Quadrupole Oscillations in Bose-Fermi Mixtures of Ultracold Atomic Gases made of Yb atoms in the Time-Dependent Gross-Pitaevskii and Vlasov equations

TL;DR

This paper investigates quadrupole oscillations in ultracold Yb Bose-Fermi mixtures using time-dependent Gross-Pitaevskii and Vlasov equations, revealing mode behaviors and interaction effects on oscillation dynamics.

Contribution

It introduces a dynamical approach combining Gross-Pitaevskii and Vlasov equations to analyze collective modes in Yb mixtures with different interaction strengths, highlighting differences from small amplitude approximations.

Findings

Boson oscillations have a single collective mode.

Fermions exhibit boson-forced and intrinsic oscillation modes.

Discrepancies between dynamical and RPA approaches depend on fermion distribution changes.

Abstract

We study quadrupole collective oscillations in the bose-fermi mixtures of ultracold atomic gases of Yb isotopes, which are realized by Kyoto group. Three kinds of combinations are chosen, Yb170-Yb171, Yb170-Yb173 and Yb174-Yb173, where boson-fermion interactions are weakly repulsive, strongly attractive and strongly repulsive respectively. Collective oscillations in these mixtures are calculated in a dynamical time-evolution approach formulated with the time-dependent Gross-Pitaevskii and the Vlasov equations. The boson oscillations are shown to have one collective mode, and the fermions are shown to have the boson-forced and two intrinsic modes, which correspond to the inside- and outside-fermion oscillations for the boson-distributed regions. In the case of the weak boson-fermion interactions, the dynamical calculations are shown to be consistent with the results obtained in the small amplitude approximations as the random phase approximation in early stage of oscillation, but, in later stage, these two approaches are shown to give the different results. Also, in the case of the strong boson-fermion interactions, discrepancies appear in early stage of oscillation. We also analyze these differences in two approaches, and show that they originated in the change of the fermion distributions through oscillation.