Macroscopic Angular Momentum States of Bose-Einstein Condensates in Toroidal Traps

Abstract

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 ${\Psi }_l(\rho ,\theta )\sim \sqrt{N}{\Phi }_l(\rho )e^{il\theta }$ for integer $l$ spread up to $\rho \lesssim {\rho }_{max}\sim (N{U}_0{)}^{1/4}\gg {\rho }_p$. The spreading lowers rotational energies, so estimated low metastability barriers can support large $l\lesssim l_{max}\sim (N{U}_0{)}^{1/4},\lesssim 10$ 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 ${\rho }_0/{\rho }_{max}\ll 1$.

4 pages, 2 figures (included), submitted to Phys. Rev. Lett