We study an atomic Fermi gas interacting through repulsive contact forces in a one-dimensional harmonic trap. Bethe-ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation, the edges cause a giant increase of the separation between these modes.

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Physics Letters A

Correlated fermionic densities for many harmonically trapped particles interacting with repulsive forces

M. L. Glasser, Norman Henry March, Luis Miguel Nieto

Published Apr 15, 2010• 0 citations

Publisher

DOI: 10.1016/j.physleta.2010.02.060

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For

N

spin-polarized fermions with harmonic pair interactions in a one-dimensional trap an odd-even effect is found. The spectrum of the one-particle reduced density matrix of the system's ground state differs qualitatively for

N

odd and

N

even. This effect only occurs for strong attractive and repulsive interactions. Since it does not exist for bosons, it must originate from the repulsive nature implied by the fermionic exchange statistics. In contrast to the spectrum, the one-particle density and correlation function for strong attractive interactions do not show any sensitivity on the number parity. This also suggests that reduced-density-matrix-functional theory has a more subtle

N

dependency than density-functional theory.

C

is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.