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Journal of Physics B Atomic Molecular and Optical Physics

The stability condition and collective excitation of a trapped Bose–Einstein condensate with higher-order interactions

Wei Qi, Zhaoxin Liang, Zhang Zhi-dong

Published Aug 19, 2013• 15 citations
Publisher

Abstract

We take into account the higher-order corrections in two-body scattering interactions within a mean-field description, and investigate the stability conditions and collective excitations of a harmonically trapped Bose–Einstein condensate (BEC). Our results show that the presence of higher-order corrections causes drastic changes to the stability condition of a BEC. In particular, we predict that with the help of the higher-order interaction, a BEC can now collapse even for positive scattering lengths; whereas, a usually unstable BEC with a negative scattering length can be stabilized by positive higher-order effects. The low-lying collective excitations are significantly modified as well, compared to those without the higher-order corrections. The conditions for a possible experimental scenario are also proposed.

DOI
10.1088/0953-4075/46/17/175301

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We take into account the higher-order corrections in two-body scattering interactions within a mean-field description, and investigate the stability conditions and collective excitations of a harmonically trapped Bose–Einstein condensate (BEC). Our results show that the presence of higher-order corrections causes drastic changes to the stability condition of a BEC. In particular, we predict that with the help of the higher-order interaction, a BEC can now collapse even for positive scattering lengths; whereas, a usually unstable BEC with a negative scattering length can be stabilized by positive higher-order effects. The low-lying collective excitations are significantly modified as well, compared to those without the higher-order corrections. The conditions for a possible experimental scenario are also proposed.
We study the stability of Bose-Einstein condensate (BEC) with repulsive and attractive interatomic interactions in a harmonic plus quartic trap $[V(r)=\frac{1}{2}m{\ensuremath{\omega}}^{2}{r}^{2}+\ensuremath{\lambda}{r}^{4}]$. We find that BEC with repulsive interaction becomes more stable for $\ensuremath{\lambda}>0$. For $\ensuremath{\lambda}<0$, we observe a different metastability of the condensate even when the scattering length is positive. For BEC with attractive interaction, we observe dramatic change in the stability factor Acr∣asc∣aho\frac{{A}_{\text{cr}}|{a}_{\text{sc}}|}{{a}_{\text{ho}}}aho​Acr​∣asc​∣​ due to the anharmonicity. The frequencies of the collective excitations are also modified by the atomic interaction and by the anharmonicity.
In this paper, we investigate the stability of a recently introduced Bose–Einstein condensate (BEC) which involves logarithmic interaction between atoms. The Gaussian variational approach is employed to derive equations of motion for condensate widths in the presence of a harmonic trap. Then we derive the analytical solutions for these equations and find them to be in good agreement with numerical data. By analyzing deeply the frequencies of collective oscillations, and the mean-square radius, we find that the system is always stable for both negative and positive week logarithmic coupling. However, for strong interaction the situation is quite different: Our condensate collapses for positive coupling and oscillates with fixed frequency for negative one. These special results remain the most characteristic features of the logarithmic BEC compared to that involving two-body and three-body interactions.
Abstract So far, attractive , trapless Bose–Einstein condensate (BEC) has been stabilized by considering the temporal modulation of the scattering length. However, there is no scope to stabilize the repulsive , trapless BEC even in the presence of the temporal modulation of the two-body interaction. However, in the present study, we stabilize the repulsive , trapless BEC by incorporating higher-order interaction. We also discuss the possibilities of the stabilization of repulsive, trapless BEC in the presence of time-varying higher-order interaction. Additionally, we verify our analytical findings by direct numerical simulation using the split-step Crank-Nicholson method.
We consider the stability of an ultracold trapped Bose-Einstein condensate near a Feshbach resonance. Using a modified Gross-Pitaevskii equation that includes higher-order terms and a multichannel model of Feshbach resonances, we find regions where stability can be enhanced or suppressed around experimentally measured resonances. We suggest a number of ways to probe the stability diagram. Using scattering length zero crossings huge deviations are found for the critical particle number. Effects are enhanced for narrow resonances or tighter traps. Macroscopic tunneling of the condensate is another possible probe for higher-order interactions; however, to see this requires very narrow resonances or very small particle numbers.
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 suggest that crucial effect on Bose-Einstein condensation in systems with attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic potential. Stability properties of the condensate are similar to those for thermodynamic systems in statistical physics which have first order phase transitions. We have shown that there are three possible type of stationary solutions corresponding to stable, metastable and unstable phases. Results are discussed in relation to recently observed 7 Li condensate.