Spinor Bose Condensates in Optical Traps

We show that in an optical trap the ground states of spin-1 bosons such as ^23Na, ^39K, and ^87Rb can be either ferromagnetic or ``polar" states, depending on the scattering lengths in different angular momentum channels. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of ^3He-A.