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Nuclear spin exchange occurs in ultracold collisions of fermionicalkaline-earth-like atoms due to a difference between s- and p-wave phaseshifts. We study the use of an optical Feshbach resonance, excited on the${}^1S_0 \to {}^3P_1$ intercombination line of ${}^{171}$Yb, to affect a largemodification of the s-wave scattering phase shift, and thereby opticallymediate nuclear exchange forces. We perform a full multichannel calculation ofthe photoassociation resonances and wave functions and from these calculate thereal and imaginary parts of the scattering length. As a figure of merit of thisinteraction, we estimate the fidelity to implement a $\sqrt{SWAP}$ entanglingquantum logic gate for two atoms trapped in the same well of an opticallattice. For moderate parameters one can achieve a gate fidelity of $\sim95% $in a time of $\sim 50 \mu$s.

Controlling nuclear spin exchange via optical Feshbach resonances in ${}^{171}$Yb