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arXiv:cond-mat/0601321 · Physical Review A

Pairing of a trapped resonantly interacting fermion mixture with unequal spin populations

Masudul Haque, Henk T. C. Stoof

Published Jul 18, 2006• 83 citations
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Abstract

We consider the phase separation of a trapped atomic mixture of fermions with unequal spin populations near a Feshbach resonance. In particular, we determine the density profile of the two spin states and compare with the recent experiments of Partridge et al. [Science 311, 503 (2006)]. Overall we find quite good agreement. We identify the remaining discrepancies, which provide important clues for the complete understanding of the experiment.

DOI
10.1103/physreva.74.011602

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We consider the phase separation of a trapped atomic mixture of fermions with unequal spin populations near a Feshbach resonance. In particular, we determine the density profile of the two spin states and compare with the recent experiments of Partridge et al. [Science 311, 503 (2006)]. Overall we find quite good agreement. We identify the remaining discrepancies, which provide important clues for the complete understanding of the experiment.
We investigate the phase separation of resonantly interacting fermions in a trap with imbalanced spin populations, both at zero and at finite temperatures. We directly minimize the thermodynamical potential under the local density approximation instead of using the gap equation, as the latter may give unstable solutions. On the BEC side of the resonance, one may cross three different phases from the trap center to the edge; while on the BCS side or at resonance, typically only two phases show up. We compare our results with the recent experiment, and the agreement is remarkable.
We investigate trapped resonant fermions with unequal populations within the local density approximation above the superfluid transition temperature. By tuning the attractive interaction between fermions via Feshbach resonance, the system evolves from weakly interacting fermi gas to strongly interacting fermi gas, and finally becomes a Bose-Fermi mixture. The density profiles of fermions are examined and compared with experiments. We also point out the simple relationships between the local density, the axial density, and the gas pressure within the local density approximation.
The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.
We study via mean-field theory the pairing between fermions of different masses, especially at the unitary limit. At equal populations, the thermodynamic properties are identical with the equal mass case provided an appropriate rescaling is made. At unequal populations, for sufficiently light majority species, the system does not phase separate. For sufficiently heavy majority species, the phase separated normal phase have a density larger than that of the superfluid. For atoms in harmonic traps, the density profiles for unequal mass fermions can be drastically different from their equal-mass counterparts.