Nuclear spin exchange occurs in ultracold collisions of fermionic alkaline-earth-metal-like atoms due to a difference between $s$- and $p$-wave phase shifts. We study the use of an optical Feshbach resonance, excited on the ${{}^{1}S}_0\to {{}^{3}P}_1$ intercombination line of ${}^{171}\text{Y}\text{b}$, to affect a large modification of the $s$-wave scattering phase shift and thereby optically mediate nuclear exchange forces. We perform a full multichannel calculation of the photoassociation resonances and wave functions and from these calculate the real and imaginary parts of the scattering length. As a figure of merit of this interaction, we estimate the fidelity to implement a $\sqrt{\text{SWAP}}$ entangling quantum logic gate for two atoms trapped in the same well of an optical lattice. For moderate parameters one can achieve a gate fidelity of $\sim 95\%$ in a time of $\sim 50\mu \text{s}$.

• Received 1 June 2009

DOI:https://doi.org/10.1103/PhysRevA.80.020701