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10-18 Optical Atomic Clock Comparisons within the Boulder Atomic Clock Network
Abstract
We demonstrate optical frequency comparison of the ¹⁷¹ Yb, ²⁷ Al ⁺ and ⁸⁷ Sr atomic clocks with measurement uncertainties below 1 part in 10 ¹⁷ , and discuss how phase-coherent and synchronous clock comparisons can be used to improve measurement stability.
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We conduct frequency comparisons between a state-of-the-art strontium optical lattice clock, a cryogenic crystalline silicon cavity, and a hydrogen maser to set new bounds on the coupling of ultralight dark matter to standard model particles and fields in the mass range of 10−16−10−21 eV. The key advantage of this two-part ratio comparison is the differential sensitivity to time variation of both the fine-structure constant and the electron mass, achieving a substantially improved limit on the moduli of ultralight dark matter, particularly at higher masses than typical atomic spectroscopic results. Furthermore, we demonstrate an extension of the search range to even higher masses by use of dynamical decoupling techniques. These results highlight the importance of using the best-performing atomic clocks for fundamental physics applications, as all-optical timescales are increasingly integrated with, and will eventually supplant, existing microwave timescales.
We report on the first Earth-scale quantum sensor network based on optical atomic clocks aimed at dark matter (DM) detection. Exploiting differences in the susceptibilities to the fine-structure constant of essential parts of an optical atomic clock, i.e., the cold atoms and the optical reference cavity, we can perform sensitive searches for DM signatures without the need for real-time comparisons of the clocks. We report a two orders of magnitude improvement in constraints on transient variations of the fine-structure constant, which considerably improves the detection limit for the standard model (SM)–DM coupling. We use Yb and Sr optical atomic clocks at four laboratories on three continents to search for both topological defect and massive scalar field candidates. No signal consistent with a DM coupling is identified, leading to considerably improved constraints on the DM-SM couplings.
The passage of time is tracked by counting oscillations of a frequency reference, such as Earth’s revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the 10⁻¹⁷ level1–5. However, the theory of relativity prescribes that the passage of time is not absolute, but is affected by an observer’s reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate local optical clock measurements that surpass the current ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented values of three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of 1.4 × 10⁻¹⁸, measurement instability of 3.2 × 10⁻¹⁹ and reproducibility characterized by ten blinded frequency comparisons, yielding a frequency difference of [−7 ± (5)stat ± (8)sys] × 10⁻¹⁹, where ‘stat’ and ‘sys’ indicate statistical and systematic uncertainty, respectively. Although sensitivity to differences in gravity potential could degrade the performance of the clocks as terrestrial standards of time, this same sensitivity can be used as a very sensitive probe of geopotential5–9. Near the surface of Earth, clock comparisons at the 1 × 10⁻¹⁸ level provide a resolution of one centimetre along the direction of gravity, so the performance of these clocks should enable geodesy beyond the state-of-the-art level. These optical clocks could further be used to explore geophysical phenomena¹⁰, detect gravitational waves¹¹, test general relativity¹² and search for dark matter13–17.
Optical clocks benefit from tight atomic confinement enabling extended interrogation times as well as Doppler- and recoil-free operation. However, these benefits come at the cost of frequency shifts that, if not properly controlled, may degrade clock accuracy. Numerous theoretical studies have predicted optical lattice clock frequency shifts that scale nonlinearly with trap depth. To experimentally observe and constrain these shifts in an Yb optical lattice clock, we construct a lattice enhancement cavity that exaggerates the light shifts. We observe an atomic temperature that is proportional to the optical trap depth, fundamentally altering the scaling of trap-induced light shifts and simplifying their parametrization. We identify an "operational" magic wavelength where frequency shifts are insensitive to changes in trap depth. These measurements and scaling analysis constitute an essential systematic characterization for clock operation at the level and beyond.
