Systematic Study of the $^{87}$Sr Clock Transition in an Optical Lattice*

The $^{1}$S$_{0}-^{3}$P$_{0}$ transition in $^{87}$Sr is studied for the realization of an optical atomic clock, using $\mu $K atoms in a magic wavelength optical lattice [1]. The probe laser frequency is measured with an octave-spanning fs comb, which is referenced to a hydrogen maser (directly calibrated by the NIST primary Cs fountain clock) allowing high precision evaluation of potential systematic frequency shifts . By varying the lattice wavelength and trapping depth we find that the magic wavelength for the clock transition is 813.418(10) with a clock sensitivity to lattice deviations of $\sim $2 mHz/MHz for lattice intensities of 10 kW/cm$^{2}$. To explore the effect of atomic collisions on the clock frequency we varied the atomic density by a factor of 50 and did not find any shifts at the 3 x10$^{-14}$ level. Dependence of the clock transition on magnetic fields has been examined as the hyperfine interaction (I = 9/2), which provides the small transition moment for the doubly forbidden clock transition, also results in a differential g factor of the $^{3}$P$_{0}$ and $^{1}$S$_{0}$ levels. We will report the latest results of this optical clock system. [1] A.D. Ludlow et al., \textit{Phys Rev Lett} \textbf{96}, 033003 (2006).