Theory of spinor Fermi and Bose gases in tight atom waveguides

Divergence-free pseudo-potentials 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 $S_z$.

Figure 1

Log-log plot of scaled ground state energy per particle $e=2m\epsilon ∕{\hslash }^2{n}^2$ for the spatially antisymmetric spinor Fermi gas, vs dimensionless fermionic coupling constant ${\gamma }_F$.