Destroying superfluidity by rotating a Fermi gas at unitarity

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a non rotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity $n_{\rm N}/n_{\rm S}= 0.85$, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.