Kinetic energy of a trapped Fermi gas interacting with a Bose-Einstein condensate

TL;DR

This paper investigates how interactions in a trapped boson-fermion mixture affect the fermionic kinetic energy, providing a framework to infer interaction signs and understand thermal effects.

Contribution

It introduces two scaling variables that determine the system's state and explores the impact of interactions on fermionic kinetic energy in a confined mixture.

Findings

Interactions significantly influence fermionic kinetic energy.

The ratio of cloud radii and interaction strengths are key parameters.

Experimental study can reveal the sign of the boson-fermion scattering length.

Abstract

We study a confined mixture of bosons and fermions in the regime of quantal degeneracy, with particular attention to the effects of the interactions on the kinetic energy of the fermionic component. We are able to explore a wide region of system parameters by identifying two scaling variables which completely determine its state at low temperature. These are the ratio of the boson-fermion and boson-boson interaction strengths and the ratio of the radii of the two clouds. We find that the effect of the interactions can be sizeable for reasonable choices of the parameters and that its experimental study can be used to infer the sign of the boson-fermion scattering length. The interplay between interactions and thermal effects in the fermionic kinetic energy is also discussed.