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  • Letter
  • Open Access

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

Francesc Sabater1,2, Abel Rojo-Francás1,2, Grigori E. Astrakharchik3, and Bruno Juliá-Díaz1,2

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Phys. Rev. Research 7, L032007 – Published 7 July, 2025

DOI: https://doi.org/10.1103/cqkw-bf3v

Abstract

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.

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Phys. Rev. Research 7, L032007– Published 7 July, 2025
  • Received 19 July 2024
  • Revised 19 November 2024
  • Accepted 12 June 2025
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