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:physics/0511168 · Journal of Physics B Atomic Molecular and Optical Physics

Laser frequency stabilization to a single ion

E. Peik, T. Schneider, Chr. Tamm

Published Dec 7, 2005• 125 citations
arXivHTMLPDF

Abstract

A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171 Yb + . Experimentally, an instability σ y (100 s) = 9 × 10 −16 is obtained in the frequency difference between both standards.

DOI
10.1088/0953-4075/39/1/012

Related papers

Comparison of two single-ion optical frequency standards at the hertz level

T. Schneider, Chr. Tamm, E. Peik

We describe experimental investigations of an optical frequency standard based on a single laser-cooled /sup 171/Yb/sup +/ ion confined in a radiofrequency Paul trap. The electric quadrupole transition from the /sup 2/S/sub 1/2 /(F=0) ground state to the /sup 2/D/sub 3/2/(F=2) state at 435.5 nm is used as the reference transition. The transition was resolved with a Fourier-limited width of approximately 30 Hz. In order to investigate the instability and accuracy of a future frequency standard based on the reference transition, a first experiment was done comparing two laser frequencies stabilized individually to two separate ions in different traps. As a result we found a relative frequency instability /spl sigma//sub y/(640 s)=1.5/spl middot/10/sup -15/ for the difference of the two laser frequencies. We also derived a first estimate /spl Theta/(/sup 2/D/sub 3/2/)=(3.9/spl plusmn/1.9)ea/sub 0//sup 2/ for the electric quadrupole moment of the /sup 2/D/sub 3/2/ state.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Jul 8, 2004•6 citations

Suppression of servo error uncertainty to 10−18 level using double integrator algorithm in ion optical clock*

Jinbo Yuan, Jian Zhong Cao, Kaifeng Cui +5 more

A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator. Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9 × 10−18, which is meaningful for the systematic uncertainty of the transportable single 40Ca+ ion optical clock entering the 10−18 level.

Chinese Physics B•Apr 19, 2021•5 citations

Sr88+ single-ion optical clock with a stability approaching the quantum projection noise limit

P. Dubé, Alan A. Madej, Andrew D. Shiner +1 more

A number of optical frequency standards have been evaluated with fractional uncertainties between ${10}^{\ensuremath{-}17}$ and ${10}^{\ensuremath{-}18}$. Reduction of the statistical uncertainty of a clock comparison to this level is challenging, requiring the best possible stability to avoid excessively long averaging times. We report recent improvements of our $^{88}\mathrm{Sr}{}^{+}$ single-ion standard that have reduced its 1-s Allan deviation from $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ to $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, yielding an order of magnitude decrease in averaging time for a given statistical uncertainty level. Among the improvements made are the implementation of a clear-out laser that transfers the ion from the metastable state to the ground state at each cycle, followed by a state preparation step that transfers the ion to the ground-state magnetic sublevel of the probed transition. With these changes, the ion clock transition interacts with the probe laser at every interrogation cycle. The stability of our optical standard is essentially limited by the quantum projection noise for pulse lengths up to $\ensuremath{\approx}100$ ms.

Physical Review A•Oct 22, 2015•50 citations

COMPARISON OF TWO SINGLE-ION OPTICAL FREQUENCY STANDARDS AT THE SUB-HERTZ LEVEL

Chr. Tamm, T. Schneider, E. Peik

We describe experimental investigations on an optical frequency standard based on a laser cooled 171Yb+ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the 2S1/2(F=0) ground state to the 2D3/2(F=2) state at the wavelength of 436 nm is used as the reference transition. The reference transition is probed by a frequency-doubled, frequency-stabilized diode laser and is resolved with a Fourier-limited full halfwidth of approximately 30 Hz. In order to compare two 171Yb+ standards, separate frequency shift and servo systems are employed to stabilise the probe frequency to the reference transition line centers of two independently stored 171Yb+ ions. The present experimental results indicate a relative instability (Allan standard deviation)of the optical frequency difference between the two systems of sigma_y(1000 s)=1.0E-15 and a mean frequency difference of 0.2 Hz. Shifts in the range of several Hertz are observed in the frequency difference if a stationary electric field gradient is superimposed on the radiofrequency trap field. This measurement permits a first experimental estimate of the electric quadrupole moment of the 2D3/2 state of Yb+.

