Shrinking of a condensed fermionic cloud in a trap approaching the BEC limit

TL;DR

This paper investigates how a fermionic atomic cloud's size and density profile change at zero temperature as the interaction strength increases, transitioning from BCS to BEC regimes, using a generalized Thomas-Fermi approximation.

Contribution

It introduces a continuous model for the density profile of fermionic superfluids across all coupling regimes, bridging BCS and BEC limits.

Findings

Significant shrinking of the cloud size with increased interaction strength.

Order of magnitude increase in central density during the BCS to BEC transition.

Validation of the generalized Thomas-Fermi approximation for superfluid states.

Abstract

We determine the zero-temperature density profile of a cloud of fermionic atoms in a trap subject to a mutual attractive interaction, as the strength of the interaction is progressively increased. We find a significant decrease of the size of the atomic cloud as it evolves from the weak-coupling (BCS) regime of overlapping Cooper pairs to the strong-coupling (Bose-Einstein) regime of non-overlapping bound-fermion pairs. Most significantly, we find a pronounced increase of the value of the density at the center of the trap (even by an order of magnitude) when evolving between the two regimes. Our results are based on a generalized Thomas-Fermi approximation for the superfluid state, that covers continuously all coupling regimes.