Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2310.08835 · Physical Review Applied

Demonstration of chronometric leveling using transportable optical clocks beyond laser coherence limit

Yi Yuan, Kaifeng Cui, Daoxin Liu, Jinbo Yuan, Jian Zhong Cao, Dehao Wang, Sijia Chao, Hualin Shu, Xue-Ren Huang

Published Apr 29, 2024• 12 citations
arXivHTMLPDF

Abstract

An optical clock network requires the establishment of an optical frequency transmission link between multiple optical clocks, utilizing narrow-linewidth lasers. Despite achieving link noise levels of ${10}^{\ensuremath{-}20}$, the final accuracy is limited by the phase noise of the clock laser. Correlation spectroscopy has been developed to transmit frequency information between two optical clocks directly, enabling optical clock comparison beyond the phase noise limit of clock lasers, and significantly enhancing the measurement accuracy or shortening the measurement time. In this article, two compact transportable ${}^{40}\mathrm{Ca}{}^{+}$ clocks are employed to accomplish a correlation spectroscopy comparison, demonstrating a 10-cm level measurement accuracy of chronometric leveling using a mediocre clock laser with linewidth of 200 Hz. The relative frequency instability reaches $6.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}/\sqrt{\ensuremath{\tau}/s}$, which is about 20 times better than the result with Rabi spectroscopy using the same clock laser. This method circumvents the harsh requirements on the performance of the clock laser, so that an ordinary stable laser can also be employed in the construction of an optical clock network, which is essential for field applications, especially for chronometric leveling.

DOI
10.1103/physrevapplied.21.044052

Related papers

Leveraging correlated laser noise to improve optical frequency comparisons

Ethan Clements, M. Bohman, May E. Kim +14 more

Laser noise usually limits the stability of optical frequency ratio measurements, limiting the speed and precision one can compare two atomic frequency standards. In this talk I will describe two methods, correlation and differential spectroscopy, which utilize correlations in laser noise to increase the achievable interrogation time and thus increase the frequency comparison stability. Correlation spectroscopy is a technique which uses a parity measurement following a synchronized Ramsey interrogation to measure the relative frequency of two similar frequency atomic clocks. With this technique we achieve a measurement instability of (4×10^(-16))⁄√(τ⁄s) for a comparison of two single 27Al+ ion clocks. Differential spectroscopy uses an atomic clock with low projection noise, here a 171Yb lattice clock, to correct the phase noise of a second, higher frequency clock’s local oscillator thereby reducing the measurement instability to the level of the first. This can be further extended using two lattice clocks in a zero dead time configuration to correct the phase noise beyond the interrogation time reachable for a single Yb lattice clock. With these techniques we achieve measurement stabilities of (2.5×10^(-16))⁄√(τ⁄s) and (2×10^(-16))⁄√(τ⁄s) for a comparison between a single 27Al+ ion clock and a 171Yb lattice clock running as single clock and in a zero dead time configuration respectively. In addition to these techniques, I will also discuss recent progress towards characterizing the systematics of the NIST 40Ca+/27Al+ optical atomic clock.

Optical and Quantum Sensing and Precision Metrology II•Mar 9, 2022•0 citations

Optical coherence between atomic species at the second scale: improved clock comparisons via differential spectroscopy

May E. Kim, William F. McGrew, Nicholas V. Nardelli +9 more

Comparisons of high-accuracy optical atomic clocks \cite{Ludlow2015} are essential for precision tests of fundamental physics \cite{Safronova2018}, relativistic geodesy \cite{McGrew2018, Grotti2018, Delva2019}, and the anticipated redefinition of the SI second \cite{Riehle2018}. The scientific reach of these applications is restricted by the statistical precision of interspecies comparison measurements. The instability of individual clocks is limited by the finite coherence time of the optical local oscillator (OLO), which bounds the maximum atomic interrogation time. In this letter, we experimentally demonstrate differential spectroscopy \cite{Hume2016}, a comparison protocol that enables interrogating beyond the OLO coherence time. By phase-coherently linking a zero-dead-time (ZDT) \cite{Schioppo2017} Yb optical lattice clock with an Al$^+$ single-ion clock via an optical frequency comb and performing synchronised Ramsey spectroscopy, we show an improvement in comparison instability relative to our previous result \cite{network2020frequency} of nearly an order of magnitude. To our knowledge, this result represents the most stable interspecies clock comparison to date.

arXiv:2109.09540•Sep 20, 2021•3 citations

Development and characterization of a transportable aluminum ion quantum logic optical clock setup

Stephan Hannig

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.

