We investigate the ground and low excited states of a rotating, weakly interacting Bose-Einstein condensed gas in a harmonic trap for a given angular momentum. Analytical results in various limits as well as numerical results are presented, and these are compared with those of previous studies. Within the mean-field approximation and for repulsive interaction between the atoms, we find that for very low values of the total angular momentum per particle, $L/\stackrel{\ensuremath{\rightarrow}}{N}0,$ where $L\ensuremath{\Elzxh}$ is the angular momentum and N is the total number of particles, the angular momentum is carried by quadrupole
(∣m∣=2) surface modes. For
L/N=1, a vortexlike state is formed and all the atoms occupy the
m=1 state. For small negative values of $L/N\ensuremath{-}1,$ the states with
m=0 and
m=2 become populated, and for small positive values of $L/N\ensuremath{-}1,$ atoms in the states with
m=5 and
m=6 carry the additional angular momentum. In the whole region
0< L/N< 1, we have strong analytic and numerical evidence that the interaction energy drops linearly as a function of
L/N. We have also found that an array of singly quantized vortices is formed as
L/N increases. Finally, we have gone beyond the mean-field approximation and have calculated the energy of the lowest state up to order N for small negative values of $L/N\ensuremath{-}1,$ as well as the energy of the low-lying excited states.
We study the spectrum of rotating Bose-Einstein condensates in the limit of weak repulsive interactions and present analytical and numerical results for energies and wave functions. While the low-lying states are of collective nature, the high-lying states are dominated by single-particle excitations and can be accurately approximated by simple polynomial expressions. In the limit that the number of particles is large compared to the number of excited quanta, the single-particle states become excellent approximations to the eigenstates, and a rather simple ordering scheme is obtained.
We derive exact analytical results for the many-body wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weak repulsive interactions under rotation. The wave functions are universal as they do not depend on the matrix elements of the two-body interaction. A comparison with the results from numerical diagonalization shows that the analytical solutions describe the ground state, as well as a set of low-lying excited states for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.
We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-
N expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.
We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.