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Precision spectroscopy with single ions Spectroscopy is a powerful tool that can identify chemical species used in a wide range of settings. Usually, the samples are formed of ensembles, and this can limit the resolution with which the different species can be detected or identified. Chou et al. demonstrate an optical frequency comb technique with a single pair of trapped ions, Ca + and CaH + , to obtain the rotational spectrum of a single trapped ion, CaH + . With the ions isolated and the ensemble interactions removed, the rotational structure of the trapped molecular ion can then be obtained with high precision. As the trapping and manipulation process is general, this technique could be applied to a number of chemical species for specific purposes. Science , this issue p. 1458

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8x10$^{-13}$/$\sqrt{\tau}$ for times less than 100 s and a flicker noise floor of 1x10$^{-14}$ out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the AC Stark shift. The retrace was measured to 5.7x10$^{-13}$ after 30 hours of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the SI meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser., Comment: 5 pages, 5 figures

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.

Using frequency comb mediated phase-coherent and synchronous clock comparisons we demonstrate close to a factor of 10 improvement in short-term measurement instability, σy(τ) < 2 x 10-16 @ 1s averaging, between 171Yb and 27Al+ optical clocks.

We generate 10 GHz microwave signals from an optical reference cavity using the transfer oscillator scheme with a free-running optical frequency comb. We demonstrate phase noise < -100 dBc/Hz at 1 Hz frequency offset from the carrier.

Microwaves with 1×10-18 absolute instability were derived from two independent Yb optical clocks. The optical clock phase is reproduced at 10 GHz with 1×10-19 fidelity, demonstrating that state-of-the-art optical clock uncertainty and instability can be converted to microwaves without any degradation.

We use frequency comb-based optical two-way time-frequency transfer (O-TWTFT) to measure the optical frequency ratio of state-of-the-art ytterbium and strontium optical atomic clocks separated by a 1.5 km open-air link. Our free-space measurement is compared to a simultaneous measurement acquired via a noise-cancelled fiber link. Despite non-stationary, ps-level time-of-flight variations in the free-space link, ratio measurements obtained from the two links, averaged over 30.5 hours across six days, agree to $6\times10^{-19}$, showing that O-TWTFT can support free-space atomic clock comparisons below the $10^{-18}$ level.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Optical atomic clocks are poised to redefine the SI second, thanks to stability and accuracy more than one hundred times better than the current microwave atomic clock standard. However, the best optical clocks have not seen their performance transferred to the electronic domain, where radar, navigation, communications, and fundamental research rely on less stable microwave sources. By comparing two independent optical-to-electronic signal generators, we demonstrate a 10 GHz microwave signal with phase that exactly tracks that of the optical clock phase from which it is derived, yielding an absolute fractional frequency instability of 1*10-18 in the electronic domain. Such faithful reproduction of the optical clock phase expands the opportunities for optical clocks both technologically and scientifically for time-dissemination, navigation, and long-baseline interferometric imaging., 19 page, 10 figures (including Supplementary Text)

Optical atomic clocks are poised to redefine the Système International (SI) second, thanks to stability and accuracy more than 100 times better than the current microwave atomic clock standard. However, the best optical clocks have not seen their performance transferred to the electronic domain, where radar, navigation, communications, and fundamental research rely on less stable microwave sources. By comparing two independent optical-to-electronic signal generators, we demonstrate a 10-gigahertz microwave signal with phase that exactly tracks that of the optical clock phase from which it is derived, yielding an absolute fractional frequency instability of 1 × 10

We demonstrate optical frequency comparison of the 171Yb, 27Al+ and 87Sr atomic clocks with measurement uncertainties below 1 part in 1017, and discuss how phase-coherent and synchronous clock comparisons can be used to improve measurement stability.

We generate 10-GHz microwaves, derived from independent Yb optical clocks, with 2.4*10-18 absolute fractional frequency stability, no significant offset at the 10-19 level, and femtosecond-precision transfer of the optical clock phase to the microwave domain.

We developed a measurement system that combines on-wafer metrology and high-frequency network analysis to characterize the response of transmission-line integrated Er-GaAs and InGaAs photomixers up to 1 THz to support the telecommunication and electronics industry.

We generate a high stability 10 GHz microwave signals with close to 30 dB of comb noise suppression via optical frequency division using a transfer oscillator scheme.