The comparison of optical atomic clocks with frequency instabilities reaching 1 part in at 1 s will enable more stringent tests of fundamental physics. These comparisons, mediated by optical frequency combs, require optical synthesis and measurement with a performance better than, or comparable to, the best optical clocks. Fiber-based mode-locked lasers have shown great potential for compact, robust, and efficient optical clockwork but typically require multiple amplifier and fiber optic paths that limit the achievable fractional frequency stability near 1 part in at 1 s. Here we describe an erbium-fiber laser frequency comb that overcomes these conventional challenges by ensuring that all critical fiber paths are common mode and within the servo-controlled feedback loop. Using this architecture, we demonstrate a fractional optical measurement uncertainty below and fractional frequency instabilities less than at 1 s and at 1000 s.
The pursuit of better atomic clocks has advanced many research areas, providing better quantum state control, new insights in quantum science, tighter limits on fundamental constant variation, and improved tests of relativity. The record for the best stability and accuracy is currently held by
optical lattice clocks. This work takes an important step towards realizing the full potential of a many-particle clock with a state-of-the-art stable laser. Here, we achieve fractional stability of 2.2e-16 at 1 s by using seconds-long coherent interrogations of our clock transition in a low-density system not limited by atomic interactions. With this better stability, we perform a new accuracy evaluation of our clock, improving many systematic uncertainties that limited our previous measurements, such as the lattice ac Stark and blackbody radiation (BBR) shifts. For the lattice ac Stark systematic, we identify the lattice laser frequency where the scalar and tensor components of the shift cancel, allowing for state independent trapping with clock shifts at the 1e-18 level. For the BBR systematic, we improve our measurement of the atoms' thermal environment using accurate radiation thermometry traceable to the NIST ITS-90 absolute temperature scale. We also directly measure the component of the strontium atomic structure that is chiefly responsible for the spectral
response to room-temperature BBR. Our combined measurements have reduced the total uncertainty of the JILA Sr clock to 2.1e-18 in fractional frequency units.
Although a single-mode optical fiber is a convenient and efficient interface/connecting medium, it introduces phase-noise modulation, which corrupts high-precision frequency-based applications by broadening the spectrum toward the kilohertz domain. We describe a simple double-pass fiber noise measurement and control system, which is demonstrated to provide millihertz accuracy of noise cancellation.
We transfer an optical frequency over 251 km of optical fiber with a residual instability of 6 × 10 − 19 at 100 s . This instability and the associated timing jitter are limited fundamentally by the noise on the optical fiber and the link length. We give a simple expression for calculating the achievable instability and jitter over a fiber link. Transfer of optical stability over this long distance requires a highly coherent optical source, provided here by a cw fiber laser locked to a high finesse optical cavity. A sufficient optical carrier signal is delivered to the remote fiber end by incorporating two-way, in-line erbium-doped fiber amplifiers to balance the 62 dB link loss.
We describe an optical atomic clock based on quantum-logic spectroscopy of the S01↔P30 transition in Al+27 with a systematic uncertainty of 9.4×10−19 and a frequency stability of 1.2×10−15/τ. A Mg+25 ion is simultaneously trapped with the Al+27 ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous Al+27 clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous Al+27 clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.
We present an extended model for the lattice-induced light shifts of the clock frequency in optical lattice clocks, applicable to a wide range of operating conditions. The model extensions cover radial motional states with sufficient energies to invalidate the harmonic approximation of the confining potential. We reevaluate lattice-induced light shifts in our Yb optical lattice clock with an uncertainty of 6.1×10−18 under typical clock operating conditions.
Its been over a decade since the first edition of Measurement Error in Nonlinear Models splashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition has been revamped and extensively updated to offer the most comprehensive and up-to-date survey of measurement error models currently available. What's new in the Second Edition? • Greatly expanded discussion and applications of Bayesian computation via Markov Chain Monte Carlo techniques • A new chapter on longitudinal data and mixed models • A thoroughly revised chapter on nonparametric regression and density estimation • A totally new chapter on semiparametric regression • Survival analysis expanded into its own separate chapter • Completely rewritten chapter on score functions • Many more examples and illustrative graphs • Unique data sets compiled and made available online In addition, the authors expanded the background material in Appendix A and integrated the technical material from chapter appendices into a new Appendix B for convenient navigation. Regardless of your field, if youre looking for the most extensive discussion and review of measurement error models, then Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition is your ideal source.