arXiv:physics/0402120•Laser Spectroscopy•Feb 1, 2004•3 citations

Optimum measurement strategies for trapped ion optical frequency standards

Erling Riis, Alastair G. Sinclair

The experimental parameters required in order to maximize the stability of a single-ion based optical clock are analysed. This stability is a trade-off between on the one hand the steepness of the discriminant signal derived from the laser excitation of the ion and on the other the binomial noise associated with the excitation of a single particle. Optimum conditions are found for both Rabi and Ramsey excitation of the clock transition.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 7, 2004•28 citations

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
A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171 Yb + . Experimentally, an instability σ y (100 s) = 9 × 10 −16 is obtained in the frequency difference between both standards.
We describe experimental investigations of an optical frequency standard based on a single laser-cooled /sup 171/Yb/sup +/ ion confined in a radiofrequency Paul trap. The electric quadrupole transition from the /sup 2/S/sub 1/2 /(F=0) ground state to the /sup 2/D/sub 3/2/(F=2) state at 435.5 nm is used as the reference transition. The transition was resolved with a Fourier-limited width of approximately 30 Hz. In order to investigate the instability and accuracy of a future frequency standard based on the reference transition, a first experiment was done comparing two laser frequencies stabilized individually to two separate ions in different traps. As a result we found a relative frequency instability /spl sigma//sub y/(640 s)=1.5/spl middot/10/sup -15/ for the difference of the two laser frequencies. We also derived a first estimate /spl Theta/(/sup 2/D/sub 3/2/)=(3.9/spl plusmn/1.9)ea/sub 0//sup 2/ for the electric quadrupole moment of the /sup 2/D/sub 3/2/ state.
A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator. Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9 × 10−18, which is meaningful for the systematic uncertainty of the transportable single 40Ca+ ion optical clock entering the 10−18 level.
A number of optical frequency standards have been evaluated with fractional uncertainties between ${10}^{\ensuremath{-}17}$ and ${10}^{\ensuremath{-}18}$. Reduction of the statistical uncertainty of a clock comparison to this level is challenging, requiring the best possible stability to avoid excessively long averaging times. We report recent improvements of our 88Sr+^{88}\mathrm{Sr}{}^{+}88Sr+ single-ion standard that have reduced its 1-s Allan deviation from $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ to $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, yielding an order of magnitude decrease in averaging time for a given statistical uncertainty level. Among the improvements made are the implementation of a clear-out laser that transfers the ion from the metastable state to the ground state at each cycle, followed by a state preparation step that transfers the ion to the ground-state magnetic sublevel of the probed transition. With these changes, the ion clock transition interacts with the probe laser at every interrogation cycle. The stability of our optical standard is essentially limited by the quantum projection noise for pulse lengths up to $\ensuremath{\approx}100$ ms.
We describe experimental investigations on an optical frequency standard based on a laser cooled 171Yb+ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the 2S1/2(F=0) ground state to the 2D3/2(F=2) state at the wavelength of 436 nm is used as the reference transition. The reference transition is probed by a frequency-doubled, frequency-stabilized diode laser and is resolved with a Fourier-limited full halfwidth of approximately 30 Hz. In order to compare two 171Yb+ standards, separate frequency shift and servo systems are employed to stabilise the probe frequency to the reference transition line centers of two independently stored 171Yb+ ions. The present experimental results indicate a relative instability (Allan standard deviation)of the optical frequency difference between the two systems of sigma_y(1000 s)=1.0E-15 and a mean frequency difference of 0.2 Hz. Shifts in the range of several Hertz are observed in the frequency difference if a stationary electric field gradient is superimposed on the radiofrequency trap field. This measurement permits a first experimental estimate of the electric quadrupole moment of the 2D3/2 state of Yb+.
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.