This paper describes the recent National Institute of Standards and Technology (NIST) work on incorporating an optical clock into a time scale. We simulate a time scale composed of continuously operating commercial hydrogen masers and an optical frequency standard that does not operate continuously as a clock. The simulations indicate that to achieve the same performance of a continuously operating Cs-fountain time scale, it is necessary to run an optical frequency standard 12 minutes per half a day, or 1 hour per day, or 4 hours per 2.33 day, or 12 hours per week. Following the simulations, a Yb optical clock at NIST was frequently operated during the periods of 2017 March – April and 2017 late October – late December. During this operation, comb-mediated measurements between the Yb clock and a hydrogen maser had durations ranging from a few minutes to a few hours, depending on the experimental arrangements. This paper analyzes these real data preliminarily and discusses the results. More data are needed to make a more complete assessment.

Optical frequency combs were developed nearly two decades ago to support the world’s most precise atomic clocks. Acting as precision optical synthesizers, frequency combs enable the precise transfer of phase and frequency information from a high-stability reference to hundreds of thousands of tones in the optical domain. This versatility, coupled with near-continuous spectroscopic coverage from microwave frequencies to the extreme ultra-violet, has enabled precision measurement capabilities in both fundamental and applied contexts. This review takes a tutorial approach to illustrate how 20 years of source development and technology has facilitated the journey of optical frequency combs from the lab into the field. Optical frequency combs were realized nearly two decades ago to support the development of the world’s most precise atomic clocks, but their versatility has since made them useful instruments well beyond their original goal, and spans across a wide variety of fundamental and applied physics in a wide range of wavelengths. Fortier and Baumann present a comprehensive review of developments in optical frequency comb technology and a view to the future with these technologies.

We demonstrate Ramsey-Borde (RB) atom interferometry for high performance laser stabilization with fractional frequency instability

An aluminum ion clock has a fractional-frequency uncertainty of less than one part in ${10}^{18}$, a four-decades-long goal in precision.

We demonstrate a time scale based on a phase stable optical carrier that accumulates an estimated time error of $48\pm94$ ps over 34 days of operation. This all-optical time scale is formed with a cryogenic silicon cavity exhibiting improved long-term stability and an accurate $^{87}$Sr lattice clock. We show that this new time scale architecture outperforms existing microwave time scales, even when they are steered to optical frequency standards. Our analysis indicates that this time scale is capable of reaching a stability below $1\times10^{-17}$ after a few months of averaging, making timekeeping at the $10^{-18}$ level a realistic prospect., 13 pages, 12 Figures

The pursuit of ever more precise measures of time and frequency motivates redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on the microwave hyperfine transition in Cs133, it is necessary to measure the absolute frequency of candidate optical standards relative to primary cesium references. Armed with independent measurements, a stringent test of optical clocks can be made by comparing ratios of absolute frequency measurements against optical frequency ratios measured via direct optical comparison. Here we measure the S01→P03 transition of Yb171 using satellite time and frequency transfer to compare the clock frequency to an international collection of national primary and secondary frequency standards. Our measurements consist of 79 runs spanning eight months, yielding the absolute frequency to be 518 295 836 590 863.71(11) Hz and corresponding to a fractional uncertainty of 2.1×10−16. This absolute frequency measurement, the most accurate reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency measurement loop at an uncertainty

We demonstrate Ramsey-Bordé (RB) atom interferometry for high performance laser stabilization with fractional frequency instability2×10^{-16} for timescales between 10 and 1000s. The RB spectroscopy laser interrogates two counterpropagating ^{40}Ca beams on the ^{1}S_{0}-^{3}P_{1} transition at 657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detection of the excited state population is performed on the (4s4p) ^{3}P_{1}-(4p^{2}) ^{3}P_{0} transition at 431 nm. Minimal thermal shielding and no vibration isolation are used. These stability results surpass performance from other thermal atomic or molecular systems by 1 to 2 orders of magnitude, and further improvements look feasible.

A time scale is a procedure for accurately and continuously marking the passage of time. It is exemplified by Coordinated Universal Time (UTC), and provides the backbone for critical navigation tools such as the Global Positioning System (GPS). Present time scales employ microwave atomic clocks, whose attributes can be combined and averaged in a manner such that the composite is more stable, accurate, and reliable than the output of any individual clock. Over the past decade, clocks operating at optical frequencies have been introduced which are orders of magnitude more stable than any microwave clock. However, in spite of their great potential, these optical clocks cannot be operated continuously, which makes their use in a time scale problematic. In this paper, we report the development of a hybrid microwave-optical time scale, which only requires the optical clock to run intermittently while relying upon the ensemble of microwave clocks to serve as the flywheel oscillator. The benefit of using clock ensemble as the flywheel oscillator, instead of a single clock, can be understood by the Dick-effect limit. This time scale demonstrates for the first time sub-nanosecond accuracy for a few months, attaining a fractional frequency uncertainty of 1.45*10-16 at 30 days and reaching the 10-17 decade at 50 days, with respect to UTC. This time scale significantly improves the accuracy in timekeeping and could change the existing time-scale architectures.