•Jan 1, 2018•0 citations

Exploiting phase coherence for improved resolution in optical atomic frequency ratios

Tara M. Fortier

Optical atomic clocks that operate at frequencies up to 100,000 times higher than their microwave counterparts permit better resolutions and accuracies, while also providing more leeway in environmental control for out of lab applications. Many of the precision applications of these clocks, including relativistic geodesy and tests of fundamental physics rely on the intercomparison of at least two optical clocks. Relative comparisons that include single ion clocks, however, can require close to one month of continuous averaging to achieve measurement instabilities near 1 part in 1018. The long averaging times result from limits imposed on the quantum project noise as a result of signal detection from a single ion, as well as atom probe time limitations due to laser-atom decoherence. In this talk I will describe how the phase coherent properties of an optical frequency comb can be used to enable correlated and synchronous measurement of atomic clocks as a means to improve their relative measurement instability by close to a factor of 10, and nearly 100 times speed up in averaging time over conventional measurement techniques.

Optical and Quantum Sensing and Precision Metrology•Mar 4, 2021•0 citations

Lifetime-Limited Interrogation of Two Independent Al + 27 Clocks Using Correlation Spectroscopy

Ethan Clements, May E. Kim, Kaifeng Cui +7 more

Laser decoherence limits the stability of optical clocks by broadening the observable resonance linewidths and adding noise during the dead time between clock probes. Correlation spectroscopy avoids these limitations by measuring correlated atomic transitions between two ensembles, which provides a frequency difference measurement independent of laser noise. Here, we apply this technique to perform stability measurements between two independent clocks based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+}. By stabilizing the dominant sources of differential phase noise between the two clocks, we observe coherence between them during synchronous Ramsey interrogations as long as 8 s at a frequency of 1.12×10^{15} Hz. The observed contrast in the correlation spectroscopy signal is consistent with the 20.6 s ^{3}P_{0} state lifetime and represents a measurement instability of (1.8±0.5)×10^{-16}/sqrt[τ/s] for averaging periods longer than the probe duration when dead time is negligible.

arXiv:2007.02193•Physical Review Letters•Dec 9, 2020•39 citations

Probing beyond the laser coherence time in optical clock comparisons

David B. Hume, David R. Leibrandt

We develop differential measurement protocols that circumvent the laser noise limit in the stability of optical clock comparisons by synchronous probing of two clocks using phase-locked local oscillators. This allows for probe times longer than the laser coherence time, avoids the Dick effect, and supports Heisenberg-limited measurement precision. We present protocols for such frequency comparisons and develop numerical simulations of the protocols with realistic noise sources. These methods provide a route to reduce frequency ratio measurement durations by more than an order of magnitude.

