The invention of the atomic clock has enabled applications like the global navigation satellite system, are important for telecommunication and are used for the definition of the SI second. Nowadays, optical clocks allow for measurement of height differences on the centimeter scale and can be employed for tests of the standard model of particle physics. Among the various implementations of optical clocks, this thesis focuses on an Al⁺ clock. For this work an optical resonator is examined, which enables the simultaneous frequency stabilization of two laser on the same mirror pair through the use of a dual-wavelength coating. Various contributions on the frequency stability are characterized and correlations are investigated. This cavity enables high fidelities in coherent manipulation of trapped ions, as required to operate the Al⁺ clock. This thesis partly builds upon the findings presented in Ref. Kramer, 2023. The setup and the systematic shifts are revisited and a detailed evaluation of the shifts is conducted, resulting in a total fractional frequency uncertainty of 1.6×10⁻¹⁸. The biggest contribution is from an ac-Stark shift induced by cooling during the clock interrogation, resulting in a shift of −9.3(1.1) × 10⁻¹⁸. The cooling reduces the second order Doppler shift to −1.6(0.2)×10⁻¹⁸. Additionally, a position dependent micromotion of the ion was investigated, which contributes an uncertainty of 0.38 × 10⁻¹⁸. Moreover, the first-order Doppler shift, servo error, ac-Stark shift of the clock laser and the phase chirp are determined for the first time, showing uncertainties below 10⁻¹⁸. The first frequency comparison between the Al⁺ clock and the ¹¹⁵In⁺, ¹⁷¹Yb⁺ and ⁸⁷Sr clocks at PTB are demonstrated. Measurements against Sr reveal a stability of the Al+ clock of 5.9 × 10⁻¹⁶ at 1s , which is one of the best single ion clock stabilities to date. All measured frequency ratios fall within the 10⁻¹⁸ uncertainty regime. The ratio between Sr/Al⁺ exhibits a significant deviation of more than 8.6𝜎 from published measurement data, underscoring the importance of inter-institutional frequency ratio measurements to verify the uncertainty budgets and reproducibility of optical clocks.
The invention of the atomic clock has enabled applications like the global navigation satellite system, are important for telecommunication and are used for the definition of the SI second. Nowadays, optical clocks allow for measurement of height differences on the centimeter scale and can be employed for tests of the standard model of particle physics. Among the various implementations of optical clocks, this thesis focuses on an Al⁺ clock. For this work an optical resonator is examined, which enables the simultaneous frequency stabilization of two laser on the same mirror pair through the use of a dual-wavelength coating. Various contributions on the frequency stability are characterized and correlations are investigated. This cavity enables high fidelities in coherent manipulation of trapped ions, as required to operate the Al⁺ clock. This thesis partly builds upon the findings presented in Ref. Kramer, 2023. The setup and the systematic shifts are revisited and a detailed evaluation of the shifts is conducted, resulting in a total fractional frequency uncertainty of 1.6×10⁻¹⁸. The biggest contribution is from an ac-Stark shift induced by cooling during the clock interrogation, resulting in a shift of −9.3(1.1) × 10⁻¹⁸. The cooling reduces the second order Doppler shift to −1.6(0.2)×10⁻¹⁸. Additionally, a position dependent micromotion of the ion was investigated, which contributes an uncertainty of 0.38 × 10⁻¹⁸. Moreover, the first-order Doppler shift, servo error, ac-Stark shift of the clock laser and the phase chirp are determined for the first time, showing uncertainties below 10⁻¹⁸. The first frequency comparison between the Al⁺ clock and the ¹¹⁵In⁺, ¹⁷¹Yb⁺ and ⁸⁷Sr clocks at PTB are demonstrated. Measurements against Sr reveal a stability of the Al+ clock of 5.9 × 10⁻¹⁶ at 1s , which is one of the best single ion clock stabilities to date. All measured frequency ratios fall within the 10⁻¹⁸ uncertainty regime. The ratio between Sr/Al⁺ exhibits a significant deviation of more than 8.6𝜎 from published measurement data, underscoring the importance of inter-institutional frequency ratio measurements to verify the uncertainty budgets and reproducibility of optical clocks.
