Bardeen-Cooper-Schrieffer state representation and pairing detection in the fermionic Tonks-Girardeau gas

We demonstrate that the ground state of the fermionic Tonks-Girardeau gas is a number-conserving Bardeen-Cooper-Schrieffer (BCS) state. This offers a compelling new perspective on describing the ground-state wave function of the fermionic Tonks-Girardeau gas, enabling a complete description in secon...

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Bibliographic Details
Main Authors: Francesc Sabater, Abel Rojo-Francás, Grigori E. Astrakharchik, Bruno Juliá-Díaz
Format: Article
Language:English
Published: American Physical Society 2025-07-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/cqkw-bf3v
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Summary:We demonstrate that the ground state of the fermionic Tonks-Girardeau gas is a number-conserving Bardeen-Cooper-Schrieffer (BCS) state. This offers a compelling new perspective on describing the ground-state wave function of the fermionic Tonks-Girardeau gas, enabling a complete description in second quantization. The proposed wave function is constructed based on the occupation numbers and natural orbitals of the one-body density matrix and is valid under any external potential. Specifically, we provide the exact coefficients that allow one to describe the fermionic Tonks-Girardeau gas as a number-conserving BCS state. Furthermore, the proposed wave function's form in second quantization allows us to derive the necessary expectation values to detect pairing in the fermionic Tonks-Girardeau gas. Through this approach, we demonstrate and show how to detect that the fermionic Tonks-Girardeau gas not only exhibits nontrivial quantum correlations but also is a paired state.
ISSN:2643-1564