Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants

Scheme for Quantum-Logic Based Transfer of Accuracy in Polarizability Measurement for Trapped Ions Using a Moving Optical Lattice

Optical atomic clocks based on trapped ions suffer from systematic frequency shifts of the clock transition due to interaction with blackbody radiation from the environment. These shifts can be compensated if the blackbody radiation spectrum and the differential dynamic polarizability is known to a sufficient precision. Here, we present a new measurement scheme, based on quantum logic that allows a direct transfer of precision for polarizability measurements from one species to the other. This measurement circumvents the necessity of calibrating laser power below the percent level, which is the limitation for state-of-the-art polarizability measurements in trapped ions. Furthermore, the presented technique allows one to reference the polarizability transfer to hydrogenlike ions for which the polarizability can be calculated with high precision.

Observation of a Low-Lying Metastable Electronic State in Highly Charged Lead by Penning-Trap Mass Spectrometry

Highly charged ions (HCIs) offer many opportunities for next-generation clock research due to the vast landscape of available electronic transitions in different charge states. The development of extreme ultraviolet frequency combs has enabled the search for clock transitions based on shorter wavelengths in HCIs. However, without initial knowledge of the energy of the clock states, these narrow transitions are difficult to be probed by lasers. In this Letter, we provide experimental observation and theoretical calculation of a long-lived electronic state in Nb-like Pb^{41+} that could be used as a clock state. With the mass spectrometer PENTATRAP, the excitation energy of this metastable state is directly determined as a mass difference at an energy of 31.2(8) eV, corresponding to one of the most precise relative mass determinations to date with a fractional uncertainty of 4×10^{-12}. This experimental result agrees within 1σ with two partially different ab initio multiconfiguration Dirac-Hartree-Fock calculations of 31.68(13) eV and 31.76(35) eV, respectively. With a calculated lifetime of 26.5(5.3) days, the transition from this metastable state to the ground state bears a quality factor of 1.1×10^{23} and allows for the construction of a HCI clock with a fractional frequency instability of <10^{-19}/sqrt[τ].

Narrow and Ultranarrow Transitions in Highly Charged Xe Ions as Probes of Fifth Forces

Optical frequency metrology in atoms and ions can probe hypothetical fifth forces between electrons and neutrons by sensing minute perturbations of the electronic wave function induced by them. A generalized King plot has been proposed to distinguish them from possible standard model effects arising from, e.g., finite nuclear size and electronic correlations. Additional isotopes and transitions are required for this approach. Xenon is an excellent candidate, with seven stable isotopes with zero nuclear spin, however it has no known visible ground-state transitions for high resolution spectroscopy. To address this, we have found and measured twelve magnetic-dipole lines in its highly charged ions and theoretically studied their sensitivity to fifth forces as well as the suppression of spurious higher-order standard model effects. Moreover, we identified at 764.8753(16) nm a E2-type ground-state transition with 500 s excited state lifetime as a potential clock candidate further enhancing our proposed scheme.

Continuous optical generation of microwave signals for fountain clocks

For the optical generation of ultrastable microwave signals for fountain clocks, we developed a setup based on a cavity stabilized laser and a commercial frequency comb. The robust system, in operation since 2020, is locked to a 100 MHz output frequency of a hydrogen maser and provides an ultrastable 9.6 GHz signal for the interrogation of atoms in two cesium fountain clocks, acting as primary frequency standards. Measurements reveal that the system provides a phase noise level that enables quantum projection noise limited fountain frequency instabilities at the low 10-14(τ/s)-1/2 level. At the same time, it offers largely maintenance-free operation.

Optical frequency averaging of light

The use of averaging has long been known to reduce noise in statistically independent systems that exhibit similar levels of stochastic fluctuation. This concept of averaging is general and applies to a wide variety of physical and man-made phenomena such as particle motion, shot noise, atomic clock stability, measurement uncertainty reduction, and methods of signal processing. Despite its prevalence in use for reducing statistical uncertainty, such averaging techniques so far remain comparatively undeveloped for application to light. We demonstrate here a method for averaging the frequency uncertainty of identical laser systems as a means to narrow the spectral linewidth of the resulting radiation. We experimentally achieve a reduction of frequency fluctuations from 40 Hz to 28 Hz by averaging two separate laser systems each locked to a fiber resonator. Only a single seed laser is necessary here as acousto-optic modulation is used to enable independent control of the second path. This technique of frequency averaging provides an effective solution to overcome the linewidth constraints of a single laser alone, particularly when limited by fundamental noise sources such as thermal noise, irrespective of the spectral shape of noise.

