Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length

TL;DR

This paper investigates a four-fermion system under harmonic confinement, demonstrating universal relations between energy, contact intensity, and distributions across different interaction strengths using a numerical approach.

Contribution

It provides a detailed numerical analysis of the four-fermion system, explicitly confirming universal relations and a generalized virial theorem for finite-range interactions.

Findings

Energy and distributions relate through the contact intensity I(a).

Universal relations hold across the interaction crossover.

Generalized virial theorem accounts for finite-range effects.

Abstract

A two-component four-fermion system with equal masses, interspecies s-wave scattering length a and vanishing intraspecies interactions under external spherically symmetric harmonic confinement is considered. Using a correlated Gaussian basis set expansion approach, we determine the energies and various structural properties of the energetically lowest-lying gas-like state throughout the crossover for various ranges of the underlying two-body potential. Extrapolating to the zero-range limit, our numerical results show explicitly that the total energy, the trap energy as well as certain aspects of the pair distribution function and of the momentum distribution are related through the so-called integrated contact intensity I(a). Furthermore, it is shown explicitly that the total energy and the trap energy are related through a generalized virial theorem that accounts for a non-zero range.