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Spectroscopy schemes for improved optical clock stability

Filip Butuc-Mayer

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Frequency metrology underpins precise measurements. At the forefront of this field are optical clocks which can perform measurements that are accurate to more digits than those in the number representing seconds elapsed from the beginning of the universe. Frequency estimation errors in the operation of optical clocks lead to frequency instability, prohibiting them from reaching high accuracies on short to medium time scales, and limiting access to interesting measurements of the atomic environment and exotic external perturbations such as gravity fields or fields of fundamentally new physical origins. Optical lattice traps are typically employed in state-of-the-art optical clocks to suppress Doppler effects. By carefully tuning the optical lattice to the magic wavelength, unwanted Stark shifts can be suppressed significantly, allowing operation with thousands of atoms and minimising the fundamental source of frequency estimation errors, namely the quantum projection noise, to around 3 × 10−17 at 1 s. In this thesis, the status of the two Strontium optical lattice clocks at NPL, Sr1 and Sr2, is presented going over a few interesting measurement campaigns from the past years involving Sr1 and the latest experimental efforts to re-enable operation of Sr2. A model of clock stability is developed by incorporating known and new frameworks to characterise the relation between the operating parameters of optical clocks and their performance, with relevance to the NPL lattice clocks and beyond. In particular, a method is identified for addressing the main technical noise for optical lattice clocks, the Dick effect, which typically has a magnitude of 10−16 at 1 s and prevents optical lattice clocks from reaching the quantum projection noise level. By taking advantage of dynamical decoupling we can engineer an optimised duty cycle with benefits in general for systems limited by the optical coherence of the clock laser. Moreover, a study of other noise sources in the NPL lattice clocks is conducted using synchronous measurements between Sr1 and Sr2, revealing a large contribution from linear Zeeman shifts, also at the 10−16 level, and a plan to tackle them is detailed. A hybrid clock architecture is discussed showing how optical lattice clocks can improve the optical coherence of ion clocks thanks to their higher servo rate, and a preliminary experimental demonstration is reported. Finally, a new type of spectroscopy is presented which completely avoids aliasing of linear Zeeman shifts by simultaneously driving transitions with opposite Zeeman sensitivities. Such a technique also enables the continuous interrogation of atoms, a crucial missing component in the Dick-free conveyor belt lattice clock concept heralded as the next standard of stable optical clocks.

