Theory of spinor Fermi and Bose gases in tight atom waveguides

TL;DR

This paper develops a theoretical framework for understanding spinor Fermi and Bose gases in tight waveguides, deriving pseudopotentials, and exploring ground state properties and spin separation under magnetic fields.

Contribution

It introduces divergence-free pseudopotentials for spinor gases and relates fermionic and bosonic systems via Fermi-Bose mapping, analyzing ground states and spin effects.

Findings

Ground states depend on even and odd-wave interaction strengths.

Near a p-wave Feshbach resonance, the fermionic ground state maps to a spinless bosonic Lieb-Liniger gas.

Magnetic field gradients induce Stern-Gerlach spin separation.

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 $S_z$.