Bosonic Pair Production and Squeezing for Optical Phase Measurements in Long-Lived Dipoles Coupled to a Cavity

We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.

Gravitational redshift test using Rb clocks of eccentric GPS satellites

This paper reports a test of gravitational redshift, which is a consequence of the Einstein equivalence principle, using the Rb clocks of GPS Block IIF satellites. The fractional deviation in the gravitational redshift was measured using 6,640 days of data from three Rb clocks onboard GPS Block IIF satellites. The systematic effects related to orbital uncertainty, temperature, and magnetic field were modeled conservatively. The fractional deviation in the gravitational redshift from the general relativity prediction was measured with ( 0.23 ± 1.34 ) × 10 - 3 at one sigma.

Search for Ultralight Dark Matter from Long-Term Frequency Comparisons of Optical and Microwave Atomic Clocks

We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between a ^{171}Yb optical lattice clock and a ^{133}Cs fountain microwave clock that span 298 days with an uptime of 15.4%. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from 10^{-22} to 10^{-20}  eV/c^{2} are set, assuming that each of these couplings is the dominant source of the modulation in the frequency ratio. The absolute frequency of the ^{171}Yb clock transition is also determined as 518 295 836 590 863.69(28) Hz, which is one of the important contributions toward a redefinition of the second in the International System of Units.

Analog transmission of time-frequency signal in atmospheric turbulence environment

The high-precision time-frequency transfer of the optical atomic clock signals over ground-to-satellite and terrestrial free-space laser paths is of great significance in the fields of fundamental and applied sciences. However, the phase noises caused by atmospheric turbulence severely degrade the measurement precision. In this paper, a new method to simulate the transmission of time-frequency signal propagating through atmospheric turbulence is investigated. An analog transmission system comparable to the practical out-field link has been demonstrated, which can provide a deep insight into the phase distortion of time-frequency signal of free-space optical communication links.

Cooling of an integrated Brillouin laser below the thermal limit

Photonically integrated resonators are promising as a platform for enabling ultranarrow linewidth lasers in a compact form factor. Owing to their small size, these integrated resonators suffer from thermal noise that limits the frequency stability of the optical mode to ∼100 kHz. Here, we demonstrate an integrated stimulated Brillouin scattering (SBS) laser based on a large mode-volume annulus resonator that realizes an ultranarrow thermal-noise-limited linewidth of 270 Hz. In practice, yet narrower linewidths are required before integrated lasers can be truly useful for applications such as optical atomic clocks, quantum computing, gravitational wave detection, and precision spectroscopy. To this end, we employ a thermorefractive noise suppression technique utilizing an auxiliary laser to reduce our SBS laser linewidth to 70 Hz. This demonstration showcases the possibility of stabilizing the thermal motion of even the narrowest linewidth chip lasers to below 100 Hz, thereby opening the door to making integrated microresonators practical for the most demanding future scientific endeavors.

Dual optical frequency combs with ultra-low relative phase jitters from 550 nm to 1020 nm for precision spectroscopy

Here, ultra-low relative phase jitters over a wide optical spectrum were achieved for dual Ti:Sapphire optical frequency combs. The two optical frequency combs were independently phase-locked to a Sr optical lattice clock laser delivered through a commercial optical fiber network. We confirmed that the relative phase jitters between the two combs integrated from 8.3 mHz to 200 kHz were below 1 rad, corresponding to a relative linewidth of below 8.3 mHz, over the entire wavelength of the optical frequency combs ranging from 550 nm to 1020 nm. Our work paves the way for ultrahigh-precision dual-comb spectroscopy covering a wide optical spectral range with a simple setup, and provides an absolute optical frequency reference with great stability over a wide range of wavelengths.

Improving Short-Term Stability in Optical Lattice Clocks by Quantum Nondemolition Measurement

We propose a multimeasurement estimation protocol for quantum nondemolition (QND) measurements in a Rabi clock interferometer. The method is well suited for current state-of-the-art optical lattice clocks with QND measurement capabilities. The protocol exploits the correlations between multiple nondestructive measurements of the initially prepared coherent spin state. A suitable Gaussian estimator for the clock laser detuning is presented, and an analytic expression for the sensitivity of the protocol is derived. We use this analytic expression to optimize the protocol using available experimental parameters, achieving an improvement of 7.9 dB with respect to the standard quantum limit in terms of clock stability. We also discuss the measurement back-action effects of our protocol into the atomic state.

