arXiv subjects

Erik Benkler

Publications and source records attributed to Erik Benkler.

18 recordsLinked to original sources

arXiv2026

Interspecies clock comparison below $5 \times 10^{-18}$ uncertainty with a transportable clock

We report a measurement of the optical frequency ratio between the $^2\mathrm{S}_{1/2}(F=0)$--${^2\mathrm{F}_{7/2}(F=3)}$ electric-octupole (E3) transition of $^{171}$Yb$^{+}$ and the $^1\mathrm{S}_0$--${^3\mathrm{P}_0}$ transition of $^{87}$Sr, $\nu_{\mathrm{Yb}^{+}}/\nu_\mathrm{Sr} = 1.495\,991\,618\,544\,900\,588\,1(65)$. Reaching a fractional uncertainty of $4.3 \times 10^{-18}$, this result improves upon the previous best by more than a factor of three and is among the few that meet the requirements for interspecies clock comparisons specified by the roadmap towards the redefinition of the SI second. The comparison is between a transportable optical lattice clock and a stationary single-ion clock. It spans a period of nearly two years, during which the transportable clock was intermittently operated off-campus. The ratio was reproducibly measured during four separate campaigns, which are consistent within their statistical uncertainties. The results demonstrate reproducible $10^{-18}$ level operation of the transportable clock and thus validate its application for chronometric geodesy and as a transfer standard for inter-institute clock comparisons, e.g., in the absence of optical fiber links.

physics.atom-ph↗

arXiv2026

An Al$^+$ clock with $1.6\times10^{-18}$ 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 $^{27}\mathrm{Al}^+$ single-ion clock, and the measurement of its absolute frequency and frequency ratio with a $^{87}$Sr optical lattice clock at PTB. The evaluated total systematic fractional frequency uncertainty is $1.6\times10^{-18}$, 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 $\nu_{\mathrm{Al}^+}=1 121 015 393 207 859.19(24)\,$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 $\nu_{\mathrm{Al}^+}/\nu_{^{87}\mathrm{Sr}}=2.611 701 431 781 462 668(36)$, limited by the accuracy of the Sr clock. This ratio differs by $8.6\sigma$ and $1.2\sigma$ 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.

physics.atom-ph↗

arXiv2026

International Optical Clock Comparison Using the European Optical Fiber Network

Optical clocks have achieved remarkable estimated fractional frequency uncertainties reaching the $10^{-18}$ level and below, enabling applications in fundamental physics, general relativity, and geodesy. However, the challenge of verifying the international consistency of optical clocks remains critical as efforts intensify toward redefining the SI second based on an optical transition or transitions. We report on a two-month international clock comparison campaign involving seven optical clocks in four national metrology institutes (INRIM, LNE-OP, NPL, and PTB) connected via the optical fiber network established in Europe. The campaign resulted in optical frequency ratios with uncertainties ranging from $7.7\times10^{-18}$ to $6.1\times10^{-17}$. Among the results, the $^{171}$Yb$^+$(E3) clocks at NPL and PTB demonstrated agreement within an uncertainty of $7.7\times10^{-18}$, marking the first international verification of two independently developed optical clocks below one part in $10^{17}$. The operation of the $^{199}$Hg clock at LNE-OP (formerly LNE-SYRTE) resulted in frequency ratios with improved uncertainties with $^{171}$Yb$^+$(E3), $^{171}$Yb, and $^{87}$Sr optical clocks. These results provide input for the redefinition of the second and underscore how fiber-linked clock networks can advance metrology and scientific applications.

physics.atom-ph↗

arXiv2025

A high-stability optical clock based on a continuously ground-state cooled Al$^+$ ion without compromising its accuracy

Single ion optical clocks have shown systematic frequency uncertainties below $10^{-18}$, but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically-induced transparency (EIT) of an \Al clock ion via a co-trapped \Ca ion during clock interrogation suppresses the heating of the ions. \Al can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time dilation shift of $(-1.69\pm0.20)\times10^{-18}$. The \Ca cooling light introduces an additional light shift on the \Al clock transition of $(-9.27\pm 1.03)\times10^{-18}$. We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with $10^{-19}$ motional and cooling laser-induced uncertainties for \Al and can be employed in other ion clocks as well.

