Possibility of Stark-insensitive cotrapping of two atomic species in optical lattices

Much effort has been devoted to removing differential Stark shifts for atoms trapped in specially tailored ``magic" optical lattices, but thus far work has focused on a single trapped atomic species. In this work, we extend these ideas to include two atomic species sharing the same optical lattice. We show qualitatively that, in particular, scalar $J=0$ divalent atoms paired with non-scalar state atoms have the necessary characteristics to achieve such Stark shift cancellation. We then present numerical results on ``magic" trapping conditions for $^{27}$Al paired with $^{87}$Sr, as well as several other divalent atoms.