arXiv:0704.3483 · Physical Review A

Collective oscillations of a Bose-Fermi mixture: Effect of unequal masses of Bose and Fermi particles

Arup Banerjee

Published Aug 27, 2007• 14 citations

Abstract

We investigate the effect of unequal masses of the Bose and Fermi particles on the collective oscillations of the degenerate boson-fermion mixtures. In particular, we consider the monopole and the quadrupole modes of the oscillations and study their characters and the frequencies by using variational-sum-rule approach. We find that for both the modes there exist critical values of the ratio of boson-fermion masses below and above which the character and frequency of the respective modes are significantly different.

DOI: 10.1103/physreva.76.023611

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arXiv:0704.3483 · Physical Review A

Collective oscillations of a Bose-Fermi mixture: Effect of unequal masses of Bose and Fermi particles

Arup Banerjee

Published Aug 27, 2007• 14 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.76.023611

Related papers

Dipole oscillations of a Bose–Fermi mixture: effect of unequal masses of Bose and Fermi particles

Arup Banerjee

Journal of Physics B Atomic Molecular and Optical PhysicsNov 18, 20099 citations

Sum-rule approach to collective oscillations of a boson-fermion mixed condensate of alkali-metal atoms

T. Miyakawa, T. Suzuki, Hiroyuki Yabu

The behavior of collective oscillations of a trapped boson-fermion mixed condensate is studied in the sum-rule approach. Mixing angle of bosonic and fermionic multipole operators is introduced so that the mixing characters of the low-lying collective modes are studied as functions of the boson-fermion interaction strength. For an attractive boson-fermion interaction, the low-lying monopole mode becomes a coherent oscillation of bosons and fermions and shows a rapid decrease in the excitation energy towards the instability point of the ground state. In contrast, the low-lying quadrupole mode keeps a bosonic character over a wide range of the interaction strengths. For the dipole mode the boson-fermion in-phase oscillation remains to be the eigenmode under the external oscillator potential. For weak repulsive values of the boson-fermion interaction strengths we found that an average energy of the out-of-phase dipole mode stays lower than the in-phase oscillation. Physical origin of the behavior of the multipole modes against boson-fermion interaction strength is discussed in some detail.The behavior of collective oscillations of a trapped boson-fermion mixed condensate is studied in the sum-rule approach. Mixing angle of bosonic and fermionic multipole operators is introduced so that the mixing characters of the low-lying collective modes are studied as functions of the boson-fermion interaction strength. For an attractive boson-fermion interaction, the low-lying monopole mode becomes a coherent oscillation of bosons and fermions and shows a rapid decrease in the excitation energy towards the instability point of the ground state. In contrast, the low-lying quadrupole mode keeps a bosonic character over a wide range of the interaction strengths. For the dipole mode the boson-fermion in-phase oscillation remains to be the eigenmode under the external oscillator potential. For weak repulsive values of the boson-fermion interaction strengths we found that an average energy of the out-of-phase dipole mode stays lower than the in-phase oscillation. Physical origin of the behavior of the multipole modes against boson-fermion interaction strength is discussed in some detail.

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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,

^{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.

^{6}\mathrm{Li}

and bosonic

^{7}\mathrm{Li}

atoms, which approximately have the same masses, is discussed.

{}^{87}

Rb-

{}^{40}

K for different values of the density imbalance. We then analyze the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation, the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.