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Karbala International Journal of Modern Science

Low-lying modes of trapped condensed atoms in anharmonic trap

Hamid Al-Jibbouri

Published Apr 14, 2016• 2 citations
Publisher

Abstract

We describe the physical properties of a Bose-Einstein condensate (BEc) confined by a three-dimensional harmonic plus cubic and quartic trap. To this end, we solve the time-dependent Gross–Pitaevskii (GP) equation within a variational approach in order to obtain a set of second ordinary differential equations for the condensate widths. We then discuss in detail the low-lying oscillation modes, in an anharmonic trap where the anharmonicity of the confining potential leads to significant effect on the collective excitations of the system.

DOI
10.1016/j.kijoms.2016.03.002

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We describe the physical properties of a Bose-Einstein condensate (BEc) confined by a three-dimensional harmonic plus cubic and quartic trap. To this end, we solve the time-dependent Gross–Pitaevskii (GP) equation within a variational approach in order to obtain a set of second ordinary differential equations for the condensate widths. We then discuss in detail the low-lying oscillation modes, in an anharmonic trap where the anharmonicity of the confining potential leads to significant effect on the collective excitations of the system.
The collective excitations of low-dimensional Bose–Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross–Pitaevskii–Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion (adding cubic, quartic, or quintic term to a harmonic trap) are studied.
The dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.
The stability and collective excitation of Bose–Einstein condensates with both two- and three-body interactions in a two-dimensional anharmonic trap (i.e., harmonic plus quartic trap) are investigated. By using the variational method, the influence of the three-body interaction and the anharmonicity on the stability are discussed in detail. It is found that the anharmonicity of the trap and the three-body interaction have significant effect on the stability and collective excitations of the system.
It is investigated that the collective excitations of a one-dimensional Bose-Einstein condensate(BEC) with repulsive interaction between atoms in a quadratic plus quartic trap V(x)=12(x~2+λx~4).By using the variational approach,the analytical expressions are derived for two low-energy collective modes,and the effect of the anharmonicity of the potential trap on BEC collective excitations is studied.When(λ0) the frequencies will be blue shifted and when λ0 the frequencies will be red shifted.Meanwhile,the variations of the center-of-mass of the condensate and its width under different values of the driving amplitude are discussed.It is found that the two modes couple each other due to the anharmonicity,and the beating structure for the variation of the width occur.Finally,the response result corresponding to the frequency driving is given.
The collective excitations of a one-dimensional dipolar Bose—Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.