Ultra-high resolution spectroscopy with a $^{87}$Sr lattice clock

We have performed ultra-high resolution spectroscopy using a $^{87}$Sr optical lattice clock. With the addition of a small magnetic bias field, the high line Q of the $^1S_0$-$^3P_0$ clock transition has allowed us to resolve the nuclear-spin sublevels, and make a precision measurement of the differential Land\'{e} g-factor between the $^1S_0$ and $^3P_0$ states arising from hyperfine mixing of the $^3P_0$ with the $^3P_1$ and $^1P_1$ states. Breaking the nuclear-spin degeneracy allows for a better characterization of systematic errors, and we have made measurements of these nuclear-spin related effects including the linear Zeeman shift and tensor polarizability. The ability to directly manipulate individual nuclear-spin levels also makes this an attractive system for quantum information. Recent progress towards an all optical comparison of atomic clocks, including the construction of a new strontium three-dimensional optical lattice will also be presented.