Ground and Excited States of an Anisotropically Confined Condensed Bose Gas

徐志君, 李海彬, 辛晓天 +2 more

Alexander L. Fetter

Barry I. Schneider, David L. Feder

The ground and excited states of a weakly interacting and dilute Bose-Einstein condensed gas, confined in a completely anisotropic harmonic oscillator potential, are determined at zero temperature within the Bogoliubov approximation. The numerical calculations employ a computationally efficient procedure based on a discrete variable representation (DVR) of the Hamiltonian. The DVR is efficient for problems where the interaction potential may be expressed as a local function of interparticle coordinates. In order to address condensates that are both very large ($\ensuremath{\sim}{10}^{6}$ atoms) and fully anisotropic, the ground state is found using a self-consistent field approach. Experience has demonstrated, however, that standard iterative techniques applied to the solution of the nonlinear partial differential equation for the condensate are nonconvergent. This limitation is overcome using the method of direct inversion in the iterated subspace (DIIS). In addition, the sparse structure of the DVR enables the efficient application of iterative techniques such as the Davidson and/or Lanczos methods, to extract the eigenvalues of physical interest. The results are compared with recent experimental data obtained for Bose-Einstein condensed alkali-metal vapors confined in magnetic traps.

Pedro C. Diniz, Eduardo A. B. Oliveira, Aristeu R. P. Lima +1 more

We consider the ground state and the collective excitations of dipolar Bose-Einstein condensates in a bubble trap, i.e., a shell-shaped spherically symmetric confining potential. By means of an appropriate Gaussian ansatz, we determine the ground-state properties in the case where the particles interact by means of both the isotropic and short-range contact and the anisotropic and long-range dipole-dipole potential in the thin-shell limit. Moreover, with the ground state at hand, we employ the sum-rule approach to study the monopole, the two-, the three-dimensional quadrupole as well as the dipole modes. We find situations in which neither the virial nor Kohn's theorem can be applied. On top of that, we demonstrate the existence of anisotropic particle density profiles, which are absent in the case with repulsive contact interaction only. These significant deviations from what one would typically expect are then traced back to both the anisotropic nature of the dipolar interaction and the novel topology introduced by the bubble trap.

Shingo Otsuka

Daisuke Kushibe, Masaki Mutou, Tōru Morishita +2 more

Excitation of an atomic-gas Bose-Einstein condensate (BEC) in the zeroth-order ground-state channel is studied with the hyperspherical adiabatic method of Bohn et al. [Bohn et al., Phys. Rev. A 58, 584 (1998)] suitably generalized to accommodate the anisotropic trapping potential. The method exploits the system's size as an adiabatic parameter so that the explicit size dependence is immediately conducive to the virial theorem. The oscillation frequencies associated with the monopole (breathing) and quadrupole modes thus emerge naturally and converge to the well-known Thomas-Fermi limits. Analysis of the single-particle density and the projected excitation wave function shows that the excitation in the single hyperspherical ground-state channel merely represents a progressive increase in occupancy of the first excited single-particle state. The work paves the way for applying the adiabatic picture to other BEC phenomena.