We perform absolute measurement of the 27Al+ single-ion and 87Sr neutral lattice clock frequencies at the National Institute of Standards and Technology and JILA at the University of Colorado against a global ensemble of primary frequency standards. Over an eight month period multiple measurements yielded the mean optical atomic transition frequencies ν Al + = 1 121 015 393 207 859.50 ( 0.36 ) Hz and ν Sr = 429 228 004 229 873.19(0.15) Hz, where the stated uncertainties are dominated by statistical noise and gaps in the observation interval (‘dead-time’ uncertainty).

Fundamental science, as well as all communications and navigation systems, are heavily reliant on the phase, timing, and synchronization provided by low-noise and agile frequency sources. Although research into varied photonic and electronic schemes have strived to improve upon the spectral purity of microwave and millimeter-wave signals, the reliance on conventional electronic synthesis for tuning has resulted in limited progress in broadband sources. Using a digital-photonic synthesizer architecture that derives its time-base from a high-stability optical reference cavity, we generate frequency-agile and wideband microwave signals with exceptional dynamic range and with a fractional frequency instability of 1 × 10−15 at 1 s. The presented architecture demonstrates digitally controlled, user defined and broadband frequency tuning from RF to 100 GHz with orders-of-magnitude improvement in noise performance over room-temperature electronic wide-bandwidth synthesis schemes.

Precise measurements of the frequencies of light waves have become common with mode-locked laser frequency combs1. Despite their huge success, optical frequency combs currently remain bulky and expensive laboratory devices. Integrated photonic microresonators are promising candidates for comb generators in out-of-the-lab applications, with the potential for reductions in cost, power consumption and size. Such advances will significantly impact fields ranging from spectroscopy and trace gas sensing to astronomy, communications and atomic time-keeping. Yet, in spite of the remarkable progress shown over recent years, microresonator frequency combs (‘microcombs’) have been without the key function of direct f–2f self-referencing, which enables precise determination of the absolute frequency of each comb line. Here, we realize this missing element using a 16.4 GHz microcomb that is coherently broadened to an octave-spanning spectrum and subsequently fully phase-stabilized to an atomic clock. We show phase-coherent control of the comb and demonstrate its low-noise operation.

We demonstrate laser frequency stabilization at the $\pmb{10^{-16}}$ fractional frequency level in one second through spectroscopy on a 650°C calcium atomic beam. The calcium beam is interrogated with a cavity stabilized 657 nm laser arranged in a Ramsey-Borde configuration. A second laser at 431 nm reads off the final atomic state populations while allowing for high signal-to-noise. Limitations of this method are being explored and, and, based on current noise analysis, there is potential to achieve fractional frequency stabilities in the $\pmb{10^{-17}}$ range or below.

This paper describes the recent NIST work on incorporating an optical clock into a time scale. We simulate a time scale composed of continuously-operating commercial hydrogen masers and an optical frequency standard that does not operate continuously as a clock. The simulations indicate that to achieve the same performance of a continuously-operating Cs-fountain time scale, it is necessary to run an optical frequency standard 12 min per half a day, or 1 hour per day, or 4 hours per 2.33 day, or 12 hours per week. Following the simulations, a Yb optical clock at NIST was frequently operated during the periods of 2017 March – April and 2017 late October – late December. During this operation, comb-mediated measurements between the Yb clock and a hydrogen maser had durations ranging from a few minutes to a few hours, depending on the experimental arrangements. This paper analyzes these real data preliminarily, and discusses the results. More data are needed to make a more complete assessment.

We present agreement in the measurement of optical clock transition frequencies using two independent optical frequency combs to sub-millihertz levels and discuss experiments to improve the measurement instability via coherent atomic clock spectroscopy.

We show

Analog photonic links require high-fidelity, high-speed optical-to-electrical conversion for applications such as radio-over-fiber, synchronization at kilometer-scale facilities, and low-noise electronic signal generation. Photodetector nonlinearity is a particularly vexing problem, causing signal distortion and excess noise, especially in systems utilizing ultrashort optical pulses. Here we show that photodetectors designed for high power handling and high linearity can perform optical-to-electrical conversion of ultrashort optical pulses with unprecedented linearity over a large photocurrent range. We also corroborate and expand upon the physical understanding of how the broadband, complex impedance of the circuit following the photodiode modifies the linearity - in some cases quite significantly. By externally manipulating the circuit impedance, we extend the detector's linear range to higher photocurrents, with over 50 dB rejection of amplitude-to-phase conversion for photocurrents up to 40 mA. This represents a 1000-fold improvement over state-of-the-art photodiodes and significantly extends the attainable microwave power by a factor of four. As such, we eliminate the long-standing requirement in ultrashort pulse detection of precise tuning of the photodiode's operating parameters to coincide with a nonlinearity minimum. These results should also apply more generally to reduce nonlinear distortion in a range of other microwave photonics applications.

