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Equal-spin and opposite-spin density-density correlations in the BCS-BEC crossover: Gauge symmetry, Pauli exclusion principle, Wick's theorem, and experiments

Nikolai Kaschewski1,*, Axel Pelster1, and Carlos A. R. Sá de Melo2

  • *Contact author: kaschews@rptu.de
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Phys. Rev. A 114, 023323 – Published 25 August, 2026

DOI: https://doi.org/10.1103/xjhs-7z5w

Abstract

We develop a general theory of spin-dependent density-density correlations, that is valid for any temperature, interactions, dimensions, and mass or population status of Fermi gases with two internal states. We use gauge invariance and the Pauli principle to establish constraints on the spin-dependent density-density correlations that are consistent with the fluctuation-dissipation and Wick's theorem. As an example, we study the spin-dependent density-density correlations from the BCS to the Bose regime in two dimensions at zero temperature, inspired by recent continuum quantum gas microscope experiments in Li6. We show that two-particle irreducible contributions, involving collective excitations, many-particle scattering, and vertex corrections, are essential to describe the experimental data. In particular, the two-particle irreducible terms are responsible for the emergence of an experimentally observed minimum in the opposite-spin density-density correlations.

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Phys. Rev. A 114, 023323– Published 25 August, 2026
  • Received 11 March 2026
  • Accepted 30 July 2026
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