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 S 1/2 → 2 F 7/2 electric octupole (E3) transition in 171 Yb + against two caesium fountain clocks as f (E3) = 642 121 496 772 645.36(25) 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 S 1/2 → 2 D 3/2 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. The search for variations of fundamental constants is motivated by theories unifying the fundamental interactions and is regarded as an opportunity to open a window to new physics with implications on cosmology as well as on particle physics [1][2][3][4]. While early proposals for such a search using atomic spectroscopy have been made shortly after the discovery of the expansion of the universe [5], sensitive observational and experimental tools became available only recently. Astrophysical observations of absorption spectra of interstellar matter have led to claims for [6][7][8] and against [9-13] variations of the fine structure constant α and the proton-to-electron mass ratio µ = m p /m e at relative uncertainties in the range 10 −5 to 10 −7 on a cosmological time scale of several billion years. In the laboratory, the high precision of atomic clocks that now reach relative uncertainties of 10 −16 and below in frequency ratios has been used to infer limits on variations of α and µ in the present epoch [14][15][16][17].In this Letter we present a high-accuracy absolute frequency measurement of the 2 S 1/2 → 2 F 7/2 electric octupole transition in 171 Yb + that possesses a strong sensitivity to changes of α. Together with recently reported frequency measurements of the 2 S 1/2 → 2 D 3/2 electric quadrupole transition in the same ion [18] this allows us to constrain possible temporal changes of both transition frequencies relative to caesium clocks. Besides confirming limits on dα/dt in the low 10 −17 /yr range these data provide the most stringent limit on dµ/dt from a laboratory experiment.171 Yb + is particularly attractive for a search for variations of fundamental constants because there are two transitions with low natural linewidth from the ground state to metastable states that have rather different electronic configurations [see Fig. 1(a)]. In case of the 2 S 1/2 (F = 0) → 2 D 3/2 (F = 2, m F = 0) electric quadrupole (E2) transition at 436 nm the 6s va- lence electron is promoted to the 5d level, while on the 2 S 1/2 (F = 0) → 2 F 7/2 (F = 3, m F = 0) electric octupole (E3) transitio...

We have measured the absolute frequency of the optical lattice clock based on 87 Sr 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 s 2 1 S 0 -5s5p 3 P 0 transition in 87 Sr 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.

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.

Optical clocks are not only powerful tools for prime fundamental research, but are also deemed for the re-definition of the SI base unit second as they now surpass the performance of caesium 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 the optical clocks that made a continuous realization of a timescale impractical. In this paper, we demonstrate how this situation can be resolved and that a timescale based on an optical clock can be established that is superior to one based on even the best caesium 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.

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, m F = 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 center, the central Ramsey fringe has a width of 0.9 Hz. About 3 × 10 4 atoms, 30% of the initial number in the |F = 3, m F = 0 state, are detected after their second interaction with the microwave field. Stabilizing the microwave frequency to the center 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.