Static and dynamic properties of trapped fermionic Tonks-Girardeau gases

We investigate some static and dynamic properties of harmonically trapped fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive p-wave interactions induced by a Feshbach resonance. An exact solution for the one-body density matrix 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 orbital coincides with the ground harmonic oscillator orbital. A dynamical consequence of this is that when the interactions are turned off the on-axis density remains a maximum for an odd number of fermions, whereas a minimum develops for an even number.