Effects of collisions against thermal impurities in the dynamics of a trapped fermion gas

TL;DR

This paper models the dynamics of ultracold fermionic gases with thermal bosonic impurities, revealing how certain parameters can shift the system from collisionless to collisional regimes.

Contribution

It provides a theoretical framework using Vlasov-Landau equations to analyze fermion-impurity interactions in trapped gases, highlighting conditions that induce collisional behavior.

Findings

Gases are near collisionless under current experimental parameters.

Heavier impurities or matching impurity momentum width to Fermi momentum induce collisional regimes.

Analytical and numerical methods complement the study of fermion-impurity dynamics.

Abstract

We present a theoretical study of the dynamical behavior of a gas made of ultracold fermionic atoms, which during their motions can collide with a much smaller number of thermal bosonic impurities. The atoms are confined inside harmonic traps and the interactions between the two species are treated as due to s-wave scattering with a negative scattering length modeling the 40K-87Rb fermion-boson system. We set the fermions into motion by giving a small shift to their trap center and examine two alternative types of initial conditions, referring to (i) a close-to-equilibrium situation in which the two species are at the same temperature (well below the Fermi temperature and well above the Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case in which the impurities are given a Boltzmann distribution of momenta while the fermions are at very low temperatures. The dynamics of the gas is evaluated by the numerical solution of the Vlasov-Landau equations for the one-body distribution functions, supported by some analytical results on the collisional properties of a fermion gas. We find that the trapped gaseous mixture is close to the collisionless regime for values of the parameters corresponding to current experiments, but can be driven towards a collisional regime even without increasing the strength of the interactions, either by going over to heavier impurity masses or by matching the width of the momentum distribution of the impurities to the Fermi momentum of the fermion gas.