physics.atom-ph↗

arXiv2025

Entanglement-enhanced optical ion clock

Entangled states hold the promise of improving the precision and accuracy of quantum sensors. We experimentally demonstrate that spectroscopy of an optical clock transition using entangled states can outperform its classical counterpart. Two ^{40}\text{Ca}^{+} ions are entangled in a quantum state with vanishing first-order magnetic field sensitivity, extending the coherence time of the atoms and enabling near lifetime-limited probe times of up to 550 ms. In our protocol, entangled ions reach the same instability as uncorrelated ions, but at half the probe time, enabling faster cycle times of the clock. We run two entangled ^{40}\text{Ca}^{+} ions as an optical clock and compare its frequency instability with a ^{87}\text{Sr} lattice clock. The instability of the entangled ion clock is below a clock operated with classically correlated states for all probe times. We observe instabilities below the theoretically expected quantum projection noise limit of two uncorrelated ions for interrogation times below 100 ms. The lowest fractional frequency instability of 7e-16 / sqrt(tau / 1 s) is reached for 250 ms probe time, limited by residual phase noise of the probe laser. This represents the lowest instability reported to date for a ^{40}\text{Ca}^{+} ion clock.

physics.atom-ph↗

arXiv2025

Coordinated international comparisons between optical clocks connected via fiber and satellite links

Optical clocks provide ultra-precise frequency references that are vital for international metrology as well as for tests of fundamental physics. To investigate the level of agreement between different clocks, we simultaneously measured the frequency ratios between ten optical clocks in six different countries, using fiber and satellite links. This is the largest coordinated comparison to date, from which we present a subset of 38 optical frequency ratios and an evaluation of the correlations between them. Four ratios were measured directly for the first time, while others had significantly lower uncertainties than previously achieved, supporting the advance towards a redefinition of the second and the use of optical standards for international time scales.

physics.atom-ph↗

arXiv2025

Guidelines for designs for ultrastable laser with $\mathbf{10^{-17}}$ fractional frequency instability

Lasers with long coherence time and narrow linewidth are an essential tool for quantum sensors and clocks. Ultrastable cavities and laser systems are now commercially available with fractional frequency instabilities in the mid $10^{-16}$ range. This document aims to provide technical guidance for researchers starting in the field of ultrastable lasers and to give an outlook toward the next generation of improved ultrastable lasers. These guidelines have arisen from the scope of the EMPIR project ``Next generation ultrastable lasers'' ( https://www.ptb.de/empir2021/nextlasers ) with contributions from the European project partners.

physics.optics↗

arXiv2025

Excited-state magnetic properties of carbon-like $\text{Ca}^{14+}$

We measured the $g$-factor of the excited state $^3\text{P}_1$ in $\text{Ca}^{14+}$ ion to be $g = 1.499032(6)$ with a relative uncertainty of $4\times10^{-6}$. The magnetic field magnitude is derived from the Zeeman splitting of a $\text{Be}^+$ ion, co-trapped in the same linear Paul trap as the highly charged $\text{Ca}^{14+}$ ion. Furthermore, we experimentally determined the second-order Zeeman coefficient $C_2$ of the $^3\text{P}_0$ - $^3\text{P}_1$ clock transition. For the $m_J=0\rightarrow m_{J'}=0$ transition, we obtain $C_2 = 0.39\pm0.04\text{HzmT}^{-2}$, which is to our knowledge the smallest reported for any atomic transition to date. This confirms the predicted low sensitivity of highly charged ions to higher-order Zeeman effects, making them ideal candidates for high-precision optical clocks. Comparison of the experimental results with our state-of-the art electronic structure calculations shows good agreement, and demonstrates the significance of the frequency-dependent Breit contribution, negative energy states and QED effects on magnetic moments.

physics.atom-ph↗

arXiv2024

International comparison of optical frequencies with transportable optical lattice clocks

Optical clocks have improved their frequency stability and estimated accuracy by more than two orders of magnitude over the best caesium microwave clocks that realise the SI second. Accordingly, an optical redefinition of the second has been widely discussed, prompting a need for the consistency of optical clocks to be verified worldwide. While satellite frequency links are sufficient to compare microwave clocks, a suitable method for comparing high-performance optical clocks over intercontinental distances is missing. Furthermore, remote comparisons over frequency links face fractional uncertainties of a few $10^{-18}$ due to imprecise knowledge of each clock's relativistic redshift, which stems from uncertainty in the geopotential determined at each distant location. Here, we report a landmark campaign towards the era of optical clocks, where, for the first time, state-of-the-art transportable optical clocks from Japan and Europe are brought together to demonstrate international comparisons that require neither a high-performance frequency link nor information on the geopotential difference between remote sites. Conversely, the reproducibility of the clocks after being transported between countries was sufficient to determine geopotential height offsets at the level of 4 cm. Our campaign paves the way for redefining the SI second and has a significant impact on various applications, including tests of general relativity, geodetic sensing for geosciences, precise navigation, and future timing networks.