An Al+ clock with 1.6×10−18 systematic uncertainty and its frequency ratios
Advances in optical clocks motivate a redefinition of the second, requiring rigorous evaluations of systematic uncertainties and robust consistency among the clocks. Here, we report the full evaluation of the systematic frequency shifts of an 27Al+ single-ion clock, and the measurement of its absolute frequency and frequency ratio with a 87Sr optical lattice clock at PTB. The evaluated total systematic fractional frequency uncertainty is 1.6×10−18, mainly limited by the accuracy of the relevant atomic coefficients and by background gas collisions. The absolute frequency of the clock has been measured to be νAl+=1121015393207859.19(24)Hz, obtained by comparison with two primary caesium fountain clocks at PTB. The frequency ratio between the Al and Sr optical clocks has been determined to be νAl+/ν87Sr=2.611701431781462668(36), limited by the accuracy of the Sr clock. This ratio differs by 8.6σ and 1.2σ from the 2021 and 2025 frequency ratio published by the BACON collaboration, respectively. These results represent an important contribution toward a future redefinition of the second using optical clocks, and underscore the importance of independent measurements of clock-candidate frequency ratios across different institutions.
Atomic clocks constitute a fundamental tool for time and frequency metrology and their application is widespread in many technological fields. In particular, the International System of units (SI) defines the second on a microwave transition of Caesium atoms. The realization is made by clocks reaching uncertainties of few parts in 10^−16, making the second to be the quantity realized with the smallest uncertainty in the SI. However, a new generation of atomic clocks, called optical clocks, have already demonstrated to surpass Caesium standards both in accuracy and stability. The research performed during my PhD activity has been focused on the development and characterization of Ytterbium (Yb) optical lattice clocks. These systems operate with a large number of ultra-cold neutral atoms having a clock transition in the visible region of the electromagnetic spectrum. The atomic sample is trapped in an periodical optical potential called optical lattice that gives the advantage to interrogate many quantum absorbers for an extended time, with small perturbations, allowing to achieve an unprecedented stability and accuracy. The main experimental work has been carried out in the laboratories of the Istituto Nazionale di Ricerca Metrologica (INRIM) in Turin, where several atomic clocks are present including the Italian primary frequency standard, the Caesium fountain ITCsF2, and where an Yb optical lattice clock is currently being developed. This thesis describes the functioning of the system along with the full characterization of systematic effects, the complete uncertainty budget and its first absolute frequency measurement against the primary frequency standard. The clock exhibited an accuracy of 1.6 × 10^−16 and the comparison with the Cs fountain resulted in a frequency of f171Yb = 518 295 836 590 863.59(31) Hz, limited by the fountain uncertainty. This measurement is in agreement with the ytterbium frequency recommended as a secondary representation of the second in the SI and constitutes the first measurement of a Yb clock in Europe and the second one in the world against a primary frequency standard. Several upgrades have been applied after the absolute measurement. In particular, the design and realization a system capable to frequency stabilize several lasers on a single optical cavity is illustrated. This cavity has been implemented to lock the lasers used to cool and trap the atomic sample at 399, 556 and 759nm using the offset sideband locking technique, a modified version of the Pound–Drever–Hall method that gives an extended frequency tunability. The system proved to be an easy-to-use and reliable tool for the experimental activity showing a linewidth below 300 Hz at 556nm, which is the wavelength that requires the most stringent performance, and a long term drift below 20 kHz per day at 759nm. That is suitable for operating the lattice laser with a light shift uncertainty below 1 × 10−18. During my PhD I have been guest researcher at the National Institute of Standards and Technology (NIST) of Boulder, Colorado, for nine months in 2016. In these laboratories two Yb optical lattice clocks are operative. I worked on the instability measurement of a composite system exploiting the two clocks to suppress the Dick effect, called zero-dead-time (ZDT) clock, which demonstrated a fractional instability of 3 × 10−17 at 1s. The two clocks can also be operated to extend the interrogation time obtaining a spectroscopic feature after 4 s of 120(20)mHz corresponding to a quality factor Q > 4 × 10^15. I also worked on the characterization of several systematic shifts that allowed to complete the uncertainty budget of the clocks at 1.6 × 10^−18. In particular, I contributed to the characterization of lattice light shifts considering the effect of atomic sample temperature and the identification of a metrological regime called operational magic frequency where frequency shifts are insensitive to changes in trap depth.
