Parity effect in a mesoscopic Fermi gas

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. Zürn 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.

7 pages, 1 figure

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• Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
• Mesoscopic pairing without superconductivity
• Unconventional pairing in few-fermion systems at finite temperature
• Few-body perspective on fermionic pairing in one spatial dimension
• One-Dimensional Quantum Systems - From Few to Many Particles
• Few-to-many-particle crossover of pair excitations in a superfluid
• Unconventional pairing in few-fermion systems tuned by external confinement