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 $^{171}$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 $10^{-18}$ level and beyond., 5 + 2 pages, 3 figures, added supplemental

We present an experimental study of the nonlinearity of modified uni-traveling carrier (MUTC) photodiodes at cryogenic temperatures. At 120 K, the amplitude-to-phase (AM-to-PM) conversion nonlinearity is reduced by up to 10 dB, resulting in nearly 40 dB AM-to-PM rejection over a broad photocurrent range.

Optical clocks combined with frequency combs are the future of precision timekeeping, as well as a key enabling technology for applications in communication, navigation, relativistic geodesy, quantum physics, and fundamental measurements. Using a silicon nitride waveguide to spectrally broaden a telecom-frequency comb, the authors perform an optical-clock comparison. Additionally, they present measurements and analysis to support an ``all-in-one'' waveguide design for a next-generation clock network. Such devices will be very useful not just in metrology labs, but also in the field---including space missions.

We describe a system for high-performance laser stabilization using Ramsey-Borde interferometry with calcium.

We describe an erbium-fiber laser frequency comb that supports optical frequency synthesis at the millihertz level, or fractionally as 3×10−18 τ−1/2, by ensuring all critical fiber paths are within the servo-controlled feedback loop.

A simple, rigidly-held 25 mm-long reference cavity is presented. A laser stabilized to it supports 10 GHz generation with phase noise near −100 dBc/Hz at 1 Hz offset and 600 Hz.

Supercontinuum generation in dispersion engineered silicon nitride waveguides is used to perform frequency comb metrology by measuring the relative stability of two cavity-referenced optical clock lasers at 3.8×10−15 at τ = 2 seconds.

We present the design of a novel, ultralow-phase-noise frequency synthesizer implemented with extremely-low-noise regenerative frequency dividers. This synthesizer generates eight outputs, viz. 1.6 GHz, 320 MHz, 160 MHz, 80 MHz, 40 MHz, 20 MHz, 10 MHz and 5 MHz for an 8 GHz input frequency. The residual single-sideband (SSB) phase noises of the synthesizer at 5 and 10 MHz outputs at 1 Hz offset from the carrier are -150 and -145 dBc/Hz, respectively, which are unprecedented phase noise levels. We also report the lowest values of phase noise to date for 5 and 10 MHz RF signals achieved with our synthesizer by dividing an 8 GHz signal generated from an ultra-stable optical-comb-based frequency division. The absolute SSB phase noises achieved for 5 and 10 MHz signals at 1 Hz offset are -150 and -143 dBc/Hz, respectively; at 100 kHz offset, they are -177 and -174 dBc/Hz, respectively. The phase noise of the 5 MHz signal corresponds to a frequency stability of approximately 7.6 × 10(-15) at 1 s averaging time for a measurement bandwidth (BW) of 500 Hz, and the integrated timing jitter over 100 kHz BW is 20 fs.

We present an optically stabilized Yb:KYW fs- laser frequency comb. We use an f-2f nonlinear interfer- ometer to measure the carrier envelope offset frequency (f0) and the heterodyne beatnote between the comb and a stable CW laser at 1068 nm to detect fluctuations in the comb repetition rate (frep). Both of these degrees of free- dom of the comb are then controlled using phase-locked loops. As a demonstration of the frequency-stabilized comb, we generate low-phase-noise 10 GHz microwaves through detection of the pulse train on a high bandwidth photodiode. The phase noise of the resulting 10 GHz microwaves was -99 dBc/Hz at 1 Hz and the corre- sponding Allen deviation was \2.6 9 10 -15 at 1 s, mea

We demonstrate a Brillouin microresonator laser operating at 1560 nm that is frequency doubled and stabilized to Rubidium to improve the microresonator's drift by 1000×, reaching a fractional frequency stability of 4.8×10−12 at 1000 s.

I will discuss the recent developments at the National Institute of Standards in the generation and broadband synthesis of ultra-low noise microwave signals from optical sources.

We demonstrate an single branch Er:fiber laser for simultaneous access to all optical standards at NIST and that enables optical measurement instabilities at an unprecedented level of less than 4 × 10−18 at 1 s averaging time, and averaging down as τ−1/2.