A perturbation method is developed for calculating the oscillating frequencies of collective modes of trapped superfluid Fermi gases from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensation (BEC). Based on the complete and orthogonal eigenfunction set obtained recently and a series expansion of the equation of state beyond the mean-field approximation, the corrections of eigenfrequencies and eigenfunctions of all collective modes are given systematically, which are valid for various superfluid regimes in the BCS-BEC crossover beyond the mean-field approximation. Expressions of frequency correction of the collective modes for both spherical and axial symmetric traps excited near the BCS, BEC, and unitarity limits are provided explicitly, and their dependence on interatomic interaction strength and anisotropic trapping parameter is also discussed in detail.A perturbation method is developed for calculating the oscillating frequencies of collective modes of trapped superfluid Fermi gases from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensation (BEC). Based on the complete and orthogonal eigenfunction set obtained recently and a series expansion of the equation of state beyond the mean-field approximation, the corrections of eigenfrequencies and eigenfunctions of all collective modes are given systematically, which are valid for various superfluid regimes in the BCS-BEC crossover beyond the mean-field approximation. Expressions of frequency correction of the collective modes for both spherical and axial symmetric traps excited near the BCS, BEC, and unitarity limits are provided explicitly, and their dependence on interatomic interaction strength and anisotropic trapping parameter is also discussed in detail.

Physical Review AJan 23, 200913 citations

Collective Excitations in Fermi and Bose Systems

C. A. Bertulani, L. Felipe Canto, Mahir Saleh Hussein

Jun 17, 19992 citations

Collective Excitations of a Bose-Einstein Condensate in a Dilute Gas

D. S. Jin, J. R. Ensher, M. R. Matthews +2 more

WORLD SCIENTIFIC eBooksJan 1, 20081 citation

Collective Excitations of Trapped Bose–Fermi Mixture of Atomic Gases in RPA

Takaaki Sogo, Takahiko Miyakawa, T. Suzuki +1 more

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.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.

Journal of the Physical Society of JapanJan 1, 20030 citations

Elementary Excitations in Trapped Bose-Einstein Condensed Gases Beyond the Mean-Field Approximation

L. Pitaevskii, S. Stringari

Using the hydrodynamic theory of superfluids and the Lee-Huang-Yang equation of state for interacting Bose gases, we derive the first correction to the collective frequencies of a trapped gas, due to effects beyond the mean field approximation. The corresponding frequency shift, which is calculated at zero temperature and for large $N$ , is compared with other corrections due to finite size, nonlinearity, and temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean-field correction is the leading contribution and amounts to about $1%$ . The role of the deformation of the trap is also discussed.Using the hydrodynamic theory of superfluids and the Lee-Huang-Yang equation of state for interacting Bose gases, we derive the first correction to the collective frequencies of a trapped gas, due to effects beyond the mean field approximation. The corresponding frequency shift, which is calculated at zero temperature and for large $N$, is compared with other corrections due to finite size, nonlinearity, and temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean-field correction is the leading contribution and amounts to about $1%$. The role of the deformation of the trap is also discussed.

arXiv:cond-mat/9807396Physical Review LettersNov 23, 1998100 citations

N

, is compared with other corrections due to finite size, nonlinearity, and temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean-field correction is the leading contribution and amounts to about

1%

. The role of the deformation of the trap is also discussed.