A Low Temperature Coefficient Time-to-Digital Converter with 1.3 ps Resolution Implemented in a 28 nm FPGA

Time-to-digital converter (TDC) is the key technology to realize accurate time delay measurement in high-precision optical fiber time-frequency transmission and synchronization, optical sensing and many scientific applications. The performance of FPGA-TDC based on the carry chain is sensitive to the operating temperature. This paper presents a parallel multichain cross segmentation method, without multitime measurements, which merges multichain into an equivalent chain, achieving low temperature coefficient and maintaining high precision. The equivalent chain breaks the limit of the intrinsic cell delay of a single carry chain, improves the precision and reduces the impact of temperature variation significantly. A two-channel TDC based on parallel multichain cross segmentation method is implemented in a 28 nm fabrication process Kintex-7 FPGA. The results show that the performance of TDC is improved with the increase of the number of chains. The 10-chain TDC with 1.3 ps resolution, 4.6 ps single-shot precision performs much better than the plain TDC with 11.4 ps resolution, 8.7 ps single-shot precision. The resolution is stable with 0.0002 ps/°C temperature coefficient under an operating temperature range from 25 °C to 70 °C. Moreover, the proposed method reduces the complexity of the circuit and the resource usage.

Ultrastable Free-Space Laser Links for a Global Network of Optical Atomic Clocks

A global network of optical atomic clocks will enable unprecedented measurement precision in fields including tests of fundamental physics, dark matter searches, geodesy, and navigation. Free-space laser links through the turbulent atmosphere are needed to fully exploit this global network, by enabling comparisons to airborne and spaceborne clocks. We demonstrate frequency transfer over a 2.4 km atmospheric link with turbulence comparable to that of a ground-to-space link, achieving a fractional frequency stability of 6.1×10^{-21} in 300 s of integration time. We also show that clock comparison between ground and low Earth orbit will be limited by the stability of the clocks themselves after only a few seconds of integration. This significantly advances the technologies needed to realize a global timescale network of optical atomic clocks.

Comparing ultrastable lasers at 7 × 10-17 fractional frequency instability through a 2220 km optical fibre network

Ultrastable lasers are essential tools in optical frequency metrology enabling unprecedented measurement precision that impacts on fields such as atomic timekeeping, tests of fundamental physics, and geodesy. To characterise an ultrastable laser it needs to be compared with a laser of similar performance, but a suitable system may not be available locally. Here, we report a comparison of two geographically separated lasers, over the longest ever reported metrological optical fibre link network, measuring 2220 km in length, at a state-of-the-art fractional-frequency instability of 7 × 10-17 for averaging times between 30 s and 200 s. The measurements also allow the short-term instability of the complete optical fibre link network to be directly observed without using a loop-back fibre. Based on the characterisation of the noise in the lasers and optical fibre link network over different timescales, we investigate the potential for disseminating ultrastable light to improve the performance of remote optical clocks.

Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation

We report a measurement of the radiative lifetime of the ^{2}F_{7/2} level of ^{171}Yb^{+} that is coupled to the ^{2}S_{1/2} ground state via an electric octupole transition. The radiative lifetime is determined to be 4.98(25)×10^{7}  s, corresponding to 1.58(8) yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.

Simultaneous bicolor interrogation in thulium optical clock providing very low systematic frequency shifts

Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10⁻¹⁸ level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10⁻¹⁸ in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout.

There are continuous efforts in improving the stability and systematic shifts of optical clocks. Here the authors demonstrate thulium optical clock utilizing bicolor scheme involving interrogation of both hyperfine levels and they are able to cancel the quadratic Zeeman shift.

Prospects of a Pb^{2+} Ion Clock

We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have I=J=F=0, where I, J, and F are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation, second order Zeeman, Doppler), accommodates "magic" rf trapping, and is robust against decoherence mechanisms that can otherwise limit clock stability. By driving the transition as a two-photon E1+M1 process, the accompanying probe Stark shift is appreciable yet manageable for practical Rabi frequencies.