physics.atom-ph↗

arXiv2023

An Optical Atomic Clock Based on a Highly Charged Ion

Optical atomic clocks are the most accurate measurement devices ever constructed and have found many applications in fundamental science and technology. The use of highly charged ions (HCI) as a new class of references for highest accuracy clocks and precision tests of fundamental physics has long been motivated by their extreme atomic properties and reduced sensitivity to perturbations from external electric and magnetic fields compared to singly charged ions or neutral atoms. Here we present the first realisation of this new class of clocks, based on an optical magnetic-dipole transition in Ar$^{13+}$. Its comprehensively evaluated systematic frequency uncertainty of $2.2\times10^{-17}$ is comparable to that of many optical clocks in operation. From clock comparisons we improve by eight and nine orders of magnitude upon the uncertainties for the absolute transition frequency and isotope shift ($^{40}$Ar vs. $^{36}$Ar), respectively. These measurements allow us to probe the largely unexplored quantum electrodynamic nuclear recoil, presented as part of improved calculations of the isotope shift which reduce the uncertainty of previous theory by a factor of three. This work establishes forbidden optical transitions in HCI as references for cutting-edge optical clocks and future high-sensitivity searches for physics beyond the standard model.

physics.atom-ph↗

arXiv2020

Universal formalism for data sharing and processing in clock comparison networks

We present a mathematical framework adapted to the comparison of atomic clocks remotely connected by a complex network of optical or microwave links. This framework facilitates the computation of frequency ratios using a generic set of equations that are valid for a wide variety of clock architectures, making the comparison of a large number of clocks practical. This formalism suggests a generic data exchange protocol that can be used in clock comparison collaborations, for which data logging and decision taking are completely local procedures, independently implemented by the participants.

physics.atom-ph↗

arXiv2020

Simple and compact diode laser system stabilized to Doppler-broadened iodine-lines at 633 nm

We present a compact iodine-stabilized laser system at 633 nm, based on a distributed-feedback laser diode. Within a footprint of $27\times 15$ cm$^2$ the system provides 5 mW of frequency stabilized light from a single-mode fiber. Its performance was evaluated in comparison to Cs clocks representing primary frequency standards, realizing the SI unit Hz via an optical frequency comb. With the best suited absorption line the laser reaches a fractional frequency instability below $10^{-10}$ for averaging times above 10 s. The performance was investigated at several iodine lines and a model was developed to describe the observed stability on the different lines.

physics.optics↗

arXiv2020

Optical frequency ratio of a ${}^{171}\mathrm{Yb}^+$ single-ion clock and a ${}^{87}\mathrm{Sr}$ lattice clock

We report direct measurements of the frequency ratio of the 642 THz ${}^2S_{1/2} (F=0)$--${}^2F_{7/2} (F=3)$ electric octupole transition in ${}^{171}\mathrm{Yb}^+$ and the 429 THz ${}^1S_0$--${}^3P_0$ transition in ${}^{87}\mathrm{Sr}$. A series of 107 measurements has been performed at the Physikalisch-Technische Bundesanstalt between December 2012 and October 2019. Long-term variations of the ratio are larger than expected from the individual measurement uncertainties of few $10^{-17}$. The cause of these variations remains unknown. Even taking these into account, we find a fractional uncertainty of the frequency ratio of $2.5 \times 10^{-17}$, which improves upon previous knowledge by one order of magnitude. The average frequency ratio is $ν_{\mathrm{Yb}^+} / ν_{\mathrm{Sr}} = 1.495\,991\,618\,544\,900\,537(38)$. This represents one of the most accurate measurements between two different atomic species to date.

physics.atom-ph↗

arXiv2020

Coherent excitation of the highly forbidden electric octupole transition in ${}^{172}$Yb$^+$

We report on the first coherent excitation of the highly forbidden $^2S_{1/2}\rightarrow{}^2F_{7/2}$ electric octupole (E3) transition in a single trapped ${}^{172}$Yb$^+$ ion, an isotope without nuclear spin. Using the transition in ${}^{171}$Yb$^+$ as a reference, we determine the transition frequency to be $642\,116\,784\,950\,887.6(2.4)\,$Hz. We map out the magnetic field environment using the forbidden $^2S_{1/2} \rightarrow{}^2D_{5/2}$ electric quadrupole (E2) transition and determine its frequency to be $729\,476\,867\,027\,206.8(4.4)\,$Hz. Our results are a factor of $1\times10^5$ ($3\times10^{5}$) more accurate for the E2 (E3) transition compared to previous measurements. The results open up the way to search for new physics via precise isotope shift measurements and improved tests of local Lorentz invariance using the metastable $^2F_{7/2}$ state of Yb$^+$.

