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Physical Review Letters

Frequency Ratio of Hg 199 and Sr 87 Optical Lattice Clocks beyond the SI Limit

K. Yamanaka, Noriaki Ohmae, Ichiro Ushijima, Masao Takamoto, Hidetoshi Katori

Published Jun 10, 2015• 104 citations
Publisher

Abstract

We report on a frequency ratio measurement of a $^{199}\mathrm{Hg}$-based optical lattice clock referencing a $^{87}\mathrm{Sr}$-based clock. Evaluations of lattice light shift, including atomic-motion-dependent shift, enable us to achieve a total systematic uncertainty of $7.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ for the Hg clock. The frequency ratio is measured to be ${\ensuremath{\nu}}_{\mathrm{Hg}}/{\ensuremath{\nu}}_{\mathrm{Sr}}=2.629\text{ }314\text{ }209\text{ }898\text{ }909\text{ }60(22)$ with a fractional uncertainty of $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$, which is smaller than the uncertainty of the realization of the International System of Units (SI) second, i.e., the SI limit.

DOI
10.1103/physrevlett.114.230801

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Atomic clock frequency ratios with fractional uncertainty ≤3.2×10−18\leq 3.2 \times 10^{-18}≤3.2×10−18
We report high-precision frequency ratio measurements between optical atomic clocks based on 27^{27}27Al+^++, 171^{171}171Yb, and 87^{87}87Sr. With total fractional uncertainties at or below 3.2×10−183.2 \times 10^{-18}3.2×10−18, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in 87^{87}87Sr ratios at approximately 1×10−161\times10^{-16}1×10−16 and the Al+^++/Yb ratio at 1.6×10−171.6\times10^{-17}1.6×10−17 in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key innovation in this work is the use of a common ultrastable reference delivered to all clocks via a 3.6 km phase-stabilized fiber link between two institutions. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of 1.3×10−161.3 \times 10^{-16}1.3×10−16 at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.
We report high-precision frequency ratio measurements between optical atomic clocks based on ^{27}Al^{+}, ^{171}Yb, and ^{87}Sr. With total fractional uncertainties at or below 3.2×10^{-18}, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in ^{87}Sr ratios at approximately 1×10^{-16} and the Al^{+}/Yb ratio at 1.6×10^{-17} in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key upgrade from our previous work is the use of a common ultrastable reference delivered to all clocks via a 3.6-km phase-stabilized fiber link between two institutions, enabling better accuracy and stability in frequency transfer. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2-3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of 1.3×10^{-16} at 1 s. Identifying individual clock stabilities with a three-corner-hat measurement, we demonstrate the most stable optical lattice and trapped-ion clocks used in a multispecies comparison. By enabling faster comparisons, this stability will improve sensitivity to nonwhite noise processes and other underlying limits of state-of-the-art optical frequency standards.
An Al+^++ clock with 1.6×10−181.6\times10^{-18}1.6×10−18 systematic uncertainty and its frequency ratios
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A Wannier-Stark optical lattice clock has demonstrated unprecedented measurement precision for optical atomic clocks. We present a systematic evaluation of the lattice light shift, a necessary next step for establishing this system as an accurate atomic clock. With precise control of the atomic motional states in the lattice, we report accurate measurements of the multipolar and the hyperpolar contributions and the operational lattice light shift with a fractional frequency uncertainty of 3.5×10^{-19}.
We report an optical lattice clock with a total systematic uncertainty of 8.1×10^{-19} in fractional frequency units, representing the lowest uncertainty of any clock to date. The clock relies on interrogating the ultranarrow ^{1}S_{0}→^{3}P_{0} transition in a dilute ensemble of fermionic strontium atoms trapped in a vertically-oriented, shallow, one-dimensional optical lattice. Using imaging spectroscopy, we previously demonstrated record high atomic coherence time and measurement precision enabled by precise control of collisional shifts and the lattice light shift. In this work, we revise the black body radiation shift correction by evaluating the 5s4d ^{3}D_{1} lifetime, necessitating precise characterization and control of many body effects in the 5s4d ^{3}D_{1} decay. Last, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition. All other systematic effects have uncertainties below 1×10^{-19}.
Atomic clocks occupy a unique position in measurement science, exhibiting higher accuracy than any other measurement standard and underpinning six out of seven base units in the SI system. By exploiting higher resonance frequencies, optical atomic clocks now achieve greater stability and lower frequency uncertainty than existing primary standards. Here, we report frequency ratios of the 27^{27}27Al+^++, 171^{171}171Yb and 87^{87}87Sr optical clocks in Boulder, Colorado, measured across an optical network spanned by both fiber and free-space links. These ratios have been evaluated with measurement uncertainties between 6×10−186\times10^{-18}6×10−18 and 8×10−188\times10^{-18}8×10−18, making them the most accurate reported measurements of frequency ratios to date. This represents a critical step towards redefinition of the SI second and future applications such as relativistic geodesy and tests of fundamental physics.