Absolute phase marking technology and fiber-optic remote coherent phase transmission

Fiber-optic time and frequency synchronization technology demonstrates ultra-high synchronization performance and has been gradually applied in various fields. Based on frequency synchronization, this study addressed the problems of period ambiguity and initial phase uncertainty of the phase signal to realize the coherent transmission of the phase. An absolute phase marking technology was developed based on high-speed digital logic with zero-crossing detection and an optimized control strategy. It can realize picosecond-level absolute phase marking and provide a picosecond-level ultra-low peak-to-peak jitter pulse marking signal to eliminate phase period ambiguity and determine initial phase and transmission delay. Thus, by combining the high-precision phase measurement capability of the synchronized frequency signal and long-distance ambiguity elimination capability of the pulse-per-second signal, a high-precision remote coherent phase transmission over an optical fiber is realized. After frequency synchronization, the peak-to-peak jitter between the local and remote phase-marking signals can be only 3.3 ps within 10,000 s measurement time. The uncertainty of the coherent phase transmission is 2.577 ps. This technology can significantly improve the phase coherence of fiber-optic time and frequency transmission and provide a new approach to achieve peak-to-peak picosecond-level reference phase marking and high-precision fiber-optic remote coherent phase transmission. This demonstrates broad application prospects in coherence fields such as radar networking.

Development of a deep-ultraviolet pulse laser source operating at 234 nm for direct cooling of Al+ ion clocks

We report on the development of a 250-MHz 234 nm deep-ultraviolet pulse source based on a flexible wavelength-conversion scheme. The scheme is based on a frequency-doubled optical parametric oscillator (FD-OPO) together with a cascaded frequency conversion process. We use a χ⁽²⁾ nonlinear envelope equation to guide the design of an intra-cavity OPO crystal, demonstrating a flexible broadband tunable feature and providing as high as watt-level of a frequency-doubled signal output centered at 850 nm, which is served as an input wave for the cascaded frequency conversion process. As much as 3.0 mW of an average power at 234 nm is obtained, with an rms power stability of better than 1% over 20 minutes. This deep-ultraviolet pulse laser source can be used for many applications in quantum optics and for direct laser cooling of Al⁺ ion clocks.

Frequency ratio measurements at 18-digit accuracy using an optical clock network

Atomic clocks are vital in a wide array of technologies and experiments, including tests of fundamental physics¹. Clocks operating at optical frequencies have now demonstrated fractional stability and reproducibility at the 10^-18 level, two orders of magnitude beyond their microwave predecessors². Frequency ratio measurements between optical clocks are the basis for many of the applications that take advantage of this remarkable precision. However, the highest reported accuracy for frequency ratio measurements has remained largely unchanged for more than a decade^3-5. Here we operate a network of optical clocks based on ²⁷Al⁺ (ref. ⁶), ⁸⁷Sr (ref. ⁷) and ¹⁷¹Yb (ref. ⁸), and measure their frequency ratios with fractional uncertainties at or below 8 × 10^-18. Exploiting this precision, we derive improved constraints on the potential coupling of ultralight bosonic dark matter to standard model fields^9,10. Our optical clock network utilizes not just optical fibre¹¹, but also a 1.5-kilometre free-space link^12,13. This advance in frequency ratio measurements lays the groundwork for future networks of mobile, airborne and remote optical clocks that will be used to test physical laws¹, perform relativistic geodesy¹⁴ and substantially improve international timekeeping¹⁵.

Point-to-point stabilized optical frequency transfer with active optics

Timescale comparison between optical atomic clocks over ground-to-space and terrestrial free-space laser links will have enormous benefits for fundamental and applied sciences. However, atmospheric turbulence creates phase noise and beam wander that degrade the measurement precision. Here we report on phase-stabilized optical frequency transfer over a 265 m horizontal point-to-point free-space link between optical terminals with active tip-tilt mirrors to suppress beam wander, in a compact, human-portable set-up. A phase-stabilized 715 m underground optical fiber link between the two terminals is used to measure the performance of the free-space link. The active optical terminals enable continuous, cycle-slip free, coherent transmission over periods longer than an hour. In this work, we achieve residual instabilities of 2.7 × 10-6 rad2 Hz-1 at 1 Hz in phase, and 1.6 × 10-19 at 40 s of integration in fractional frequency; this performance surpasses the best optical atomic clocks, ensuring clock-limited frequency comparison over turbulent free-space links.

Improved Limits for Violations of Local Position Invariance from Atomic Clock Comparisons

We compare two optical clocks based on the ^{2}S_{1/2}(F=0)→^{2}D_{3/2}(F=2) electric quadrupole (E2) and the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition of ^{171}Yb^{+} and measure the frequency ratio ν_{E3}/ν_{E2}=0.932829404530965376(32), improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find ν_{E3}=642121496772645.10(8)  Hz, the most accurate determination of an optical transition frequency to date. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant α to 1.0(1.1)×10^{-18}/yr and of the proton-to-electron mass ratio μ to -8(36)×10^{-18}/yr. Using the annual variation of the Sun's gravitational potential at Earth Φ, we improve limits for a potential coupling of both constants to gravity, (c^{2}/α)(dα/dΦ)=14(11)×10^{-9} and (c^{2}/μ)(dμ/dΦ)=7(45)×10^{-8}.

