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 $ρ= ρ_p$. The macroscopic angular momentum states $Ψ_l(ρ,θ) \sim \sqrt{N}Φ_l(ρ) e^{i l θ}$ for integer $l$ spread up to $ρ\lesssim ρ_{max} \sim (NU_0)^{1/4} \gg ρ_p$. 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 $|Φ_l(ρ)|^2 - |Φ_0(ρ)|^2$ is a signature of BEC rotation. Results are insensitive to off-axis laser displacements $ρ_0$, for $ρ_0/ρ_{max} \ll 1$.