Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases

We investigate some exact static and dynamic properties of one-dimensional fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive p-wave interactions induced by a Feshbach resonance. A closed form solution for the one-body density matrix for harmonic trapping is analyzed in terms of its natural orbitals, with the surprising result that for odd, but not for even, numbers of fermions the maximally occupied natural orbital coincides with the ground harmonic oscillator orbital and has the maximally allowed fermionic occupancy of unity. The exact dynamics of the trapped gas following turnoff of the p-wave interactions are explored.