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arXiv:0901.0596 · Physical Review A

Quadrupole oscillations in Bose-Fermi mixtures of ultracold atomic gases made of Yb atoms in the time-dependent Gross-Pitaevskii and Vlasov equations

Tomoyuki Maruyama, Hiroyuki Yabu

Published Oct 19, 2009• 10 citations
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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, $^{170}\text{Y}\text{b-}^{171}\text{Y}\text{b}$, $^{170}\text{Y}\text{b-}^{173}\text{Y}\text{b}$ and $^{174}\text{Y}\text{b-}^{173}\text{Y}\text{b}$, 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 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. The oscillations obtained in the dynamical approach show discrepancies from the results obtained in the small-amplitude approximations, e.g., the random phase approximation, except in the case of weak boson-fermion interactions. We also analyze these discrepancies, and show that they originated in the change of the fermion distributions through oscillation.

DOI
10.1103/physreva.80.043615

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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, 170Yb-171Yb^{170}\text{Y}\text{b-}^{171}\text{Y}\text{b}170Yb-171Yb, 170Yb-173Yb^{170}\text{Y}\text{b-}^{173}\text{Y}\text{b}170Yb-173Yb and 174Yb-173Yb^{174}\text{Y}\text{b-}^{173}\text{Y}\text{b}174Yb-173Yb, 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 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. The oscillations obtained in the dynamical approach show discrepancies from the results obtained in the small-amplitude approximations, e.g., the random phase approximation, except in the case of weak boson-fermion interactions. We also analyze these discrepancies, and show that they originated in the change of the fermion distributions through oscillation.
We study the breathing oscillations in bose-fermi mixtures with Yb isotopes in the largely prolate deformed trap, which are realized by Kyoto group. We choose the three combinations of the Yb isotopes, Yb170-Yb171, Yb170-Yb173 and Yb174-Yb173, whose boson-fermion interactions are weakly repulsive, strongly attractive and strongly repulsive. The collective oscillations in the deformed trap are calculated in the dynamical time-development approach, which is formulated with the time-dependent Gross-Pitaevskii and the Vlasov equations. We analyze the results in the time-development approach with the intrinsic oscillation modes of the deformed system, which are obtained using the scaling method, and show that the damping and forced-oscillation effects of the intrinsic modes give time-variation of oscillations, especially, in the fermion transverse mode.
We study the dipole collective oscillations in Bose-Fermi mixtures in a dynamical time-dependent approach, which is formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. While the Bose gas oscillates monotonously, the fermion oscillation shows a beat and damping. We find big differences in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the sum-rule approach. When the amplitude is not minimal, the dipole oscillation of the Fermi gas cannot be described with a simple center-of-mass motion.
We study the breathing oscillations in bose-fermi mixing gases with Yb atoms in the prolate deformed trap, which are realized in Kyoto group. We choose the three combinations of the Yb isotopes, 170 Yb– 171 Yb, 170 Yb– 173 Yb and 174 Yb– 173 Yb, whose boson-fermion interactions are weakly repulsive, strongly attractive and strongly repulsive. Then we calculate the collective oscillations in the deformed trap using a dynamical time-dependent approach, which is formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation.
Collective oscillations of superfluid mixtures of ultracold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation models and ordinary differential equation models for the dynamics. An application to the recent experiment with fermionic 6Li^{6}\mathrm{Li}6Li and bosonic 7Li^{7}\mathrm{Li}7Li atoms, which approximately have the same masses, is discussed.