Parity effect in a mesoscopic Fermi gas

JOHANNES HOFMANN; ALEJANDRO M. LOBOS; VICTOR GALITSKI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2016 vol. 93 p. 61602 - 616013

1050-2947

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. Zuern 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-particle to many-particle crossover between the perturbative mesoscopic regime and nonperturbative many-body physics that the system approaches in the thermodynamic limit.