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arXiv:cond-mat/0202470 · Physical Review A

Random-phase approximation study of collective excitations in the Bose-Fermi mixed condensate of alkali-metal gases

Takaaki Sogo, T. Miyakawa, T. Suzuki, Hiroyuki Yabu

Published Jul 30, 2002• 40 citations
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Abstract

We perform a random-phase approximation study of collective excitations in a Bose-Fermi mixed degenerate gas of alkali-metal atoms at $T=0.$ The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of Bose and Fermi multipole (L) operators with $L=0,1,2,3.$ Transition densities and dynamical structure factors are calculated for collective excitations. A comparison with the sum rule prediction for the collective frequency is given. The time dependent behavior of the system after an external impulse is studied.

DOI
10.1103/physreva.66.013618

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We perform RPA (Random Phase Approximation) study of collective excitations in the bose-fermi mixed degenerate gas of Alkali-metal atoms at T = 0. The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of bose and fermi multipole (L) operators with L = 0,1,2,3. Transition densities and dynamical structure factors are calculated for collective excitations. Comparison with the sum rule prediction for the collective frequency is given. Time dependent behavior of the system after an external impulse is studied. Typeset using REVTEX 1 I.
Collective excitations of a trapped Bose–Fermi mixture of atomic gases are studied in a random-phase approximation. Density profiles in the ground states are solved in the mean field approximation for various strengths of Bose–Fermi interaction. Monopole strength distributions and the dynamical structure factors are investigated for two types of the Bose–Fermi mixture. It is found in the mixture with the large excess of bosons the fermionic strength is concentrated in a single collective state for strong Bose–Fermi interactions. The dynamical structure factors for these collective states show that fermions are correlated through the Bose condensate. Time dependent behavior of the system after an external impulse is also studied.
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We study the dynamical behavior of a Bose-Fermi mixture of trapped atomic gases which exhibits phase separation for a sufficiently strong repulsive interparticle interaction. For a dominantly bosonic mixture, the fermion density distribution and the associated single-particle spectra undergo a rapid change around the transition to the separated phase. Monopole strength distribution is studied in the random-phase approximation. The average energy calculated from the fermionic monopole strength shows a sharp minimum close to the transition point. The dynamical origin of the fermion single particle and collective properties is studied within a simple approximation.
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.