Ramsey Spectroscopy on Ultra-Cold ~Alkaline-Earth Atoms

We consider ultra-cold fermionic alkaline-earth atoms trapped in a deep 3D optical lattice. In these systems, the many-body dynamics driven by the interplay between nuclear spins and two orbital electronic degrees of freedom ($^{1}$S$_{0}$ and $^{3}$P$_{0})$ can be modeled by an effective two-band Hubbard model [Gorshkov, et al. quant-ph/0812.3660]. We analyze the role of interactions, entanglement generation, and inhomogeneities (differential g-factors, vector/tensor light shifts, g etc.) on the sensitivity of precision spectroscopy with these atoms.