Frequency comparison of two high-accuracy Al+ optical clocks

Blackbody radiation shift assessment for a lutetium ion clock

The accuracy of state-of-the-art atomic clocks is derived from the insensitivity of narrow optical atomic resonances to environmental perturbations. Two such resonances in singly ionized lutetium have been identified with potentially lower sensitivities compared to other clock candidates. Here we report measurement of the most significant unknown atomic property of both transitions, the static differential scalar polarizability. From this, the fractional blackbody radiation shift for one of the transitions is found to be −1.36(9) × 10⁻¹⁸ at 300 K, the lowest of any established optical atomic clock. In consideration of leading systematic effects common to all ion clocks, both transitions compare favorably to the most accurate ion-based clocks reported to date. This work firmly establishes Lu⁺ as a promising candidate for a future generation of more accurate optical atomic clocks.

There is a continuous effort to improve the accuracy of atomic clocks. Here the authors measure the static differential scalar polarizability of Lutetium ion resonant transitions and its lower light shift from blackbody radiation makes it a promising candidate for ion-based atomic clocks.

Thermal-noise-limited higher-order mode locking of a reference cavity

Higher-order mode locking has been proposed to reduce the thermal noise limit of reference cavities. By locking a laser to the HG₀₂ mode of a 10-cm long all ultra-low expansion (ULE) cavity and measuring its performance with the three-cornered-hat method among three independently stabilized lasers, we demonstrate a thermal-noise-limited performance of a fractional frequency instability of 4.9×10^-16. The results match the theoretical models with higher-order optical modes. The achieved laser instability improves the all ULE short cavity results to a new low level.

A single-atom 3D sub-attonewton force sensor

Forces drive all physical interactions. High-sensitivity measurement of the effect of forces enables the quantitative investigation of physical phenomena. Laser-cooled trapped atomic ions are a well-controlled quantum system whose low mass, strong Coulomb interaction, and readily detectable fluorescence signal make them a favorable platform for precision metrology. We demonstrate a three-dimensional sub-attonewton sensitivity force sensor based on a super-resolution imaging of a single trapped ion. The force is detected by measuring the ion's displacement in three dimensions with nanometer precision. Observed sensitivities were 372 ± 9, 347 ± 18, and 808 ± 51 zN/[Formula: see text], corresponding to 24×, 87×, and 21× above the quantum limit. We verified this technique by measuring a 95-zN light pressure force, an important systematic effect in optically based sensors.

A radio-frequency ion trap with string electrodes

A radio-frequency (rf) ion trap with string electrodes is introduced. In this trap configuration, the rf electrodes are made of narrow metal strings, by which a negligibly small portion of light-induced fluorescence (LIF) is blocked. Then the LIF collection solid angle can be maximized. In the demonstration, barium ions are trapped and laser-cooled in the rf trap with string electrodes successfully, and the crystallization is confirmed by the LIF spectrum.

Incorporating an Optical Clock Into a Time Scale

This paper discusses the results of a simulation of a time scale based on continuously operating commercial hydrogen masers and an optical frequency standard that does not operate continuously as a clock. The simulation compares the performance of this time scale with one that is based on the same commercial devices but incorporates a continuously operating cesium fountain instead of the optical standard. The results are independent of the detailed characteristics of the optical frequency standard; the only requirement is that the optical device be much more stable than the masers in the ensemble. We discuss two methods for realizing the results of this simulation in an operational time scale.

A highly stable monolithic enhancement cavity for second harmonic generation in the ultraviolet

We present a highly stable bow-tie power enhancement cavity for critical second harmonic generation (SHG) into the UV using a Brewster-cut β-BaB₂O₄ (BBO) nonlinear crystal. The cavity geometry is suitable for all UV wavelengths reachable with BBO and can be modified to accommodate anti-reflection coated crystals, extending its applicability to the entire wavelength range accessible with non-linear frequency conversion. The cavity is length-stabilized using a fast general purpose digital PI controller based on the open source STEMlab 125-14 (formerly Red Pitaya) system acting on a mirror mounted on a fast piezo actuator. We observe 130 h uninterrupted operation without decay in output power at 313 nm. The robustness of the system has been confirmed by exposing it to accelerations of up to 1 g with less than 10% in-lock output power variations. Furthermore, the cavity can withstand 30 min of acceleration exposure at a level of 3 g_rms without substantial change in the SHG output power, demonstrating that the design is suitable for transportable setups.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

A critical review of the proposed definitions of fundamental chemical quantities and their impact on chemical communities (IUPAC Technical Report)

In the proposed new SI, the kilogram will be redefined in terms of the Planck constant and the mole will be redefined in terms of the Avogadro constant. These redefinitions will have some consequences for measurements in chemistry. The goal of the Mole Project (IUPAC Project Number 2013-048-1-100) was to compile published work related to the definition of the quantity ‘amount of substance’, its unit the ‘mole’, and the consequence of these definitions on the unit of the quantity mass, the kilogram. The published work has been reviewed critically with the aim of assembling all possible aspects in order to enable IUPAC to judge the adequateness of the existing definitions or new proposals. Compilation and critical review relies on the broadest spectrum of interested IUPAC members.

