Dipolar Oscillation Of Trapped Bose-Fermi Mixtures

Recent experimental achievements in ultracold trapped Bose-Fermi mixtures of alkali-metal atoms have opened a new scenario in the study of quantum degenerate gases. There are a number of theoretical analyses of a trapped Bose-Fermi mixture, investigating, for instance the equilibrium ground state, the stability conditions, the low-lying collective modes, the expansion, as well as the possible implications of Bardeen-Cooper-Schrieffer (BCS) transition to a superfluid phase of the fermionic species. In this paper a mean-field analysis of the dipolar excitations of a Bose-Fermi mixture confined in both axially symmetric trap and spherical trap in the collisionless regime was presented. The analysis is based on a simple scaling theory within the Thomas-Fermi approximation.In the case of spherical trap four types of Bose-Fermi mixture are considered and the effect of the change of atom number on the frequency of dipolar oscillation is investigated. At κ=0 and κ=1, the frequency of bosion-mode and fermi-mode oscillation is equal to the frequency of external potential. Where κ is h/g (h and g are bosion-fermion and bosion-bosion interaction strength respectively). For κ<0 and κ>1,the frequency of fermion-mode oscillation increases when the strength of bosion-fermion interaction increases. When given the strength of interaction atom number has a positive effect on the amplitude of the change of frequency. The results agree well with that given by a sum-rule approach.A calculation with realistic experimental parameters has been performed. The resulst suggest a sensitive dependence of the mode frequencies on the interspecies Bose-Fermi interactions. Both cigar-shaped trap (axial frequency of the trap < radial frequency of the trap) and disk-shaped trap (axial frequency of the trap > radial frequency of the trap) are considerd. For potassium 40-rubidium 87 mixture, κ=-5.9 in experiment, the calculation gives an upshift of fermion -mode and bosion-mode frequency are around 50% and 8% respectively. For lithium 6-litium 7 mixture, κ=8.02 the calculation gives an upshift of fermion-mode and bosion-mode frequency re around 6.5% and 1.8% respectively. The prediction can be tested in the future by a refined experiment.