Narrow-line Cooling and Determination of the Magic Wavelength of Cd

We experimentally and theoretically determine the magic wavelength of the (5s²)¹S₀-(5s5p)³P₀ clock transition of ¹¹¹Cd to be 419.88(14) and 420.1(7) nm. To perform Lamb-Dicke spectroscopy of the clock transition, we use narrow-line laser cooling on the ¹S₀-³P₁ transition to cool the atoms to 6 μK and load them into an optical lattice. Cadmium is an attractive candidate for optical lattice clocks because it has a small sensitivity to blackbody radiation and its efficient narrow-line cooling mitigates higher order light shifts. We calculate the blackbody shift, including the dynamic correction, to be fractionally 2.83(8)×10⁻¹⁶ at 300 K, an order of magnitude smaller than that of Sr and Yb. We also report calculations of the Cd ¹P₁ lifetime and the ground state C₆ coefficient.