Universal composite boson formation in strongly interacting one-dimensional fermionic systems

TL;DR

This paper investigates the formation of composite bosons in strongly interacting one-dimensional fermionic systems, revealing universal occupation patterns and pairing mechanisms that resemble Bose-Einstein condensation.

Contribution

It provides analytical expressions for the eigenvalues of the one-body density matrix and demonstrates the universality of occupation numbers regardless of external potential shape.

Findings

Occupation numbers are universal and independent of potential shape.

Fermionic pairs form composite bosons with paired natural orbital occupation.

Density matches that of a Bose-Einstein condensate.

Abstract

Attractive $p$-wave one-dimensional fermions are studied in the fermionic Tonks-Girardeau regime in which the diagonal properties are shared with those of an ideal Bose gas. We study the off-diagonal properties and present analytical expressions for the eigenvalues of the one-body density matrix. One striking aspect is the universality of the occupation numbers which are independent of the specific shape of the external potential. We show that the occupation of natural orbitals occurs in pairs, indicating the formation of composite bosons, each consisting of two attractive fermions. The formation of composite bosons sheds light on the pairing mechanism of the system orbitals, yielding a total density equal to that of a Bose-Einstein condensate.