Parity effect in a mesoscopic Fermi gas

TL;DR

This paper presents an analytic theory explaining the odd-even particle number effects in a one-dimensional trapped Fermi gas, highlighting the dominance of density corrections over pairing fluctuations, and matches experimental data.

Contribution

The paper introduces a comprehensive analytic framework that accounts for trap effects, pairing fluctuations, and Hartree corrections, providing a quantitative description of the parity effect in mesoscopic Fermi gases.

Findings

Excellent agreement with experimental data and exact diagonalization.

Density (Hartree) correction dominates over pairing fluctuations.

Provides insight into the crossover from mesoscopic to many-body physics.

Abstract

We develop a quantitative analytic theory that accurately describes the odd-even effect observed experimentally in a one-dimensional, trapped Fermi gas with a small number of particles [G. Z\"urn et al., Phys. Rev. Lett. 111, 175302 (2013)]. We find that the underlying physics is similar to the parity effect known to exist in ultrasmall mesoscopic superconducting grains and atomic nuclei. However, in contrast to superconducting nanograins, the density (Hartree) correction dominates over the superconducting pairing fluctuations and leads to a much more pronounced odd-even effect in the mesoscopic, trapped Fermi gas. We calculate the corresponding parity parameter and separation energy using both perturbation theory and a path integral framework in the mesoscopic limit, generalized to account for the effects of the trap, pairing fluctuations, and Hartree corrections. Our results are in an excellent quantitative agreement with experimental data and exact diagonalization. Finally, we discuss a few-to-many particle crossover between the perturbative mesoscopic regime and non-perturbative many-body physics that the system approaches in the thermodynamic limit.