arXiv:1508.05129•Physical Review A•Mar 30, 2016•43 citations
An optical clock network requires the establishment of an optical frequency transmission link between multiple optical clocks, utilizing narrow-linewidth lasers. Despite achieving link noise levels of 10\ensuremath−20{10}^{\ensuremath{-}20}10\ensuremath−20, the final accuracy is limited by the phase noise of the clock laser. Correlation spectroscopy has been developed to transmit frequency information between two optical clocks directly, enabling optical clock comparison beyond the phase noise limit of clock lasers, and significantly enhancing the measurement accuracy or shortening the measurement time. In this article, two compact transportable 40Ca+{}^{40}\mathrm{Ca}{}^{+}40Ca+ clocks are employed to accomplish a correlation spectroscopy comparison, demonstrating a 10-cm level measurement accuracy of chronometric leveling using a mediocre clock laser with linewidth of 200 Hz. The relative frequency instability reaches 6.0\ifmmode×\else\texttimes\fi10\ensuremath−15/\ensuremathτ/s6.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}/\sqrt{\ensuremath{\tau}/s}6.0\ifmmode×\else\texttimes\fi10\ensuremath−15/\ensuremathτ/s​, which is about 20 times better than the result with Rabi spectroscopy using the same clock laser. This method circumvents the harsh requirements on the performance of the clock laser, so that an ordinary stable laser can also be employed in the construction of an optical clock network, which is essential for field applications, especially for chronometric leveling.
Laser noise usually limits the stability of optical frequency ratio measurements, limiting the speed and precision one can compare two atomic frequency standards. In this talk I will describe two methods, correlation and differential spectroscopy, which utilize correlations in laser noise to increase the achievable interrogation time and thus increase the frequency comparison stability. Correlation spectroscopy is a technique which uses a parity measurement following a synchronized Ramsey interrogation to measure the relative frequency of two similar frequency atomic clocks. With this technique we achieve a measurement instability of (4×10^(-16))⁄√(τ⁄s) for a comparison of two single 27Al+ ion clocks. Differential spectroscopy uses an atomic clock with low projection noise, here a 171Yb lattice clock, to correct the phase noise of a second, higher frequency clock’s local oscillator thereby reducing the measurement instability to the level of the first. This can be further extended using two lattice clocks in a zero dead time configuration to correct the phase noise beyond the interrogation time reachable for a single Yb lattice clock. With these techniques we achieve measurement stabilities of (2.5×10^(-16))⁄√(τ⁄s) and (2×10^(-16))⁄√(τ⁄s) for a comparison between a single 27Al+ ion clock and a 171Yb lattice clock running as single clock and in a zero dead time configuration respectively. In addition to these techniques, I will also discuss recent progress towards characterizing the systematics of the NIST 40Ca+/27Al+ optical atomic clock.
Comparisons of high-accuracy optical atomic clocks \cite{Ludlow2015} are essential for precision tests of fundamental physics \cite{Safronova2018}, relativistic geodesy \cite{McGrew2018, Grotti2018, Delva2019}, and the anticipated redefinition of the SI second \cite{Riehle2018}. The scientific reach of these applications is restricted by the statistical precision of interspecies comparison measurements. The instability of individual clocks is limited by the finite coherence time of the optical local oscillator (OLO), which bounds the maximum atomic interrogation time. In this letter, we experimentally demonstrate differential spectroscopy \cite{Hume2016}, a comparison protocol that enables interrogating beyond the OLO coherence time. By phase-coherently linking a zero-dead-time (ZDT) \cite{Schioppo2017} Yb optical lattice clock with an Al+^++ single-ion clock via an optical frequency comb and performing synchronised Ramsey spectroscopy, we show an improvement in comparison instability relative to our previous result \cite{network2020frequency} of nearly an order of magnitude. To our knowledge, this result represents the most stable interspecies clock comparison to date.
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.
Optical atomic clocks that operate at frequencies up to 100,000 times higher than their microwave counterparts permit better resolutions and accuracies, while also providing more leeway in environmental control for out of lab applications. Many of the precision applications of these clocks, including relativistic geodesy and tests of fundamental physics rely on the intercomparison of at least two optical clocks. Relative comparisons that include single ion clocks, however, can require close to one month of continuous averaging to achieve measurement instabilities near 1 part in 1018. The long averaging times result from limits imposed on the quantum project noise as a result of signal detection from a single ion, as well as atom probe time limitations due to laser-atom decoherence. In this talk I will describe how the phase coherent properties of an optical frequency comb can be used to enable correlated and synchronous measurement of atomic clocks as a means to improve their relative measurement instability by close to a factor of 10, and nearly 100 times speed up in averaging time over conventional measurement techniques.
Laser decoherence limits the stability of optical clocks by broadening the observable resonance linewidths and adding noise during the dead time between clock probes. Correlation spectroscopy avoids these limitations by measuring correlated atomic transitions between two ensembles, which provides a frequency difference measurement independent of laser noise. Here, we apply this technique to perform stability measurements between two independent clocks based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+}. By stabilizing the dominant sources of differential phase noise between the two clocks, we observe coherence between them during synchronous Ramsey interrogations as long as 8 s at a frequency of 1.12×10^{15} Hz. The observed contrast in the correlation spectroscopy signal is consistent with the 20.6 s ^{3}P_{0} state lifetime and represents a measurement instability of (1.8±0.5)×10^{-16}/sqrt[τ/s] for averaging periods longer than the probe duration when dead time is negligible.
We develop differential measurement protocols that circumvent the laser noise limit in the stability of optical clock comparisons by synchronous probing of two clocks using phase-locked local oscillators. This allows for probe times longer than the laser coherence time, avoids the Dick effect, and supports Heisenberg-limited measurement precision. We present protocols for such frequency comparisons and develop numerical simulations of the protocols with realistic noise sources. These methods provide a route to reduce frequency ratio measurement durations by more than an order of magnitude.