Momentum distribution of a trapped Fermi gas with large scattering length

TL;DR

This paper calculates the momentum distribution of a trapped ultracold Fermi gas across different interaction regimes using a scattering length parametrization and local density approximation, highlighting the key role of a specific dimensionless parameter.

Contribution

It introduces a universal parameter $N^{1/6}a/a_{ho}$ that characterizes the BCS-BEC crossover and predicts how the momentum distribution width depends on this parameter.

Findings

Momentum distribution width depends on the parameter $N^{1/6}a/a_{ho}$.

The parameter effectively characterizes the entire crossover regime.

Predictions are relevant for experiments near Feshbach resonances.

Abstract

Using a scattering length parametrization of the BCS-BEC crossover as well as the local density approximation for the density profile, we calculate the momentum distribution of a harmonically trapped atomic Fermi gas at zero temperature. Various interaction regimes are considered, including the BCS phase, the unitarity limit and the molecular regime. We show that the relevant parameter which characterizes the crossover is given by the dimensionless combination $N^{1/6}a/a_{ho}$, where $N$ is the number of atoms, $a$ is the scattering length and $a_{ho}$ is the oscillator length. The width of the momentum distribution is shown to depend in a crucial way on the value and sign of this parameter. Our predictions can be relevant for experiments on ultracold atomic Fermi gases near a Feshbach resonance.