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 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.
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.
We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett. 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of $(1\ensuremath{-}\frac{A}{{A}_{\mathit{cr}}})$,
A is the number of condensate atoms and
Acr is the critical number near collapse. We observe that the power-law exponent becomes
61 in our calculation for the pure harmonic trap and it becomes
71, for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.
In light of the interference experiment of Bose–Einstein condensates, we present an anharmonic external potential model to study ground state properties of Bose–Einstein condensates. The ground state energy and the chemical potential have been analytically obtained, which are lower than those in harmonic trap. Additionally, it is found that the anharmonic strength of the external potential has an important effect on density and velocity distributions of the ground state for the Thomas–Fermi model.
We evaluate the zero temperature properties and Bose-Einstein condensation (BEC) of hard sphere bosons in a harmonic trap using Quantum Monte Carlo methods. The chief purpose of this work is to go beyond the dilute limit, to test the limits of the Gross-Pitaevskii equation and related mean field approximations and to explore the role of interactions in determining the zero temperature properties of the trapped Bose gas. The density is increased by adjusting both the number of trapped bosons, N , and the s-wave scattering length, a, to study systems from the highly dilute region corresponding to early experiments in trapped BEC [2, 3] up to liquid He densities and beyond. Rather than relying on the perturbative Bogoliubov approximation (which assumes a large condensate fraction) to describe the condensate, we use the one-body density matrix (OBDM) formulation of BEC so that the properties of the condensate for systems with arbitrarily large interactions may be studied. In this formulation of BEC, condensate properties are obtained by diagonalizing the OBDM and obtaining the corresponding single particle “natural orbitals” and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital(s) with macroscopic occupation (N0 >> 1). Within this framework, we calculate the effects of interactions and increased density on the ground state energy, the density profile, the momentum distribution, the condensate fraction and condensate “wave-function” and several other properties.