${}^{87}\mathrm{Sr}$ Lattice Clock with Inaccuracy below ${10}^{-15}$

Aided by ultrahigh resolution spectroscopy, the overall systematic uncertainty of the ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ clock resonance for lattice-confined ${}^{87}\mathrm{Sr}$ has been characterized to $9\times {10}^{-16}$. This uncertainty is at a level similar to the Cs-fountain primary standard, while the potential stability for the lattice clocks exceeds that of Cs. The absolute frequency of the clock transition has been measured to be 429 228 004 229 874.0(1.1) Hz, where the $2.5\times {10}^{-15}$ fractional uncertainty represents the most accurate measurement of a neutral-atom-based optical transition frequency to date.

Figure 1

High resolution spectroscopy of the ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ transition. (a) A Fourier-limited resonance profile for typical experimental parameters. A ${\mathrm{sinc}}^2$ fit is shown as a red curve, giving a linewidth (FWHM) of 10.6(3) Hz ($Q\simeq 4\times {10}^{13}$). (b) Spectroscopy of an isolated nuclear-spin component yields a linewidth of 1.9(2) Hz ($Q\simeq 2.3\times {10}^{14}$), consistent with the 1.8 Hz Fourier limit for the 0.48 s probe time. The spectra in both (a) and (b) are taken without averaging or normalization, and the vertical axes are scaled by the total number of atoms ($2\times {10}^4$). The $S/N$ in (a) is limited by shot to shot atom number fluctuation (10%), whereas the probe laser frequency noise is the dominant effect in (b) [5].

Figure 2

(a) A single measurement of the lattice Stark shift achieved using four interleaved intensities during a scan of the clock transition. For this measurement, the shift is $0.4(4.4)\mathrm{Hz}/I_0$. (b) Histogram of 776 single measurements [such as in (a)] of the Stark shift for our typical intensity $I_0$. (c) Histogram of 422 measurements in which the atomic density is varied by a factor of 5 during spectroscopy. Gaussian fits (red curve) to the data in (b) and (c) are shown.

Figure 3

Effect of a magnetic field on the transition linewidth and frequency. (a) The magnetic field is calibrated using the width of the narrow resonance. The data are fit to a parabola, determining the field zero within 4 mG. (b) The result of 112 interleaved measurements where the field is varied during spectroscopy. The frequencies of the zero field values are used as a reference for presentation purposes. The slope of all of the measurements for this axis yields an average value of $26(4)\mathrm{Hz}/\mathrm{G}$. (c) Summary of field calibrations during the 24-hour absolute frequency measurement.

Figure 4

Absolute frequency measurement of the ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ transition. (a) Counting record of 880 measurements taken over a 24 h period yields a mean value of 71.8(6) Hz (corrected only for the maser offset in Table ). The offset frequency ${\nu }_0$ is 429 228 004 229 800 Hz. (b) The uncertainty averages down as $N^{-0.501(4)}$, where $N$ is the number of measurements (randomized), reaching $1.4\times {10}^{-15}$. (c) A histogram of the frequency measurements in (a) with a Gaussian fit (red curve) of the data. (d) Comparison of the final value ${\nu }_{\mathrm{Sr}}$ reported here with recent measurements by the JILA (circle), SYRTE (triangle), and Tokyo (square) groups.