physics.atom-ph↗

arXiv2020

End-to-end topology for fiber comb based optical frequency transfer at the $10^{-21}$ level

We introduce a simple and robust scheme for optical frequency transfer of an ultra-stable source light field via an optical frequency comb to a field at a target optical frequency, where highest stability is required, e.g. for the interrogation of an optical clock. The scheme relies on a topology for end-to-end suppression of the influence of optical path-length fluctuations, which is attained by actively phase-stabilized delivery, combined with common-path propagation. This approach provides a robust stability improvement without the need for additional isolation against environmental disturbances such as temperature, pressure or humidity changes. We measure residual frequency transfer instabilities by comparing the frequency transfers carried out with two independent combs simultaneously. Residual fractional frequency instabilities between two systems of $8\times10^{-18}$ at 1 s and $3\times10^{-21}$ at $10^5$ s averaging time are observed. We discuss the individual noise contributions to the residual instability. The presented scheme is technically simple, robust against environmental parameter fluctuations, and enables an ultra-stable frequency transfer, e.g. to optical clock lasers or to lasers in gravitational wave detectors.

physics.optics↗

arXiv2019

Guidelines for developing optical clocks with $10^{-18}$ fractional frequency uncertainty

There has been tremendous progress in the performance of optical frequency standards since the first proposals to carry out precision spectroscopy on trapped, single ions in the 1970s. The estimated fractional frequency uncertainty of today's leading optical standards is currently in the $10^{-18}$ range, approximately two orders of magnitude better than that of the best caesium primary frequency standards. This exceptional accuracy and stability is resulting in a growing number of research groups developing optical clocks. While good review papers covering the topic already exist, more practical guidelines are needed as a complement. The purpose of this document is therefore to provide technical guidance for researchers starting in the field of optical clocks. The target audience includes national metrology institutes (NMIs) wanting to set up optical clocks (or subsystems thereof) and PhD students and postdocs entering the field. Another potential audience is academic groups with experience in atomic physics and atom or ion trapping, but with less experience of time and frequency metrology and optical clock requirements. These guidelines have arisen from the scope of the EMPIR project "Optical clocks with $1 \times 10^{-18}$ uncertainty" (OC18). Therefore, the examples are from European laboratories even though similar work is carried out all over the world. The goal of OC18 was to push the development of optical clocks by improving each of the necessary subsystems: ultrastable lasers, neutral-atom and single-ion traps, and interrogation techniques. This document shares the knowledge acquired by the OC18 project consortium and gives practical guidance on each of these aspects.

physics.atom-ph↗

arXiv2015

On the relation between uncertainties of weighted frequency averages and the various types of Allan deviations

The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability of an oscillatory signal. It is often supposed that the statistical uncertainty of a measured average frequency is given by the ADEV at a well considered averaging time. However, this approach requires further mathematical justification and refinement, which has already been done regarding the original ADEV for certain noise types. Here we provide the necessary background to use the modified Allan deviation (modADEV) and other two-sample deviations to determine the uncertainty of weighted frequency averages. The type of two-sample deviation used to determine the uncertainty depends on the method used for determination of the average. We find that the modADEV, which is connected with $Λ$-weighted averaging, and the two sample deviation associated to a linear phase regression weighting (parADEV) are in particular advantageous for measurements, in which white phase noise is dominating. Furthermore, we derive a procedure how to minimize the uncertainty of a measurement for a typical combination of white phase and frequency noise by adaptive averaging of the data set with different weighting functions. Finally, some aspects of the theoretical considerations for real-world frequency measurement equipment are discussed.

physics.data-an↗

arXiv2014

Phase-predictable tuning of single-frequency optical synthesizers

We investigate the tuning behavior of a novel type of single-frequency optical synthesizers by phase comparison of the output signals of two identical devices. We achieve phase-stable and cycle slip free frequency tuning over 28.1 GHz with a maximum zero-to-peak phase deviation of 62 mrad. In contrast to previous implementations of single-frequency optical synthesizers, no comb line order switching is needed when tuned over more than one comb line spacing range of the employed frequency comb.

physics.optics↗