Rugged mHz-Linewidth Superradiant Laser Driven by a Hot Atomic Beam

We propose a new type of superradiant laser based on a hot atomic beam traversing an optical cavity. We show that the theoretical minimum linewidth and maximum power are competitive with the best ultracoherent clock lasers. Also, our system operates naturally in continuous wave mode, which has been elusive for superradiant lasers so far. Unlike existing ultracoherent lasers, our design is simple and rugged. This makes it a candidate for the first widely accessible ultracoherent laser, as well as the first to realize sought-after applications of ultracoherent lasers in challenging environments.

Operation of an optical atomic clock with a Brillouin laser subsystem

Microwave atomic clocks have traditionally served as the 'gold standard' for precision measurements of time and frequency. However, over the past decade, optical atomic clocks^1-6 have surpassed the precision of their microwave counterparts by two orders of magnitude or more. Extant optical clocks occupy volumes of more than one cubic metre, and it is a substantial challenge to enable these clocks to operate in field environments, which requires the ruggedization and miniaturization of the atomic reference and clock laser along with their supporting lasers and electronics^4,7,8,9. In terms of the clock laser, prior laboratory demonstrations of optical clocks have relied on the exceptional performance gained through stabilization using bulk cavities, which unfortunately necessitates the use of vacuum and also renders the laser susceptible to vibration-induced noise. Here, using a stimulated Brillouin scattering laser subsystem that has a reduced cavity volume and operates without vacuum, we demonstrate a promising component of a portable optical atomic clock architecture. We interrogate a ⁸⁸Sr⁺ ion with our stimulated Brillouin scattering laser and achieve a clock exhibiting short-term stability of 3.9 × 10^-14 over one second-an improvement of an order of magnitude over state-of-the-art microwave clocks. This performance increase within a potentially portable system presents a compelling avenue for substantially improving existing technology, such as the global positioning system, and also for enabling the exploration of topics such as geodetic measurements of the Earth, searches for dark matter and investigations into possible long-term variations of fundamental physics constants^10-12.

Precision Metrology Meets Cosmology: Improved Constraints on Ultralight Dark Matter from Atom-Cavity Frequency Comparisons

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.

Frequency ratio of an 115In+ ion clock and a 87Sr optical lattice clock

We report on the first, to the best of our knowledge, frequency ratio measurement of an ¹¹⁵In⁺ singleion clock and a ⁸⁷Sr optical lattice clock. A hydrogen maser serves as a flywheel oscillator to measure the ratio by independent optical combs. From 89,000 s of measurement time, the frequency ratio f_In/f_Sr is determined to be 2.952 748 749 874 863 3(23) with 7.7×10^-16 relative uncertainty. The measurement creates a new connection in the network of frequency ratios of optical clocks.

Optical frequency combs: Coherently uniting the electromagnetic spectrum

Optical frequency combs were introduced around 20 years ago as a laser technology that could synthesize and count the ultrafast rate of the oscillating cycles of light. Functioning in a manner analogous to a clockwork of gears, the frequency comb phase-coherently upconverts a radio frequency signal by a factor of [Formula: see text] to provide a vast array of evenly spaced optical frequencies, which is the comb for which the device is named. It also divides an optical frequency down to a radio frequency, or translates its phase to any other optical frequency across hundreds of terahertz of bandwidth. We review the historical backdrop against which this powerful tool for coherently uniting the electromagnetic spectrum developed. Advances in frequency comb functionality, physical implementation, and application are also described.

Coherent optical clock down-conversion for microwave frequencies with 10-18 instability

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^-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.

Direct measurement of the frequency ratio for Hg and Yb optical lattice clocks and closure of the Hg/Yb/Sr loop

We performed the first direct measurement of the frequency ratio between a mercury (¹⁹⁹Hg) and an ytterbium (¹⁷¹Yb) optical lattice clock to find ν_Hg/ν_Yb = 2.177 473 194 134 565 07(19) with the fractional uncertainty of 8.8 × 10^-17. The ratio is in excellent agreement with expectations from the ratios ν_Hg/ν_Sr and ν_Yb/ν_Sr obtained previously in comparisons against a strontium (⁸⁷Sr) optical lattice clock. The completed closure (ν_Hg/ν_Yb)(ν_Yb/ν_Sr)(ν_Sr/ν_Hg) - 1 = 0.4(1.3) × 10^-16 tests the frequency reproducibility of the optical lattice clocks beyond what is achievable in comparison against the current realization of the second in the International System of Units (SI).

