Macroscopic angular-momentum states of Bose-Einstein condensates in toroidal traps

We consider a Bose-Einstein condensate (BEC) of $N$ atoms of repulsive interaction $\sim U_0$, in an elliptical trap, axially pierced by a Gaussian-intensity laser beam, forming an effective (quasi-2D) toroidal trap with minimum at radial distance $\rho = \rho_p$. The macroscopic angular momentum states $\Psi_l(\rho,\theta) \sim \sqrt{N}\Phi_l(\rho) e^{i l \theta}$ for integer $l$ spread up to $\rho \lesssim \rho_{max} \sim (NU_0)^{1/4} \gg \rho_p$. The spreading lowers rotational energies, so estimated low metastability barriers can support large $l \lesssim l_{max} \sim (NU_0)^{1/4}, \lesssim 10$ for typical parameters. The $l$-dependent density profile $|\Phi_l(\rho)|^2 - |\Phi_0(\rho)|^2$ is a signature of BEC rotation. Results are insensitive to off-axis laser displacements $\rho_0$, for $\rho_0/\rho_{max} \ll 1$.