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Theory of spinor Fermi and Bose gases in tight atom waveguides

M. D. Girardeau·M. Olshanii
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Abstract

Divergence-free pseudopotentials for spatially even and odd-wave interactions in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose mapping method is used to relate the effectively one-dimensional fermionic many-body problem to that of a spinor Bose gas. Depending on the relative magnitudes of the even and odd-wave interactions, the N-atom ground state may have total spin S=0, S=N/2, and possibly also intermediate values, the case S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground state is space-antisymmetric and spin-symmetric. In this case the fermionic ground state maps to the spinless bosonic Lieb-Liniger gas. An external magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial separation of the corresponding trapped Fermi gas with respect to various values of $S_z$.

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M. D. Girardeau, M. Olshanii. 2004-04-29. Theory of spinor Fermi and Bose gases in tight atom waveguides. https://doi.org/10.1103/physreva.70.023608

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