Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas

v3: 4 pages, 2 figures, revtex4. Section on the fermionic TG gas on a ring revised, emphasizing degeneracy of ground state for even N and resultant high sensitivity to external fields.We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that the two-particle reduced density matrix exhibits maximal off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement we show that during an expansion the momentum distribution undergoes a "dynamical bosonization", approaching that of an ideal Bose gas without violating the Pauli exclusion principle