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arXiv:hep-ph/0312275 · Physical Review A

Cold asymmetrical fermion superfluids

Heron Caldas

Published Jun 4, 2004• 111 citations
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Abstract

In this work we investigate the general properties and the ground state of an asymmetrical dilute gas of cold fermionic atoms, formed by two particle species having different densities. We have shown in a recent paper, that a mixed phase composed of normal and superfluid components is the energetically favored ground state of such a cold fermionic system. Here we extend the analysis and verify that in fact, the mixed phase is the preferred ground state of an asymmetrical superfluid in various situations. We predict that the mixed phase can serve as a way of detecting superfluidity and estimating the magnitude of the gap parameter in asymmetrical fermionic systems.

DOI
10.1103/physreva.69.063602

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•Sep 20, 2004•0 citations
In this work we investigate the general properties and the ground state of an asymmetrical dilute gas of cold fermionic atoms, formed by two particle species having different densities. We have shown in a recent paper, that a mixed phase composed of normal and superfluid components is the energetically favored ground state of such a cold fermionic system. Here we extend the analysis and verify that in fact, the mixed phase is the preferred ground state of an asymmetrical superfluid in various situations. We predict that the mixed phase can serve as a way of detecting superfluidity and estimating the magnitude of the gap parameter in asymmetrical fermionic systems.
We study the phase structure of a dilute two-component Fermi system with attractive interactions as a function of the coupling and a finite number asymmetry or polarization. In weak coupling, a number asymmetry results in phase separation. A mixed phase containing symmetric superfluid matter and an asymmetric normal phase is favored. For strong coupling we show that the stress on the superfluid phase to accommodate a number asymmetry increases. Near the infinite-scattering length, we calculate the single-particle excitation spectrum and the ground-state energy. A picture of weakly interacting quasiparticles emerges for modest polarizations. In this regime a homogeneous phase with a finite population of quasiparticle states characterized by a gapless spectrum is favored over the phase separated state. These states may be realized in cold atom experiments.
We present the analytical results at the mean-field level for the asymmetrical fermion system with attractive contact interaction at zero temperature. The results can be expressed in terms of linear combinations of the elliptic integrals of the first and second kinds. In the limit of small gap parameter, we discuss how the asymmetry in fermion species affects the phases of the ground state of the system. In the limit of large gap parameter, we show that two candidate phases are competing for the system's ground state. The Sarma phase containing a pure Fermi fluid and a mixed condensate is favored at a large degree of asymmetry. The separated phase consisting of a pure Fermi fluid and a boson condensate supports the system at a small degree of asymmetry. The two phases are degenerate in the limit of infinite pairing gap.
We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean-field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger than a certain critical value, which increases from the weak-coupling BCS region to the strong-coupling Bose-Einstein condensation (BEC) side. In the strong-coupling BEC regime, the radii of the superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.