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.
Transition frequencies of atoms and ions are among the most accurately
accessible quantities in nature, playing important roles in pushing the
frontiers of science by testing fundamental laws of physics, in addition to a
wide range of applications such as satellite navigation systems. Atomic clocks
based on optical transitions approach uncertainties of , where full
frequency descriptions are far beyond the reach of the SI second. Frequency
ratios of such super clocks, on the other hand, are not subject to this
limitation. They can therefore verify consistency and overall accuracy for an
ensemble of super clocks, an essential step towards a redefinition of the
second. However, with the measurement stabilities so far reported for such
frequency ratios, a confirmation to uncertainty would
require an averaging time of multiple months. Here we report a
measurement of the frequency ratio of neutral ytterbium and strontium clocks
with a much improved stability of .
Enabled by the high stability of optical lattice clocks interrogating hundreds
of atoms, this marks a 90-fold reduction in the required averaging time over a
previous record-setting experiment that determined the ratio of Al+ and Hg+
single-ion clocks to an uncertainty of . For the Yb/Sr
ratio, we find R = 1.207 507 039 343 337 749(55), with a fractional uncertainty
of .
This paper gives the 2006 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.
Recent progress in optical lattice clocks requires unprecedented precision in
controlling systematic uncertainties at level. Tuning of nonlinear
light shifts is shown to reduce lattice-induced clock shift for wide range of
lattice intensity. Based on theoretical multipolar, nonlinear, anharmonic and
higher-order light shifts, we numerically demonstrate possible strategies for
Sr, Yb, and Hg clocks to achieve lattice-induced systematic uncertainty below
.
The transfer of high-quality time-frequency signals between remote locations
underpins a broad range of applications including precision navigation and
timing, the new field of clock-based geodesy, long-baseline interferometry,
coherent radar arrays, tests of general relativity and fundamental constants,
and the future redefinition of the second [1-7]. However, present
microwave-based time-frequency transfer [8-10] is inadequate for
state-of-the-art optical clocks and oscillators [1,11-15] that have
femtosecond-level timing jitter and accuracies below 1E-17; as such,
commensurate optically-based transfer methods are needed. While fiber-based
optical links have proven suitable [16,17], they are limited to comparisons
between fixed sites connected by a specialized bidirectional fiber link. With
the exception of tests of the fundamental constants, most applications instead
require more flexible connections between remote and possibly portable optical
clocks and oscillators. Here we demonstrate optical time-frequency transfer
over free-space via a two-way exchange between coherent frequency combs, each
phase-locked to the local optical clock or oscillator. We achieve
femtosecond-scale timing deviation, a residual instability below 1E-18 at 1000
s and systematic offsets below 4E-19, despite frequent signal fading due to
atmospheric turbulence or obstructions across the 2-km link. This free-space
transfer would already enable terrestrial links to support clock-based geodesy.
If combined with satellite-based free-space optical communications, it provides
a path toward global-scale geodesy, high-accuracy time-frequency distribution,
satellite-based relativity experiments, and "optical GPS" for precision
navigation.
We demonstrate a self-referenced, octave-spanning, mode-locked Ti:sapphire laser with a scalable repetition rate (550 MHz - 1.35 GHz). We use the frequency comb output of the laser, without additional broadening in optical fiber, for simultaneous measurements against atomic optical standards at 534, 578, 563, and 657 nm and to stabilize the laser offset frequency.
R2jags: using R to run
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Evaluating the accuracy of sampling-based approaches to calculating posterior moments
- J Geweke
Geweke, J. Evaluating the accuracy of sampling-based approaches to calculating
posterior moments. In Bayesian Statistics 4: Proceedings of the Fourth Valencia
International Meeting (eds Bernado, J. M. et al) 641-649 (Clarendon, 1992).
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Fuller, W. A. Measurement Error Models (Wiley & Sons, 1987).