  We study the use of an optical Feshbach resonance to modify the p-wave
interaction between ultracold polarized Yb-171 spin-1/2 fermions. A laser
exciting two colliding atoms to the 1S_0 + 3P_1 channel can be detuned near a
purely-long-range excited molecular bound state. Such an exotic molecule has an
inner turning point far from the chemical binding region and thus
three-body-recombination in the Feshbach resonance will be highly suppressed in
contrast to that typically seen in a ground state p-wave magnetic Feshbach
resonance. We calculate the excited molecular bound-state spectrum using a
multichannel integration of the Schr\"{o}dinger equation, including an external
perturbation by a magnetic field. From the multichannel wave functions, we
calculate the Feshbach resonance properties, including the modification of the
elastic p-wave scattering volume and inelastic spontaneous scattering rate. The
use of magnetic fields and selection rules for polarized light yields a highly
controllable system. We apply this control to propose a toy model for
three-color superfluidity in an optical lattice for spin-polarized Yb-171,
where the three colors correspond to the three spatial orbitals of the first
excited p-band. We calculate the conditions under which tunneling and on-site
interactions are comparable, at which point quantum critical behavior is
possible.