Integrated multiple wavelength stabilization on a multi-channel cavity for a transportable optical clock

We present a simple, compact, and efficient scheme for integrated multiple wavelength stabilization and continuous operation of a transportable ⁴⁰Ca⁺ optical clock using a multi-channel cavity. The fractional frequency instability of 729 nm clock laser is ∼ 1.5 ×10^-15 at 10 s with an approximate linewidth of 1 Hz. Meanwhile, frequency fluctuations of all the other lasers are less than ± 330 kHz/day. The one-day stability of this clock is measured as ∼ 5 ×10^-17 through 72 h continuous operation. This scheme is potentially useful for the realization of next-generation transportable optical clocks and other metrological systems.

Search for a Variation of the Fine Structure Constant around the Supermassive Black Hole in Our Galactic Center

Searching for space-time variations of the constants of Nature is a promising way to search for new physics beyond general relativity and the standard model motivated by unification theories and models of dark matter and dark energy. We propose a new way to search for a variation of the fine-structure constant using measurements of late-type evolved giant stars from the S star cluster orbiting the supermassive black hole in our Galactic Center. A measurement of the difference between distinct absorption lines (with different sensitivity to the fine structure constant) from a star leads to a direct estimate of a variation of the fine structure constant between the star's location and Earth. Using spectroscopic measurements of five stars, we obtain a constraint on the relative variation of the fine structure constant below 10^{-5}. This is the first time a varying constant of nature is searched for around a black hole and in a high gravitational potential. This analysis shows new ways the monitoring of stars in the Galactic Center can be used to probe fundamental physics.

Measurement of the variation of electron-to-proton mass ratio using ultracold molecules produced from laser-cooled atoms

Experimental techniques to manipulate cold molecules have seen great development in recent years. The precision measurements of cold molecules are expected to give insights into fundamental physics. Here we use a rovibrationally pure sample of ultracold KRb molecules to improve the measurement on the stability of electron-to-proton mass ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\mu = \frac{{m_{\mathrm{e}}}}{{M_{\mathrm{p}}}}} \right)$$\end{document}μ=meMp. The measurement is based upon a large sensitivity coefficient of the molecular spectroscopy, which utilizes a transition between a nearly degenerate pair of vibrational levels each associated with a different electronic potential. Observed limit on temporal variation of μ is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{\mu }\frac{{d\mu }}{{dt}} = (0.30 \pm 1.0) \times 10^{ - 14} \, {\mathrm{year}}^{ - 1}$$\end{document}1μdμdt=(0.30±1.0)×10-14year-1, which is better by a factor of five compared with the most stringent laboratory molecular limits to date. Further improvements should be straightforward, because our measurement was only limited by statistical errors.

Ultracold molecules are suitable platforms for precision measurements due to their internal degrees of freedom. Here the authors derive a limit on the variation of the electron-to-proton mass ratio by using the spectroscopy of ultracold KRb molecules.

Quadrupole Shift Cancellation Using Dynamic Decoupling

We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals and impose one of the limitations forcing current optical ion clocks to work with a single probe ion. Canceling this shift, at each interrogation cycle of the ion frequency, reduces the complexity in using N>1 ions in clocks, thus allowing for a reduction of the instability in the clock frequency by sqrt[N] according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven ^{88}Sr^{+} ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to the ≈10  mHz level where other shifts, such as the relativistic second-order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of first-order Zeeman shifts.

Direct phase-locking of a Ti:Sapphire optical frequency comb to a remote optical frequency standard

We report on an ultralow noise optical frequency transfer from a remotely located Sr optical lattice clock laser to a Ti:Sapphire optical frequency comb through telecom-wavelength optical fiber networks. The inherent narrow linewidth of the Ti:Sapphire optical frequency comb eliminates the need for a local reference high-finesse cavity. The relative fractional frequency instability of the optical frequency comb with respect to the remote optical reference was 6.7(1) × 10^-18 at 1 s and 1.05(3) × 10^-19 at 1,000 s including a 2.9 km-long fiber network. This ensured the optical frequency comb had the same precision as the optical standard. Our result paves the way for ultrahigh-precision spectroscopy and conversion of the highly precise optical frequency to radio frequencies in a simpler setup.