Phase locking of a mode-locked titanium-sapphire laser-based optical frequency comb to a reference laser using a fast piezoelectric actuator

We phase lock an octave-spanning optical frequency comb, generated using a mode-locked titanium-sapphire laser and a photonic-crystal fiber, to a continuous-wave laser line-narrowed to a reference cavity. To phase lock the pulse-repetition frequency, the cavity length of the mode-locked laser is controlled by using a fast piezoelectric-actuated mirror of a servo bandwidth up to 80 kHz. The residual phase noise is 0.35 rad, and 89% of the power is concentrated to the carrier. To apply the system to optical frequency-ratio measurements and to evaluate the phase locking, a simultaneous frequency measurement of the beat between the other mode of the comb and another laser line-narrowed to a different resonance of the common reference cavity is demonstrated.

Transportable Optical Lattice Clock with 7×10^{-17} Uncertainty

We present a transportable optical clock (TOC) with ^{87}Sr. Its complete characterization against a stationary lattice clock resulted in a systematic uncertainty of 7.4×10^{-17}, which is currently limited by the statistics of the determination of the residual lattice light shift, and an instability of 1.3×10^{-15}/sqrt[τ] with an averaging time τ in seconds. Measurements confirm that the systematic uncertainty can be reduced to below the design goal of 1×10^{-17}. To our knowledge, these are the best uncertainties and instabilities reported for any transportable clock to date. For autonomous operation, the TOC has been installed in an air-conditioned car trailer. It is suitable for chronometric leveling with submeter resolution as well as for intercontinental cross-linking of optical clocks, which is essential for a redefinition of the International System of Units (SI) second. In addition, the TOC will be used for high precision experiments for fundamental science that are commonly tied to precise frequency measurements and its development is an important step to space-borne optical clocks.

Quantum lock-in force sensing using optical clock Doppler velocimetry

Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator, thus increasing its response by the mechanical quality factor. The measurement of low-frequency forces, that are below resonance, is a more difficult task as the resulting oscillation amplitudes are significantly lower. Here we use a single-trapped ⁸⁸Sr⁺ ion as a force sensor. The ion is electrically driven at a frequency much lower than the trap resonance frequency. We measure small amplitude of motion by measuring the periodic Doppler shift of an atomic optical clock transition, enhanced using the quantum lock-in technique. We report frequency force detection sensitivity as low as 2.8 × 10⁻²⁰ NHz^−1/2.

Existing force sensors are designed for driving frequencies above tens of kHz due to heating and sensitivity loss. Here the authors demonstrate precise force metrology for below kHz frequency range by combining the Doppler-shifted optical transition in trapped ion and quantum lock-in technique.

Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock

We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.

Simple delay-limited sideband locking with heterodyne readout

We present a robust sideband laser locking technique ideally suited for applications requiring low probe power and heterodyne readout. By feeding back to a high-bandwidth voltage-controlled oscillator, we lock a first-order phase-modulation sideband to a high-finesse Fabry-Perot cavity in ambient conditions, achieving a closed-loop bandwidth of 3.5 MHz (with a single integrator) limited fundamentally by the signal delay. The measured transfer function of the closed loop agrees with a simple model based on ideal system components, and from this we suggest a modified design that should achieve a bandwidth exceeding 6 MHz with a near-causally limited feedback gain as high as 4 × 10⁷ at 1 kHz. The off-resonance optical carrier enables alignment-free heterodyne readout, alleviating the need for additional lasers or optical modulators.

Search for the Effect of Massive Bodies on Atomic Spectra and Constraints on Yukawa-Type Interactions of Scalar Particles

We propose a new method to search for hypothetical scalar particles that have feeble interactions with standard-model particles. In the presence of massive bodies, these interactions produce a nonzero Yukawa-type scalar-field magnitude. Using radio-frequency spectroscopy data of atomic dysprosium, as well as atomic clock spectroscopy data, we constrain the Yukawa-type interactions of a scalar field with the photon, electron, and nucleons for a range of scalar-particle masses corresponding to length scales >10  cm. In the limit as the scalar-particle mass m_{ϕ}→0, our derived limits on the Yukawa-type interaction parameters are Λ_{γ}≳8×10^{19}  GeV, Λ_{e}≳1.3×10^{19}  GeV, and Λ_{N}≳6×10^{20}  GeV. Our measurements also constrain combinations of interaction parameters, which cannot otherwise be probed with traditional anomalous-force measurements. We suggest further measurements to improve on the current level of sensitivity.

