  Weyl superconductivity or superfluidity, a fascinating topological state of
matter, features novel phenomena such as emergent Weyl fermionic excitations
and anomalies. Here we report that an anisotropic Weyl superfluid state can
arise as a low temperature stable phase in a 3D dipolar Fermi gas. A crucial
ingredient of our model is a rotating external field that generates a
direction-dependent two-body effective attraction. Experimental signatures are
predicted for cold gases in radio-frequency spectroscopy. The finite
temperature phase diagram of this system is studied and the transition
temperature of the Weyl superfluidity is found to be within the experimental
scope for atomic dipolar Fermi gases.