Deterministic Nonlinear Transformations of Phase Noise in Quantum-Limited Frequency Combs

Optical phase noise of femtosecond lasers is analyzed over various steps of broadband nonlinear frequency conversion. The intrinsic phase jitter of our system originates from quantum statistics in the mode-locked oscillator. Supercontinuum generation by four-wave-mixing processes preserves a noise minimum at the optical carrier frequency. From there, a quadratic increase of the comb linewidth results with mutually anticorrelated phase fluctuations of both spectral wings. Passive phase locking by difference frequency generation strongly enhances the optical phase noise to a level equaling the carrier-envelope phase jitter of the fundamental comb. The same value results from quadratic extrapolation of the optical phase noise to radio frequencies. Our findings are consistent with a fully deterministic transformation of phase noise according to the elastic tape model.

Towards a transportable aluminium ion quantum logic optical clock

With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10^-17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of ⁴⁰Ca⁺. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber ⁴⁰Ca⁺ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on ²⁷Al⁺, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for ²⁷Al⁺ has been determined to be δν_EMMν=-0.4_-0.3 ^+0.4×10^-18 and the black-body radiation shift is δν_BBR/ν = (-4.0 ± 0.4) × 10^-18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ω_rad,Ca+ ≈ 2π × 2.5 MHz (ω_ax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.

Development of 8-branch Er:fiber frequency comb for Sr and Yb optical lattice clocks

We demonstrate an 8-branch Er:fiber frequency comb with seven application ports, which can be individually optimized for applications with different wavelengths. The beat between the comb and a cw laser has a signal-to-noise ratio exceeding 30 dB at a resolution bandwidth of 300 kHz. The 8-branch frequency comb is used to perform frequency locking for four repumping and lattice lasers, and the frequency measurement of two clock lasers of strontium and ytterbium optical lattice clocks. We have achieved reliable optical lattice clock operation, thanks to the stable frequency locking and measurement obtained by using the 8-branch frequency comb. The developed frequency comb is a powerful experimental tool for various applications, including not only optical lattice clocks, but also research on quantum optics that use many frequency-stabilized lasers.

Compact laser system for a laser-cooled ytterbium ion microwave frequency standard

The development of a transportable microwave frequency standard based on the ground-state transition of ¹⁷¹Yb⁺ at ∼12.6 GHz requires a compact laser system for cooling the ions, clearing out of long-lived states and also for photoionisation. In this paper, we describe the development of a suitable compact laser system based on a 6U height rack-mounted arrangement with overall dimensions 260 × 194 × 335 mm. Laser outputs at 369 nm (for cooling), 399 nm (photoionisation), 935 nm (repumping), and 760 nm (state clearout) are combined in a fiber arrangement for delivery to our linear ion trap and we demonstrate this system by cooling of ¹⁷¹Yb⁺ ions. Additionally, we demonstrate that the lasers at 935 nm and 760 nm are close in frequency to water vapor and oxygen absorption lines, respectively; specifically, at 760 nm, we show that one ¹⁷¹Yb⁺ transition is within the pressure broadened profile of an oxygen line. These molecular transitions form convenient wavelength references for the stabilization of lasers for a ¹⁷¹Yb⁺ frequency standard.

Realization of a Rydberg-Dressed Ramsey Interferometer and Electrometer

We present the experimental realization and characterization of a Ramsey interferometer based on optically trapped ultracold potassium atoms, where one state is continuously coupled by an off-resonant laser field to a highly excited Rydberg state. We show that the observed interference signals can be used to precisely measure the Rydberg atom-light coupling strength as well as the population and coherence decay rates of the Rydberg-dressed states with subkilohertz accuracy and for Rydberg state fractions as small as one part in 10^{6}. We also demonstrate an application for measuring small, static electric fields with high sensitivity. This provides the means to combine the outstanding coherence properties of Ramsey interferometers based on atomic ground states with a controllable coupling to strongly interacting states, thus expanding the number of systems suitable for metrological applications and many-body physics studies.

A compact and robust cooling laser system for an optical strontium lattice clock

We present a simple and robust laser system for two-color, narrow-line cooling on the ⁸⁷Sr (5s²)¹S₀ → (5s5p)³P₁ transition. Two hyperfine lines of this transition are addressed simultaneously with light from a single laser source, using sidebands created by an electro-optical phase modulator. A tapered amplifier system provides laser powers up to 90 mW. We show that amplification does not affect the phase modulation of the laser. This compact and robust laser system offers excellent reliability. Therefore, it is especially well suited for transportable and spaceborne optical clocks. The design offers the potential to be miniaturized into a fully integrated package.

