective radius of the inter-atomic potential. Here the condensation of fermionic pairs is analyzed as a function of the s-wave scattering length, which can be tuned in experiments by using the technique of Feshbach resonances from a small and negative value (corresponding to the Bardeen-Cooper-Schrieffer (BCS) regime of Cooper Fermi pairs) to a small and positive value (corresponding to the regime of the Bose-Einstein condensate (BEC) of molecular dimers), crossing the unitarity regime where the scattering length diverges. In the case of bulk neutron matter the s-wave scattering length of neutron-neutron potential is negative but fixed, and the condensate fraction of neutron-neutron pairs is studied as a function of the total neutron density. Our results clearly show a BCS-quasiunitary-BCS crossover by increasing the neutron density. Finally, in the case of neutron stars, where again the neutron-neutron scattering length is negative and fixed, we determine the condensate fraction as a function of the distance from the center of the neutron star, finding that the maximum condensate fraction appears in the crust of the neutron star.