We theoretically consider a spin polarized, optically trapped condensate of ${}^{87}\mathrm{Rb}$ atoms in $F=1$. We observe a transfer of atoms to other Zeeman states due to the dipolar interaction which couples the spin and the orbital degrees of freedom. Therefore the transferred atoms acquire an orbital angular momentum. This is a realization of the Einstein–de Haas effect in systems of cold gases. We find resonances which make this phenomenon observable even in very weak dipolar systems, when the Zeeman energy difference on transfer is fully converted to rotational kinetic energy.

• Received 4 September 2006

DOI:https://doi.org/10.1103/PhysRevLett.99.130401