A cryogenic strontium lattice clock

Optical clocks have moved to the forefront of frequency metrology. Their outstanding performances enable the exploration of new fields of research such as the search for dark matter and dark energy, temporal drifts of the fine structure constant α [3-5], violations of the Einstein equivalence principle (EEP), and new applications such as chronometric leveling. State-of-the-art optical clocks outperform the current realization of the SI-unit "Second" by the ${}^{133}$cesium fountain clocks, by two orders magnitude or more in instability and accuracy which triggers a discussion on a re-definition of the second. In 2016 the Consultative Committee for Time and Frequency (CCTF) of the International Bureau of Weights and Measures (BIPM) released a roadmap towards a redefinition of the SI second${}^1$. One of the requests is the characterization of the systematic uncertainty of at least three independent clocks at the level of 10${}^{-18}$. In this work, PTB's new cryogenic strontium lattice clock, Sr3, operating on the ${}^1$S${}_0$ - ${}^3$P${}_0$ clock transition in neutral ${}^{87}$Sr is described. Its systematic uncertainty has is evaluated to 2.7 $\times$ 10${}^{-18}$ in fractional frequency units. This represents an improvement of more than a factor of 5 compared to its predecessor system Sr1. In Sr1 the dominant contribution of frequency uncertainty was about 1.4 $\times$ 10${}^{-17}$ from the uncertainty of the black-body radiation (BBR) frequency shift. It arose from temperature gradients across the in-vacuum magnetic field coils that are placed close to the atoms. Reducing the gradients was not possible which ultimately limited the systems achievable systematic uncertainty. Sr3 features an in-vacuum dual-layer environment, the cryostat, that provides a very homogeneous temperature distribution for the atoms. This translates to a lower BBR frequency shift uncertainty as Sr1 at room temperature operation. The corresponding total systematic uncertainty for room temperature operation was evaluated to about 3.5 $\times$ 10${}^{-18}$. Furthermore Sr3 features a closed-cycle pulse tube cooler that allows to operate the cryostat at any temperature ranging from room temperature to about 80K to further reduce the BBR frequency shift and uncertainty where the systematic uncertainty reaches the value of 2.7 $\times$ 10${}^{-18}$ as mentioned above. Sr3 also features an arrangement of electrodes that allow the characterization of the dc-Stark frequency shift in three dimensional space. In this work the characterization of the electrode arrangement is described and the determination of the dc Stark shift. In Sr1 the this capability was limited to one direction that was pointing along the quantization magnetic field axis. During clock operation of Sr1, several high-accuracy comparisons to other atomic clocks have been performed. This includes many absolute frequency measurements yielding in a new record uncertainty in the transition frequency. An absolute frequency of Sr1 of ν${}_{Sr1}$ = 429 228 004 229 873.00(7)Hz was measured that is in agreement withe the one measured of Sr3 of ν${}_{Sr3}$ = 429 228 004 229 872.94(19)Hz. The statistical uncertainty the measurements was significantly improved by using a H-Maser as a ywheel oscillator to either extend the dataset or to bridge downtimes of the Sr-clocks. Optical frequency ratio measurements between either of the two strontium clocks and the on-campus ${}^{171}$Yb${}^{+}$ single-ion clock have been carried out for direct determination of their frequency ratio beyond the limitation of the primary frequency standards represented by Cs fountain clocks. The ratio measurements involving Sr1 span over a period of more than seven years and more than half a year with Sr3. The measurements have also revealed that the frequency ratio of the clocks, are reproducible within their uncertainties on short time scales but exhibits unexpected large scatter in the long term. The observed variations are on the order of several 10${}^{-17}$ which is beyond any of the clocks reported systematic uncertainty. Despite an excessive search no uncontrolled frequency shifts were found. In the near future the in-vacuum cryostat is supposed to be updated with rotatable shutters. They will allow to minimize the BBR shift uncertainty during cryogenic operation. Prospectively a BBR shift uncertainty at the low 10${}^{-19}$ level can be expected which paves the way for the system to reach a total systematic uncertainty of below 1 $\times$ 10${}^{-18}$.