Resonant Electronic-Bridge Excitation of the ^{235}U Nuclear Transition in Ions with Chaotic Spectra

Electronic-bridge excitation of the 76 eV nuclear isomeric state in ^{235}U is shown to be strongly enhanced in the U^{7+} ion, potentially enabling laser excitation of this nucleus. This is because the electronic spectrum has a very high level density near the nuclear transition energy that ensures the resonance condition is fulfilled. We present a quantum statistical theory based on many-body quantum chaos to demonstrate that typical values for the electronic factor increase the probability of electronic bridge in ^{235}U^{7+} by many orders of magnitude. We also extract the nuclear matrix element by considering internal conversion from neutral uranium. The final electronic-bridge rate is comparable to the rate of the Yb^{+} octupole transition currently used in precision spectroscopy.

Uncertainty Evaluation of an 171Yb Optical Lattice Clock at NMIJ

We report an uncertainty evaluation of an ¹⁷¹Yb optical lattice clock with a total fractional uncertainty of 3.6×10^-16 , which is mainly limited by the lattice-induced light shift and the blackbody radiation shift. Our evaluation of the lattice-induced light shift, the density shift, and the second-order Zeeman shift is based on an interleaved measurement where we measure the frequency shift using the alternating stabilization of a clock laser to the 6s^{2 1}S₀-6s6p ³P₀ clock transition with two different experimental parameters. In the present evaluation, the uncertainties of two sensitivity coefficients for the lattice-induced hyperpolarizability shift d incorporated in a widely used light shift model by RIKEN and the second-order Zeeman shift a_Z are improved compared with the uncertainties of previous coefficients. The hyperpolarizability coefficient d is determined by investigating the trap potential depth and the light shifts at the lattice frequencies near the two-photon transitions 6s6p³P₀-6s8p³P₀, 6s8p³P₂, and 6s5f³F₂. The obtained values are d=-1.1(4) μ Hz and a_Z=-6.6(3) Hz/mT². These improved coefficients should reduce the total systematic uncertainties of Yb lattice clocks at other institutes.

Recent Advances Concerning the 87Sr Optical Lattice Clock at the National Time Service Center

We review recent experimental progress concerning the 87Sr optical lattice clock at the National Time Service Center in China. Hertz-level spectroscopy of the 87Sr clock transition for the optical lattice clock was performed, and closed-loop operation of the optical lattice clock was realized. A fractional frequency instability of 2.8 × 10−17 was attained for an averaging time of 2000 s. The Allan deviation is found to be 1.6 × 10−15/τ1/2 and is limited mainly by white-frequency-noise. The Landé g-factors of the (5s2)1S0 and (5s5p)3P0 states in 87Sr were measured experimentally; they are important for evaluating the clock’s Zeeman shifts. We also present recent work on the miniaturization of the strontium optical lattice clock for space applications.

Optical Pumping of TeH+: Implications for the Search for Varying mp/me

Molecular overtone transitions provide optical frequency transitions sensitive to variation in the proton-to-electron mass ratio ( μ ≡ m p / m e ). However, robust molecular state preparation presents a challenge critical for achieving high precision. Here, we characterize infrared and optical-frequency broadband laser cooling schemes for TeH + , a species with multiple electronic transitions amenable to sustained laser control. Using rate equations to simulate laser cooling population dynamics, we estimate the fractional sensitivity to μ attainable using TeH + . We find that laser cooling of TeH + can lead to significant improvements on current μ variation limits.

Octave-spanning optical frequency comb based on a laser-diode pumped Kerr-lens mode-locked Yb:KYW laser for optical frequency measurement

We developed an optical frequency comb based on a Yb:KYW laser. Soft-aperture Kerr-lens mode-locking at the cavity transverse-mode degeneration enabled us to generate 360 mW from a 750 mW pump laser diode. This resulted in spectral broadening over one octave using just a photonic crystal fiber. We achieved a free-running linewidth of 15 kHz in the carrier-envelope offset frequency by optimizing the cavity group delay dispersion, crystal position, and pump laser power, which led to a residual phase noise of 0.51 rad during phase-locking. We measured the frequency drift of a cavity-stabilized laser for a clock transition in Yb171⁺.

Atomic clocks for geodesy

We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10^-17, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international clock development and comparison. Besides further improvement in stability and accuracy of today's best clocks, a large effort is put into increasing the reliability and technological readiness for applications outside of specialized laboratories with compact, portable devices. With relative frequency uncertainties of 10^-18, comparisons of optical frequency standards are foreseen to contribute together with satellite and terrestrial data to the precise determination of fundamental height reference systems in geodesy with a resolution at the cm-level. The long-term stability of atomic standards will deliver excellent long-term height references for geodetic measurements and for the modelling and understanding of our Earth.