We have created vortices in two-component Bose-Einstein condensates. The vo
rtex state was created through a coherent process involving the spatial and
temporal control of interconversion between the two components. Using an i
nterference technique, we map the phase of the vortex state to confirm that
it possesses angular momentum. We can create vortices in either of the two
components and have observed differences in the dynamics and stability.