S. Weyers

A strontium lattice clock with 3 × 10 −17 inaccuracy and its frequency

We have measured the absolute frequency of the optical lattice clock based on 87Sr at PTB with an uncertainty of 3.9 × 10−16 using two caesium fountain clocks. This is close to the accuracy of todayʼs best realizations of the SI second. The absolute frequency of the 5 s2 1S0 – 5s5p 3P0 transition in 87Sr is 429 228 004 229 873.13(17) Hz. Our result is in excellent agreement with recent measurements performed in different laboratories worldwide. We improved the total systematic uncertainty of our Sr frequency standard by a factor of five and reach 3 × 10−17, opening new prospects for frequency ratio measurements between optical clocks for fundamental research, geodesy or optical clock evaluation.

Realization of a timescale with an accurate optical lattice clock

Optical clocks are not only powerful tools for prime fundamental research, but are also deemed for the redefinition of the SI base unit “second,” as they now surpass the performance of cesium atomic clocks in both accuracy and stability by more than an order of magnitude. However, an important obstacle in this transition has so far been the limited reliability of optical clocks, which made a continuous realization of a timescale impractical. In this paper, we demonstrate how this situation can be resolved and show that a timescale based on an optical clock can be established that is superior to one based on even the best cesium fountain clocks. The paper also gives further proof of the international consistency of strontium lattice clocks on the 10−16 accuracy level, which is another prerequisite for a change in the definition of the second.

Atomic fountain clocks

We describe and review the current state of the art in atomic fountain clocks. These clocks provide the best realization of the SI second possible today, with relative uncertainties of a few parts in 1016.

High-accuracy optical clock based on the octupole transition in 171Yb+.

We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.

Uncertainty evaluation of the atomic caesium fountain CSF1 of the PTB

A new primary frequency standard, the atomic caesium fountain CSF1, has been put into operation at the Physikalisch-Technische Bundesanstalt (PTB). 133Cs atoms are cooled in a magneto-optical trap and in optical molasses. They are launched to a height of 39 cm above the microwave cavity centre. The resulting Ramsey resonance signal has a full-width half-maximum linewidth (FWHM) of 0.88 Hz. The first uncertainty evaluation yields a relative 1 σ frequency uncertainty of 1.4 × 10−15. The short-term relative frequency instability of the CSF1 for averaging time τ is typically 3.5 × 10−13 (τ/s)−1/2, dictated by the available quartz oscillator as the local frequency source.

Improved limit on a temporal variation of mp/me from comparisons of Yb+ and Cs atomic clocks.

Accurate measurements of different transition frequencies between atomic levels of the electronic and hyperfine structure over time are used to investigate temporal variations of the fine structure constant α and the proton-to-electron mass ratio μ. We measure the frequency of the (2)S1/2→(2)F7/2 electric octupole (E3) transition in (171)Yb(+) against two caesium fountain clocks as f(E3)=642,121,496,772,645.36  Hz with an improved fractional uncertainty of 3.9×10(-16). This transition frequency shows a strong sensitivity to changes of α. Together with a number of previous and recent measurements of the (2)S1/2→(2)D3/2 electric quadrupole transition in (171)Yb(+) and with data from other elements, a least-squares analysis yields (1/α)(dα/dt)=-0.20(20)×10(-16)/yr and (1/μ)(dμ/dt)=-0.5(1.6)×10(-16)/yr, confirming a previous limit on dα/dt and providing the most stringent limit on dμ/dt from laboratory experiments.

Absolute frequency measurement of the 435.5-nm (171)Yb+-clock transition with a Kerr-lens mode-locked femtosecond laser.

We have measured the frequency of the 6s(2)S(1/2)(2)-5d D(3/2)(2) electric-quadrupole transition of (171)(Yb) (+) with a relative uncertainty of 1x10(-14) , nu(Yb)=688358 979309312Hz +/-6Hz . We used a femtosecond frequency comb generator to phase-coherently link the optical frequency derived from a single trapped ion to a cesium-fountain-controlled hydrogen maser. This measurement is one of the most accurate measurements of optical frequencies ever reported, and it represents a contribution to the development of optical clocks based on a (171)Yb(+)-ion standard.

Uncertainty evaluation of the caesium fountain clock PTB-CSF2

The uncertainty evaluation of CSF2, the second caesium fountain primary frequency standard at PTB, is presented. The fountain uses optical molasses to cool atoms down to 0.6 µK. The atoms are launched vertically in a moving optical molasses, and state selected in the |F = 3, mF = 0 hyperfine ground state. During their ballistic flight, the atoms interact twice with a microwave field, thus completing the Ramsey interaction. With a launch height of 36.5 cm above the cavity centre, the central Ramsey fringe has a width of 0.9 Hz. About 3 × 104 atoms, 30% of the initial number in the |F = 3, mF = 0 state, are detected after their second interaction with the microwave field. Stabilizing the microwave frequency to the centre of the central Ramsey fringe, a typical relative frequency instability of 2.5 × 10−13(τ/s)−1/2 is obtained. The CSF2 systematic uncertainty for realizing the SI second is estimated as 0.80 × 10−15. First comparisons with the fountain CSF1 at the Physikalisch-Technische Bundesanstalt and other fountain frequency standards worldwide demonstrate agreement within the stated uncertainties.

Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2

We evaluate the frequency error from distributed cavity phase in the caesium fountain clock PTB-CSF2 at the Physikalisch-Technische Bundesanstalt with a combination of frequency measurements and ab initio calculations. The associated uncertainty is 1.3 × 10 −16 , with a frequency bias of 0.4 × 10 −16 . The agreement between the measurements and calculations explains the previously observed frequency shifts at elevated microwave amplitude. We also evaluate the frequency bias and uncertainty due to the microwave lensing of the atomic wave packets. We report a total PTB-CSF2 systematic uncertainty of 4.1 × 10 −16 .

The 87Sr optical frequency standard at PTB

With 87Sr atoms confined in a one-dimensional optical lattice, the frequency of the optical clock transition 5s2 1S0–5s5p 3P0 has been determined to be 429 228 004 229 872.9(5) Hz. The transition frequency was measured with the help of a femtosecond-frequency comb against one of Physikalisch-Technische Bundesanstalt (PTBs) H-masers whose frequency was measured simultaneously by the PTB Cs-fountain clock CSF1. The Sr optical frequency standard contributes with a fractional uncertainty of 1.5 × 10−16 to the total uncertainty. The agreement of the measured transition frequency with previous measurements at other institutes supports the status of this transition as the secondary representation of the second with the currently smallest uncertainty.