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- Mean-field thermodynamics of a spin-polarized spherically trapped Fermi gas at unitarity
- Liu, Xia-Ji; Hu, Hui; Drummond, P. D.
- We calculate the mean-field thermodynamics of a spherically trapped Fermi gas with unequal spin populations in the unitarity limit, comparing results from the Bogoliubov-de Gennes equations and the local density approximation. We follow the usual mean-field decoupling in deriving the Bogoliubov-de Gennes equations and set up an efficient and accurate method for solving these equations. In the local density approximation we consider locally homogeneous solutions, with a slowly varying order parameter. With a large particle number these two approximation schemes give rise to essentially the same results for various thermodynamic quantities, including the density profiles. This excellent agreement strongly indicates that the small oscillation of order parameters near the edge of trap, sometimes interpreted as spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states in previous studies of Bogoliubov-de Gennes equations, is a finite-size effect. We find that a bimodal structure emerges in the density profile of the minority-spin state at finite temperature, as observed in experiments. The superfluid transition temperature as a function of the population imbalance is determined and is shown to be consistent with recent experimental measurements. The temperature dependence of the equation of state is discussed.
- Publication type
- Journal article
- Physical Review A, Vol. 75, no. 2 (2007), article no. 023614
- Publication year
- FOR Code(s)
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics; 0204 Condensed Matter Physics; 0205 Optical Physics
- Approximation theory; Bogoliubov-de Gennes equations; Equations of state; Fermi gas; Fermi liquids; Fermion systems; Ground state; Local density approximation; Numerical methods; Polarization; Size effect; Spin systems; Superconducting transition temperature; Superfluidity; Thermodynamics
- American Physical Society
- Publisher URL
- Copyright © 2007 The American Physical Society. Published version of this paper reproduced here in accordance with the copyright policy of the publisher.
- Full text
- Peer reviewed