At the time of writing, state of the art stationary optical clocks reach 10 −18 sys- tematic fractional frequency uncertainty, which allows for the search of new physics beyond the standard model and lays the foundation for new applications such as chronometric leveling, where height differences relative to the geoid are derived from frequency comparisons among optical clocks. Transportable optical clocks allow for chronometric leveling between distant lo- cations which are not connected by a direct line of sight but via length stabilized optical fiber. Moreover, they facilitate frequency comparisons between distant sta- tionary clocks via subsequent side-by-side comparisons without the necessity of a long-range fiber connection. A transportable optical clock employing a single 40Ca+ ion has been reported and a neutral atom 87Sr lattice clock has been employed in a chronometric leveling campaign. However, these clocks report an estimated systematic fractional frequency uncertainty in the high 10^−17 range, which limits their height resolution to a level of approximately 1 m. 27Al+ has one of the smallest blackbody radiation shifts, small linear and quadratic Zeeman shifts and a negligible quadrupole shift, which makes it a candidate for a highly accurate optical clock. This thesis reports on the development, set-up, and characterization of a transportable 27Al+ clock setup with 40Ca+ as logic ion. The setup is simple, modular, compact, and mechanically stable. Ions of both species are generated via pulsed laser ablation and subsequent photoionization. They are confined in a multi-layer trap with segmented loading and experiment zones. Using a single 40Ca+ ion as probe, heating rates of below 10 quanta per second have been measured in all three directions for trap frequencies around 2π × 2 MHz, and pulsed sideband cooling to mean motional quantum numbers below 0.1 quanta was demonstrated. Imaging close to the diffraction limit with a signal to noise ratio of 800 for 300 ms exposure time on a sCMOS camera was achieved using a single NA = 0.51 biaspheric lens. Simultaneously, a state discrimination error below 10^−5 in 100 µs was obtained using a PMT. From the excess micromotion second order Doppler shift, secular motion second order Doppler shift, BBR shift, and background gas collision shift, a partial systematic fractional frequency uncertainty of 1.7 × 10^−18 was inferred, which is equivalent to a height resolution of ca. 2 cm. Moreover, a highly stable mechanical monolithic enhancement cavity for SHG has been developed and demonstrated to withstand accelerations of 3 g rms for 30 min. It has been operated for an uninterrupted period of 130 h without decay in output power in the mid-UV due to O2 -purging, its sealed design, and material selection, which solves the often observed crystal degradation in UV applications. The cavity has been employed in the 27Al+ logic laser system. In conclusion, it has been shown that an 27Al+ ion quantum logic optical clock operated in the present transportable setup could reach an estimated systematic fractional frequency uncertainty of 1.7 × 10^−18 , provided that all other shifts, such as the second order Zeeman shift, are negligible. This paves the way towards chronometric leveling with an unprecedented height resolution of about 2 cm.
