Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover

TL;DR

This paper demonstrates a universal scaling behavior in the static properties of a trapped Fermi superfluid across the BCS-unitarity crossover, enabling accurate predictions for large systems based on small-system calculations.

Contribution

The study introduces a universal scaling law for the static properties of a Fermi superfluid across the BCS to unitarity crossover, validated through extensive density-functional calculations.

Findings

Universal scaling of energy, chemical potential, and radius across the crossover.

Accurate property predictions for large fermion numbers from small-system data.

Error margins of 1-2% in predictions for systems with ~10^5 fermions.

Abstract

From an extensive calculation of static properties of a trapped Fermi superfluid at zero temperature using a density-functional formulation, we demonstrate a universal behavior of its observables, such as energy, chemical potential, radius etc., over the crossover from the BCS limit to unitarity leading to scaling over many orders of magnitude in fermion number. This scaling allows to predict the static properties of the system, with a large number ($\sim 10^5$) of fermions, over the crossover with an error of 1-2%, from the knowledge of those for a small number ($\sim 10$) of fermions.