Measurement of the Angular Momentum of a Rotating Bose-Einstein Condensate

We study the quadrupole oscillation of a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ atoms confined in an axisymmetric magnetic trap, after it has been stirred by an auxiliary laser beam. The stirring may lead to the nucleation of one or more vortices, whose presence is revealed unambiguously by the precession of the axes of the quadrupolar mode. For a stirring frequency $\Omega$ below the single vortex nucleation threshold ${\Omega }_c$, no measurable precession occurs. Just above ${\Omega }_c$, the angular momentum deduced from the precession is $\sim ħ$. For stirring frequencies above ${\Omega }_c$ the angular momentum is a smooth and increasing function of $\Omega$, until an angular frequency is reached at which the vortex lattice disappears.