Shell structure in the density profiles for noninteracting fermions in anisotropic harmonic confinement

Abstract

We develop a Green's function method to evaluate the exact equilibrium particle-density profiles of noninteracting Fermi gases in external harmonic confinement in any spatial dimension and for arbitrary trap anisotropy. While in a spherically symmetric configuration the shell effects are negligible in the case of large number of particles, we find that for very anisotropic traps the quantum effects due to single-level occupancy and the deviations from the Thomas-Fermi approximation are visible also for mesoscopic clouds.

4 pages, 4 figures

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• All-Optical Production of a Degenerate Fermi Gas
• Harmonically trapped fermion gases: exact and asymptotic results in arbitrary dimensions
• Phase separation in a boson-fermion mixture of Lithium atoms
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• Temperature dependence of density profiles for a cloud of non-interacting fermions moving inside a harmonic trap in one dimension

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• Shell structure in the density profile of a rotating gas of spin-polarized fermions
• Interplay between shell structure and trap deformation in dipolar fermi gases
• Revisiting the concept of chemical potential in classical and quantum gases: A perspective from Equilibrium Statistical Mechanics
• Superfluid hydrodynamics of polytropic gases:dimensional reduction and sound velocity