The advancement of optical atomic clocks in the past two decades has motivated many potential applications in navigation, communication, and science. Accurate optical clocks that outperform the current cesium time standard also trigger a discussion about a possible redefinition of the SI second. The 27Al+ quantum logic clocks developed at the National Institute of Standards and Technology (NIST) were the first to achieve the clock fractional frequency uncertainty below 10-17 in 2010. To date, a few research groups around the world have demonstrated optical clocks based on various atomic transitions with fractional frequency uncertainty in the 10-18 range. The accuracy of the previous 27Al+ clocks was limited by the second order Doppler (time dilation) shift and the blackbody shift. Since 2010, the third 27Al+ optical clock is being developed at NIST to achieve a higher accuracy. The frequency uncertainties dominant in the previous clocks are controlled and reduced in the current optical clock. The new design of the ion trap system has reduced significantly both the blackbody radiation shift uncertainty and the time dilation shift uncertainty due to micromotion, while the time dilation shift uncertainty due to the secular motion has been reduced by more than an order of magnitude by operating the optical clock near the three dimensional zero-point energy. Despite those previously dominant uncertainties, several other systematic effects are being evaluated and some other efforts are being made to achieve a total uncertainty towards 1.0 x 10-18. In this thesis, I will document the detail of the construction and evaluation of the current 27Al+ optical clock developed at NIST.
Atomic clock frequency ratios with fractional uncertainty ≤3.2×10−18
We report high-precision frequency ratio measurements between optical atomic clocks based on 27Al+, 171Yb, and 87Sr. 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 87Sr 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 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 1.3×10−16 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.
Frequency standards based on optical transitions between electronic states of trapped ions have reached uncertainties below 10−18 [1]. The Stark shift caused by room-temperature blackbody radiation (BBR) causes the largest correction for most high-performance optical clock. The systematic uncertainty of 171Yb+ clocks based on the 2S1/2 (F = 0) → 2D3/2 (F = 2) electric quadrupole (E2) and 2S1/2 (F = 0) → 2F7/2 (F = 3) electric octupole (E3) transitions is currently limited to 28×10−18 and 1.5×10−18, respectively, by the fractional accuracy of the differential polarizability Δαdc of approximately 2% [2]. In the scope of this thesis, a dual species clock based on 171Yb+ and 88Sr+ ions was set up, operated and evaluated, to overcome this barrier. Since Δαdc is known with a smaller fractional uncertainty of 0.04% for the 2S1/2 → 2D5/2 E2 transition of 88Sr+ [3], this allows for a transfer of Δαdc from 88Sr+ to 171Yb+ following a method proposed in [4]. The optical intensity of a laser is calibrated with the Stark shift it causes on the 88Sr+ clock transition, allowing for the determination of Δαdc of the 171Yb+ clock transitions. This allows for a reduction of the fractional uncertainty of Δαdc for both 171Yb+ clock transitions below 0.4% and clock operation on the E2 and E3 transition with a fractional BBR shift uncertainty of 0.84×10−18 and 0.24×10−18 is enabled, respectively. However the value of Δαdc determined in this thesis does not agree with [2], a fractional offset of approximately 14% is observed. To investigate this discrepancy further, Δαdc is measured in the same manner as in [2] for the 88Sr+ clock transition. The same offset of approximately 14% is found, calling the accuracy of at least one of these methods into question. Finally, the first optical frequency ratio ℛ between the 88Sr+ clock transition and the 171Yb+ E3 transition is measured. The fractional uncertainty of ℛ is 23×10−18. ℛ in combination with the absolute frequency of the E3 transition allows for the determination of the 88Sr+ absolute frequency νSr+ with an uncertainty limited by the caesium references. The value of νSr+ falls outside of the recommended range, but is corroborated by measurements of the same quantity by other institutes [5, 6]. [1] M. Marshall et al., Phys. Rev. Lett. 135, 033201 (2025) [2] N. Huntemann et al., Phys. Rev. Lett. 116, 063001 (2016) [3] T. Lindvall et al., Phys. Rev. Lett. 135, 043402 (2025) [4] M. D. Barrett et al., Phys. Rev. A 100, 043418 (2019) [5] C. Marceau et al., Metrologia 62.4, 045001 (2025) [6] T. Lindvall et al., Phys. Rev. Appl. 24, 044082 (2025)