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

TL;DR

This paper investigates the exact static and dynamic properties of the fermionic Tonks-Girardeau gas, revealing its superfluid-like order, degeneracy, and a dynamical transition to bosonic behavior during expansion.

Contribution

It provides the first exact analysis of the FTG gas's properties, including off-diagonal long-range order and dynamical bosonization, highlighting novel quantum phenomena in strongly interacting 1D Fermi gases.

Findings

Maximal off-diagonal long-range order in the two-particle density matrix

Degenerate ground states with quantized rotational flux on a ring

Momentum distribution approaches that of an ideal Bose gas during expansion

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 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.