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arXiv:cond-mat/9911247

Collective Excitation of a Hybrid Atomic/Molecular Bose Einstein Condensate$^{\ast}$

Chi-Yong Lin, Mahir Saleh Hussein, A. F. R. de Toledo Piza, Eddy Timmermans

Published Nov 16, 1999• 0 citations
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Abstract

The collective excitation of hybrid atomic-molecular condensate are studied using variational method. The dipole response of the system is studied in detail. We found that the out-of-phase dipole oscillation frequency increasing slowly with the detuning parameter and is only few times large than the trap frequency making the experimental observation of this mode of vibration feasible.

DOI
10.48550/arxiv.cond-mat/9911247

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Collective Excitation of a Hybrid Atomic/Molecular Bose Einstein Condensate∗^{\ast}∗
The collective excitation of hybrid atomic-molecular condensate are studied using variational method. The dipole response of the system is studied in detail. We found that the out-of-phase dipole oscillation frequency increasing slowly with the detuning parameter and is only few times large than the trap frequency making the experimental observation of this mode of vibration feasible.
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We investigate the low-energy excitations of the spherically and axially trapped atomic Bose-Einstein condensate coupled to a molecular Bose gas by coherent Raman transitions. We apply the sum-rule approach of many-body response theory to derive the low-lying collective excitation frequencies of the hybrid atom-molecular system. The atomic and molecular ground-state densities obtained in Gross-Pitaevskii and modified Gross-Pitaevskii (including the higher order Lee-Huang-Yang term in interatomic interaction) approaches are used to find out the individual energy components and hence the excitation frequencies. We obtain different excitation energies for different angular momenta and study their characteristic dependence on the effective Raman detuning, the scattering length for atom-atom interaction, and the intensities of the coupling lasers. We show that the inclusion of the higher-order nonlinear interatomic interaction in modified Gross-Pitaevskii approach introduces significant corrections to the ground-state properties and the excitation frequencies both for axially and spherically trapped coupled 87Rb^{87}\mathrm{Rb}87Rb condensate system with the increase in the sss-wave scattering length (for peak gas-parameter $\ensuremath{\geqslant}{10}^{\ensuremath{-}3}$). It has been shown that the excitation frequencies decrease with the increase in the effective Raman detuning as well as the sss-wave scattering length, whereas excitation frequencies increase with the increase in the atom-molecular coupling strength. The frequencies in modified Gross-Pitaevskii approximation exhibit an upward trend after a certain value of scattering length and also largely deviate from the Gross-Pitaevskii results with the increase in sss-wave scattering length. The strong dependence of excitation frequencies on the laser intensities used for Raman transitions manifests the role of atom-molecular coupling strength on the control of collective excitations. The collective excitation frequencies for the hybrid atom-molecular BEC differ significantly from the excitation frequencies of a pure atomic BEC system when the atom-to-molecule conversion efficiency increases due to the decrease in the effective Raman detuning and increase in the atom-molecule coupling strength.
We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas-Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a Gaussian ansatz.
The phase separation and collective excitations of two-component Bose-Einstein condensates in traps are studied. Using the variational method, we show that the separated state is favorable in the case where the interspecies interaction is strongly repulsive and the number of atoms is large enough. This phase separation condition is explained in terms of the softening of a dipole mode collective excitation. Other low-lying excitation modes and their softenings which lead to the instability of the mixed state are also studied by use of the sum-rule approach.
Here we analyze the collective excitations as well as the expansion of a trapped Bose-Einstein condensate with a vortex line at its center. To this end, we propose a variational method where the variational parameters have to be carefully chosen in order to produce reliable results. Our variational calculations agree with numerical simulations of the Gross-Pitaevskii equation. The system considered here turns out to exhibit four collective modes of which only three can be observed at a time depending on the trap anisotropy. We also demonstrate that these collective modes can be excited using well established experimental methods such as modulation of the sss-wave scattering length.
We investigate the coupling between collective modes of a trapped Bose-Einstein condensate. We reveal the hybrid nature of these modes for certain trap geometries and show how the hybridization process leads to the formation of coherent-matter dark states. The effect of these hybrid states on mode coupling processes is discussed and studied as a function of the trap modulation. We complement the Bogoliubov approach with a time-dependent method directly simulating the axial and radial oscillations of the trapped condensate corresponding to the experimental parameters of Hechenblaikner et al. (Phys. Rev. Lett. 85, 692 (2000)).