Weakly-interacting Bose-Einstein condensates under rotation

G. M. Kavoulakis; B. Mottelson; C. J. Pethick

doi:10.1103/PhysRevA.62.063605

paper

Weakly-interacting Bose-Einstein condensates under rotation

arXiv:cond-mat/0004307 · doi:10.1103/PhysRevA.62.063605

Abstract

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, $L / N \to 0$ , where $L ℏ$ is the angular momentum and $N$ is the total number of particles, the angular momentum is carried by quadrupolar ( $∣ m ∣ = 2$ ) surface modes. For $L / N = 1$ a vortex-like state is formed and all the atoms occupy the $m = 1$ state. For small negative values of $L / N - 1$ the states with $m = 0$ and $m = 2$ become populated, and for small positive values of $L / N - 1$ atoms in the states with $m = 5$ and $m = 6$ carry the additional angular momentum. In the whole region $0 \leq L / N \leq 1$ 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 $L / N - 1$ , as well as the energy of the low-lying excited states.

9 pages, RevTex, 12 ps figures, submitted to PRA

Weakly-interacting Bose-Einstein condensates under rotation

Abstract

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