Spectroscopy of the ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ Clock Transition of ${}^{87}\mathrm{S}\mathrm{r}$ in an Optical Lattice

We report on the spectroscopy of the $5s^2{}^{1}S_0(F=9/2)\to 5s5p{}^{3}P_0(F=9/2)$ clock transition of ${}^{87}\mathrm{S}\mathrm{r}$ atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the magic wavelength, where the light shift in the clock transition vanishes, to be $813.5\pm 0.9\mathrm{n}\mathrm{m}$.

Figure 1

Energy levels for the spectroscopy. The $5s^2{}^{1}S_0$ and $5s5p{}^{3}P_0$ states are coupled to the upper respective spin states by an off-resonant standing wave light field to produce equal amounts of light shifts ($\hslash {\delta }_g$ and $\hslash {\delta }_e$) in the clock transition and to provide atoms with subwavelength confinement. The excited atoms on the $|{}^{1}S_0⟩\otimes |n⟩\to |{}^{3}P_0⟩\otimes |n⟩$ electronic-vibrational transitions in the light shift potentials were quenched into the ${}^{3}P_2$ metastable state via the rapidly decaying ${}^{3}S_1$ state. The clock transition was sensitively monitored on the ${}^{1}S_0\mathrm{\text{−}}{}^{1}P_1$ transition.

Figure 2

An external cavity laser diode (ECLD) was electronically stabilized to a high-finesse reference cavity made of ultra-low-expansion (ULE) glass. This clock laser at ${\lambda }_0=698\mathrm{n}\mathrm{m}$ was superimposed on the Ti-sapphire laser (used for trapping atoms) and coupled into a polarization-maintaining single-mode fiber. The radiation from the fiber was focused onto the ultracold atom cloud and the trapping beam alone was retroreflected to form an optical lattice, where ${\mathbf{e}}_z$ denotes the unit vector parallel to the clock and the trap laser axes.

Figure 3

The ground state population as a function of the clock laser detuning measured at lattice laser wavelength ${\lambda }_L=815\mathrm{n}\mathrm{m}$. The upper and the lower sidebands at $\approx \pm 64\mathrm{k}\mathrm{H}\mathrm{z}$ correspond to the heating and the cooling sidebands, respectively. The base line fluctuation of $\approx 15\%$ is due to the shot-to-shot fluctuation of atoms loaded into the optical lattice. The inset shows the recoilless spectrum (the carrier component) with a linewidth of 0.7 kHz (FWHM) measured at ${\lambda }_L=813\mathrm{n}\mathrm{m}$.

Figure 4

The inset shows the carrier spectrum (open circles) for the $|{}^{1}S_0⟩\otimes |n⟩\to |{}^{3}P_0⟩\otimes |n⟩$ transition measured at lattice laser wavelength ${\lambda }_L=820\mathrm{n}\mathrm{m}$. This line shape is fitted by the sum of four Lorentzians corresponding to $n=0$, 1, 2, and 3 vibrational transitions to deduce the Boltzmann factor $f_B\approx 0.5$ and the differential vibrational frequency $\delta \Omega /2\pi \approx 0.8\mathrm{k}\mathrm{H}\mathrm{z}$. The latter is plotted as a function of the lattice wavelength to determine the degenerate wavelength ($\delta \Omega =0$) to be ${\lambda }_L=813.5\pm 0.9\mathrm{n}\mathrm{m}$.