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

M. D. Girardeau; A. Minguzzi

doi:10.1103/PhysRevLett.96.080404

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

M. D. Girardeau, A. Minguzzi

DOI 10.1103/PhysRevLett.96.080404 · Physical Review Letters

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Abstract

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 its two-particle reduced density matrix exhibits superconductive 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.