Quantum Electrodynamical Shifts in Multivalent Heavy Ions

The quantum electrodynamics (QED) corrections are directly incorporated into the most accurate treatment of the correlation corrections for ions with complex electronic structure of interest to metrology and tests of fundamental physics. We compared the performance of four different QED potentials for various systems to access the accuracy of QED calculations and to make a prediction of highly charged ion properties urgently needed for planning future experiments. We find that all four potentials give consistent and reliable results for ions of interest. For the strongly bound electrons, the nonlocal potentials are more accurate than the local potential.

Suppression of Clock Shifts at Magnetic-Field-Insensitive Transitions

We show that it is possible to significantly reduce rank 2 tensor shifts of a clock transition by operating at a judiciously chosen magnetic-field-insensitive point. In some cases shifts are almost completely eliminated making the transition an effective J=0 to J=0 candidate. This significantly improves the feasibility of a recent proposal for clock operation with large ion crystals. For such multi-ion clocks, geometric constraints and selection rules naturally divide clock operation into two categories based on the orientation of the magnetic field. We discuss the limitations imposed on each type and how calibrations might be carried out for clock operation.

Superradiance on the millihertz linewidth strontium clock transition

Laser frequency noise contributes a significant limitation to today's best atomic clocks. A proposed solution to this problem is to create a superradiant laser using an optical clock transition as its gain medium. This laser would act as an active atomic clock and would be highly immune to the fluctuations in reference cavity length that limit today's best lasers. We demonstrate and characterize superradiant emission from the millihertz linewidth clock transition in an ensemble of laser-cooled ⁸⁷Sr atoms trapped within a high-finesse optical cavity. We measure a collective enhancement of the emission rate into the cavity mode by a factor of more than 10,000 compared to independently radiating atoms. We also demonstrate a method for seeding superradiant emission and observe interference between two independent transitions lasing simultaneously. We use this interference to characterize the relative spectral properties of the two lasing subensembles.

Analytically exploiting noise correlations inside the feedback loop to improve locked-oscillator performance

We introduce concepts from optimal estimation to the stabilization of precision frequency standards limited by noisy local oscillators. We develop a theoretical framework casting various measures for frequency standard variance in terms of frequency-domain transfer functions, capturing the effects of feedback stabilization via a time series of Ramsey measurements. Using this framework, we introduce an optimized hybrid predictive feedforward measurement protocol that employs results from multiple past measurements and transfer-function-based calculations of measurement covariance to improve the accuracy of corrections within the feedback loop. In the presence of common non-Markovian noise processes these measurements will be correlated in a calculable manner, providing a means to capture the stochastic evolution of the local oscillator frequency during the measurement cycle. We present analytic calculations and numerical simulations of oscillator performance under competing feedback schemes and demonstrate benefits in both correction accuracy and long-term oscillator stability using hybrid feedforward. Simulations verify that in the presence of uncompensated dead time and noise with significant spectral weight near the inverse cycle time predictive feedforward outperforms traditional feedback, providing a path towards developing a class of stabilization software routines for frequency standards limited by noisy local oscillators.

A clock network for geodesy and fundamental science

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10⁻¹⁷ via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10⁻¹⁷ is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

Comparing the frequency of two distant optical clocks will enable sensitive tests of fundamental physics. Here, the authors compare two strontium optical-lattice clocks 690 kilometres apart to a degree of accuracy that is limited only by the uncertainty of the individual clocks themselves.

1 Hz linewidth Ti:sapphire laser as local oscillator for (40)Ca(+) optical clocks

A Ti:sapphire laser at 729 nm is frequency stabilized to an ultra-stable ultra-low thermal expansion coefficient (ULE) cavity by means of Pound-Drever-Hall method. An acousto-optic modulator is used as the fast frequency feedback component. 1 Hz linewidth and 2 × 10(-15) frequency stability at 1-100 s are characterized by optical beating with a separated Fabry-Perot cavity stabilized diode laser. Compared to the universal method that the error signal feedback to inject current of a diode laser, this scheme is demonstrated to be simple and also effective for linewidth narrowing. The temperature of zero coefficient of the thermal expansion of the ULE cavity is measured with the help of a femto-second frequency comb. And the performance of the laser is well defined by locking it to the unperturbed clock transition line-center of 4 S1/2-3 D5/2 clock transition of a single laser cooled (40)Ca(+) ion. A Fourier-transform limited resonance of 6 Hz (Δv/v = 1.5 × 10(-14)) is observed. This laser is also used as the local oscillator for the comparison experiment of two (40)Ca(+) ion optical clocks and improves the stability of comparison for an order of magnitude better than the previous results.

