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arXiv:1009.0975 · Journal of Physics B Atomic Molecular and Optical Physics

Longitudinal and transverse breathing oscillations in Bose–Fermi mixtures of Yb atoms at zero temperature in the largely prolate deformed traps

Tomoyuki Maruyama, Hiroyuki Yabu

Published Feb 12, 2013• 3 citations
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Abstract

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.

DOI
10.1088/0953-4075/46/5/055201

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•Mar 25, 2009•0 citations
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 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.
We study the breathing oscillations in bose-fermi mixtures in the axially-symmetric deformed trap of prolate, spherical and oblate shapes, and clarify the deformation dependence of the frequencies and the characteristics of collective oscillations. The collective oscillations of the mixtures in deformed traps are calculated in the scaling method. In largely-deformed prolate and oblate limits and spherical limit, we obtain the analytical expressions of the collective frequencies. The full calculation shows that the collective oscillations become consistent with the analytically-obtained frequencies when the system is deformed into both prolate and oblate regions. The complicated changes of oscillation characters are shown to occur in the transcendental regions around the spherically-deformed region. We find that these critical changes of oscillation characters are explained by the level crossing behaviors of the intrinsic oscillation modes. The approximate expressions are obtained for the level crossing points that determine the transcendental regions. We also compare the results of the scaling methods with those of the dynamical approach.
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 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.
Takushi Nishimura ∗ and Tomoyuki Maruyama 3, 4, † Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Otsuka, Bunkyo, Tokyo 112-8610, Japan College of Bioresource Sciences, Nihon University, Fujisawa 252-8510, Japan Advanced Science Research Center, Japan Atomic Energy Research Institute,Tokai 319-1195, Japan Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan Abstract We theoretically investigate breathing oscillations of fermion condensates in anisotropic harmonic oscillator traps. When anisotropy of the trap is not large, the Fermi gases behave as threedimensional (3D) gases, and those breathing oscillations are studied in the previous work [1]; when the trap is super-anisotropic, the fermions show quasi-low-dimensional (QLD) properties differently from the 3D gases because of variation of one-particle energy-level densities, which exhibit specific types of shell-structures, QLD shell-structures, in super-anisotropic systems. In the present work, we study the effects of the QLD shell-structures on the breathing oscillations of the week-interacting fermion condensates with same number densities. The QLD shell-structures are described in the semi-classical Thomas-Fermi approximation (TFA) extended to the super-anisotropic systems, and the collective frequencies of the breathing oscillations are estimated in the scaling and sum-rule methods with the perturbation theory and extended TFA up to the first order in a coupling constant of inter-atomic interaction. As a result, we reveal that the effects of the QLD shell-structures on the collective frequencies disappear in transverse modes in both of the oblate and prolate deformed traps, and appear only in longitudinal modes with hierarchic structures associated with the trap anisotropy. We also demonstrate time-evolution of the oscillations in the present framework.