DOI
10.5287/ora-r5prj7yba

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Chinese Optics Letters•Jan 1, 2025•2 citations
Frequency metrology underpins precise measurements. At the forefront of this field are optical clocks which can perform measurements that are accurate to more digits than those in the number representing seconds elapsed from the beginning of the universe. Frequency estimation errors in the operation of optical clocks lead to frequency instability, prohibiting them from reaching high accuracies on short to medium time scales, and limiting access to interesting measurements of the atomic environment and exotic external perturbations such as gravity fields or fields of fundamentally new physical origins. Optical lattice traps are typically employed in state-of-the-art optical clocks to suppress Doppler effects. By carefully tuning the optical lattice to the magic wavelength, unwanted Stark shifts can be suppressed significantly, allowing operation with thousands of atoms and minimising the fundamental source of frequency estimation errors, namely the quantum projection noise, to around 3 × 10−17 at 1 s. In this thesis, the status of the two Strontium optical lattice clocks at NPL, Sr1 and Sr2, is presented going over a few interesting measurement campaigns from the past years involving Sr1 and the latest experimental efforts to re-enable operation of Sr2. A model of clock stability is developed by incorporating known and new frameworks to characterise the relation between the operating parameters of optical clocks and their performance, with relevance to the NPL lattice clocks and beyond. In particular, a method is identified for addressing the main technical noise for optical lattice clocks, the Dick effect, which typically has a magnitude of 10−16 at 1 s and prevents optical lattice clocks from reaching the quantum projection noise level. By taking advantage of dynamical decoupling we can engineer an optimised duty cycle with benefits in general for systems limited by the optical coherence of the clock laser. Moreover, a study of other noise sources in the NPL lattice clocks is conducted using synchronous measurements between Sr1 and Sr2, revealing a large contribution from linear Zeeman shifts, also at the 10−16 level, and a plan to tackle them is detailed. A hybrid clock architecture is discussed showing how optical lattice clocks can improve the optical coherence of ion clocks thanks to their higher servo rate, and a preliminary experimental demonstration is reported. Finally, a new type of spectroscopy is presented which completely avoids aliasing of linear Zeeman shifts by simultaneously driving transitions with opposite Zeeman sensitivities. Such a technique also enables the continuous interrogation of atoms, a crucial missing component in the Dick-free conveyor belt lattice clock concept heralded as the next standard of stable optical clocks.
Clocks based on optical transitions in ions and atoms are quickly moving to the forefront of the frequency standards field mainly because of the high spec-tral resolution, and therefore the potential stability and accuracy, which can be achieved. In this thesis a new optical clock based on neutral atoms trapped in an optical lattice is presented, demonstrating spectroscopy of the clock transition free of any lineshape or accuracy degradation due to atomic motion. The system simu-lates a single trapped ion clock, but allows use of thousands of atoms for improved signal to noise ratio, and clock stability. High accuracy can also be achieved as the lattice can be designed to shift the energy of the two atomic clock states equally, such that the transition frequency is unchanged. Strontium is a natural candidate for such a clock as it offers an extremely narrow optical transition (∼1 mHz) based on atomic states which are very insensitive to external fields. The strontium level structure allows efficient laser cooling to 1 µK with diode laser sources, and a con-venient wavelength of 813 nm for the zero-differential Stark shift optical lattice. The strontium lattice clock system has allowed observation of high signal-to-noise
Accurate time keeping is critical to the function and advancement of many human endeavours. Atomic clocks based on a microwave transition in atomic Cs have served as primary frequency standards to realise the SI second since their formal adoption in 1967. State-of-the-art, laser cooled, Cs fountains now routinely operate with fractional frequency uncertainties below the 10⁻¹⁵ level in laboratories throughout the world. Over the last decade, efforts to build frequency standards based on optical transitions have come to fruition and potential inaccuracies below the 10⁻¹⁷ level have been demonstrated. Such standards point to the future of time keeping and much development is being pursued to realise the potential of these 'next generation' optical clocks. One such approach, on which this work focusses, relies on a 'magic' wavelength optical lattice trap to provide (almost) Doppler- and recoil-free confinement of atoms during clock interrogation. At this 'magic' wavelength, light induced perturbation of the clock states is equal and so cancels precisely. This thesis describes the design and implementation of an optical lattice frequency standard apparatus based on 88Sr held in a 1D optical lattice. A review of the development of atomic frequency metrology is given from a historical viewpoint and the technology and limitations of current methods discussed. To tackle the blackbody radiation shift, which currently presents the greatest limitation to the Sr lattice clock, imposing at the 10⁻¹⁶ level, a scheme to measure the blackbody radiation shift coefficient at the 10⁻¹⁷ level is developed. Techniques to laser cool and trap atomic strontium are described and the implementation detailed. All laser systems required for clock operation are described including the design and implementation of extended-cavity diode lasers for precision spectroscopy. Details relevant to the eventual operation of the apparatus are discussed.
Abstract We describe a method of duty cycle engineering in optical lattice clocks to reduce clock instability through tailoring of the Dick effect noise contribution. We apply dynamically decoupled interrogation sequences to realise an estimated improvement in single clock instability approaching a factor of two, as well as providing a route to zero dead-time operation for two interleaved clocks which are otherwise unable to reach the required duty cycle. We show through simulations and synchronous measurements of clocks NPL-Sr1 and NPL-Sr2 that a quantum projection noise limited instability < 3 − 10−17 τ −1/2 can be realised in a near ideal zero dead-time configuration.
Strontium optical lattice clocks can measure the passage of time with extraordinary precision. Capitalising on this precision, we can anticipate the deployment of lattice clocks to search for new physics beyond the standard model, to build new technologies for geodesy and navigation, and potentially to underpin a future redenition of the SI second. This thesis reports on the construction and evaluation of a robust Sr optical lattice clock at NPL. We describe the apparatus needed to capture, cool, and load samples of neutral strontium atoms into a magic-wavelength, far off-resonant lattice trap at 813 nm. We provide details of our optical local oscillator - the "clock laser" - and how it is used to realise an Sr-referenced optical frequency standard. We rigorously characterise the various contributing factors which limit the performance of the clock, focusing on the standard measures of (1) frequency instability, and (2) systematic frequency uncertainty. Finally, we introduce new innovations for improving the accuracy of the 88Sr lattice clock, including methods of "modified hyper-Ramsey" and multi-photon spectroscopy of the clock transition.
Optical clocks are being developed worldwide and are at the forefront of frequency metrology. Today they outperform microwave clocks instability and inaccuracy by two orders of magnitude, raising discussion about the redefinition of the SI second. Their outstanding performances are paving the way to applications in different fields apart from metrology. Optical clocks can be used for geodetic measurements, such as chronometric levelling, and fundamental physics experiments. These applications require transportable, and even space-born optical clocks that are in development. Space optical clocks will serve as a high accurate references for intercontinental clock comparisons, and will also provide a unique test bench for fundamental physics theories, such as Einstein’s prediction of time dilation and equivalence principle. This work presents the development and characterization of a transportable strontium optical lattice clock, realised in the framework of the ESA I-SOC (Space Optical Clock on the ISS) mission. The aim of the project is to investigate new technologies and techniques, in order to develop a robust apparatus as demonstrator for space applications. Special effort has been made to reduce the size and weight of the clock, so as to meet the stringent requirements of a space mission. The system reported here is one of the most compact optical clock to date, with a total volume of only 1 m3, excluding electronics. The clock is operated with the strontium bosonic isotope 88Sr: this is preferable to the fermionic counterpart 87Sr, commonly used in optical lattice clocks, if simplicity and reliability are required. However, in terms of accuracy, bosonic clocks present some disadvantages compared with the fermionic ones, which have significantly slowed down their development for metrological applications. We characterised the relevant operating parameters and their effect on the clock accuracy and instability. Exploiting a clock laser offering an outstanding stability, we were able to demonstrate a clock fractional instability of 3×10-18 , and an inaccuracy of 2×10-17: both values represent a factor of 30 improvement compared with previous works on bosonic optical clocks. These results suggest that, in the near future, bosonic clocks may become competitive to their fermionic counterparts. This is of interest for applications such as time scale realization, transportable clocks, or for test of fundamental physics. As an example, we measured the 88Sr-87Sr isotope shift, with an uncertainty of 12 mHz.
Optical lattice clocks demonstrate advantages in metrology and frontier physics because of their high stability.Here, we present approaches to enhancing the stability by decoupling the noise related to the short-term and long-term stability.For the short-term stability, we optimize the clock laser by decoupling the frequency noise, and optimize each noise contribution individually until it is below the thermal noise limit.For the long-term stability, we introduce a method to decouple the instability caused by systematic effects.Having identified that the collision frequency shift was the main limiting factor in our systems, we thus optimized the atom number fluctuations in optical lattices.Through targeted optimization, we achieve a synchronous comparison of two clocks with an average stability of 3.2 × 10 -16 = τ p and a long-term stability of 2.4 × 10 -18 at 8000 s.This work provides an analytical framework for enhancing optical clock stability.