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

We experimentally and theoretically determine the magic wavelength of the $(5s^2){{}^{1}S}_0-(5s5p){}^3{P}_0$ clock transition of ${}^{111}\mathrm{Cd}$ 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 ${{}^{1}S}_0-{{}^{3}P}_1$ transition to cool the atoms to $6\mu \mathrm{K}$ 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 $2.83(8)\times {10}^{-16}$ at 300 K, an order of magnitude smaller than that of Sr and Yb. We also report calculations of the Cd ${}^1{P}_1$ lifetime and the ground state $C_6$ coefficient.

Figure 1

Energy levels of cadmium. Wavelengths $\lambda$, natural linewidths $\mathrm{\Gamma }/2\pi$, and, for the cooling and clock transitions, Doppler limited temperatures $T_D$ are indicated. The magic wavelength for the optical lattice is 419.88 nm, at which the ac Stark shifts of both states of the ${{}^{1}S}_0-{{}^{3}P}_0$ clock transition are identical.

Figure 2

(a) Cadmium clock schematic. The cooling and trapping lasers at 229 and 326 nm enter through antireflection-coated fused-silica view ports. The lattice light builds up in an enhancement cavity with fused-silica Brewster windows and external mirrors. (b) Sequence for laser cooling, spectroscopy, and detection.

Figure 3

Temperature of ${}^{111}\mathrm{Cd}$ versus laser intensity for a detuning of $-3{\mathrm{\Gamma }}_2$. The temperature is derived from the Doppler-broadening of the ${{}^{1}S}_0-{{}^{3}P}_0$ clock transition (see inset). A Gaussian fit (solid curve) gives a minimum temperature of $6\mu \mathrm{K}$ for a total intensity of $19I_2$.

Figure 4

Sideband spectrum of the clock transition for a lattice wavelength ${\lambda }_L=419.9\mathrm{nm}$. The blue and red curves are fits to the blue and red motional sidebands, which determines the axial trap frequency to be 209(8) kHz.

Figure 5

(a) Light shifts for six lattice wavelengths at three lattice trap depths. At each wavelength the three measured light shifts are linearly fit to extract the light shift coefficient. The slowly drifting frequency offset is subtracted at each wavelength. (b) Light shift coefficient versus lattice wavelength. This gives a magic wavelength of 419.88(14) nm, where the light shift coefficient goes to zero.