Mean-field thermodynamics of a spin-polarized spherically trapped Fermi gas at unitarity

Journal Article · Thu Feb 15 00:00:00 EST 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.75.023614· OSTI ID:20982165

Liu, Xia-Ji; Drummond, Peter D ^[1]; Hu, Hui ^[1]

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1. ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Queensland 4072 (Australia)

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.

• OSTI ID: 20982165
• Journal Information: Physical Review. A, Vol. 75, Issue 2; Other Information: DOI: 10.1103/PhysRevA.75.023614; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
BOGOLYUBOV METHOD
COMPUTER CALCULATIONS
DECOUPLING
DENSITY
EQUATIONS OF STATE
FERMI GAS
FERMIONS
MATHEMATICAL SOLUTIONS
MEAN-FIELD THEORY
ORDER PARAMETERS
SPIN
SPIN ORIENTATION
SUPERFLUIDITY
TEMPERATURE DEPENDENCE
THERMODYNAMICS
TRANSITION TEMPERATURE
TRAPPING
TRAPS
UNITARITY