We consider experimental 87Rb condensate which is trapped by harmonic plus quartic trap [V(r) = ½mω2r2 + λr4]. Keeping similarity with experiments, the anharmonic parameter (λ) is considered as a controllable parameter. The excited state energies of stable Bose-Einstein condensate are strongly influenced by the presence of an anharmonic term, even when the interatomic interaction is repulsive. The necessary dependencies of excited state energies of the trapped condensate on λ are discussed in detail. In addition, the variation of chemical potential energy as a function of λ is also investigated to explore the role of interaction. The many-particle Schrödinger equation is solved by the potential harmonic expansion method, where all possible two-body correlations are considered by utilizing the correlated two-body basis function. Specifically, we present a clear physical explanation of excited state energies and chemical potential energy of the experimental repulsive condensate confined by the anharmonic trap.
The zero-temperature ground state properties of experimental 87Rb condensate are studied in a harmonic plus quartic trap [ V(r) = ½mω2r2 + λr4 ]. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ, the many-particle Schrödinger equation is solved using the potential harmonic expansion method and determines the lowest effective many-body potential. We utilize the correlated two-body basis function, which keeps all possible two-body correlations. The use of van der Waals interaction gives realistic pictures. We calculate kinetic energy, trapping potential energy, interaction energy, and total ground state energy of the condensate in this confining potential, modelled experimentally. The motivation of the present study is to investigate the crucial dependency of the properties of an interacting quantum many-body system on λ. The average size of the condensate has also been calculated to observe how the stability of repulsive condensate depends on anharmonicity. In particular, our calculation presents a clear physical picture of the repulsive condensate in an anharmonic trap.
We report the effects of interaction on thermodynamic properties of a repulsive Bose-Einstein condensate confined in a harmonic trap by using the correlated potential harmonics expansion method. This many-body technique permits the use of a realistic interactomic interaction, which gives rise to the effective long-range interaction of the condensate in terms of the
s-wave scattering length. We have computed temperature (
T) dependence of the chemical potential, specific heat, condensate fraction, entropy, pressure, and the average energy per particle of a system containing a large number (
A) of
87Rb atoms in the Joint Institute for Laboratory Astrophysics (JILA) trap. The repulsion among the interacting bosons results in a small but measurable drop of condensate fraction and critical temperature (
Tc), compared to those of a noninteracting condensate. These are in agreement with the experiment. Although all thermodynamic quantities have a strong dependence on
A and to a smaller extent on the interatomic interaction, our numerical calculation appears to show that a thermodynamic quantity per particle follows a universal behavior as a function of
T/Tc. This shows the importance of
Tc for all thermodynamic properties of the condensate. As expected, for
T>Tc, these properties follow those of a trapped noncondensed Bose gas.
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
ahoAcr∣asc∣ due to the anharmonicity. The frequencies of the collective excitations are also modified by the atomic interaction and by the anharmonicity.
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 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.
We consider rotational motion of an interacting atomic Bose–Einstein condensate (BEC) with both two- and three-body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation (responsible for the vortex formation) in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.