Active stabilization of ion trap radiofrequency potentials

We actively stabilize the harmonic oscillation frequency of a laser-cooled atomic ion confined in a radiofrequency (rf) Paul trap by sampling and rectifying the high voltage rf applied to the trap electrodes. We are able to stabilize the 1 MHz atomic oscillation frequency to be better than 10 Hz or 10 ppm. This represents a suppression of ambient noise on the rf circuit by 34 dB. This technique could impact the sensitivity of ion trap mass spectrometry and the fidelity of quantum operations in ion trap quantum information applications.

Resolved-Sideband Laser Cooling in a Penning Trap

We report the laser cooling of a single ^{40}Ca^{+} ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole S_{1/2}↔D_{5/2} transition, broadened by a quench laser coupling the D_{5/2} and P_{3/2} levels. We find the final ground-state occupation to be 98(1)%. We measure the heating rate of the trap to be very low with n[over ¯][over ˙]≈0.3(2)  s^{-1} for trap frequencies from 150-400 kHz, consistent with the large ion-electrode distance.

Precision measurement and frequency metrology with ultracold atoms

Precision measurement and frequency metrology have pushed many scientific and technological frontiers in the field of atomic, molecular and optical physics. In this article, we provide a brief review on the recent development of optical atomic clocks, with an emphasis placed on the important inter-dependence between measurement precision and systematic effects. After presenting a general discussion on the motivation and techniques behind the development of optical lattice clocks, where the use of many atoms greatly enhances the measurement precision, we present the JILA strontium optical lattice clock as the leading system of frequency metrology with the lowest total uncertainty, and we describe other related research activities. We discuss key ingredients that have enabled the optical lattice clocks with ultracold atoms to reach the 18th digit in both precision and accuracy. Furthermore, we discuss extending the power of precision clock spectroscopy to study quantum many-body physics and to provide control for atomic quantum materials. In addition, we explore future research directions that have the potential to achieve even greater precision.

Single-Ion Atomic Clock with 3×10(-18) Systematic Uncertainty

We experimentally investigate an optical frequency standard based on the (2)S1/2(F=0)→(2)F7/2(F=3) electric octupole (E3) transition of a single trapped (171)Yb+ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1×10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16)×10(-40)  J m(2)/V(2) and a dynamic correction η(300  K)=-0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8×10(-18). The residual motion of the ion yields the largest contribution (2.1×10(-18)) to the total systematic relative uncertainty of the clock of 3.2×10(-18).

Quantum Algorithmic Readout in Multi-Ion Clocks

Optical clocks based on ensembles of trapped ions promise record frequency accuracy with good short-term stability. Most suitable ion species lack closed transitions, so the clock signal must be read out indirectly by transferring the quantum state of the clock ions to cotrapped logic ions of a different species. Existing methods of quantum logic readout require a linear overhead in either time or the number of logic ions. Here we describe a quantum algorithmic readout whose overhead scales logarithmically with the number of clock ions in both of these respects. The scheme allows a quantum nondemolition readout of the number of excited clock ions using a single multispecies gate operation which can also be used in other areas of ion trap technology such as quantum information processing, quantum simulations, metrology, and precision spectroscopy.

Frequency Comparison of Two (40)Ca(+) Optical Clocks with an Uncertainty at the 10(-17) Level

Based upon an over-one-month frequency comparison of two (40)Ca(+) optical clocks, the frequency difference between the two clocks is measured to be 3.2×10(-17) with a measurement uncertainty of 5.5×10(-17), considering both the statistic (1.9×10(-17)) and the systematic (5.1×10(-17)) uncertainties. This is the first performance of a (40)Ca(+) clock better than that of Cs fountains. A fractional stability of 7×10(-17) in 20,000 s of averaging time is achieved. The evaluation of the two clocks shows that the shift caused by the micromotion in one of the two clocks limits the uncertainty of the comparison. By carefully compensating the micromotion, the absolute frequency of the clock transition is measured to be 411 042 129 776 401.7(1.1) Hz.

Towards a Mg Lattice Clock: Observation of the ^{1}S_{0}-^{3}P_{0} Transition and Determination of the Magic Wavelength

We optically excite the electronic state 3s3p ^{3}P_{0} in ^{24}Mg   atoms, laser cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift, and the transition frequency to be 468.46(21) nm, -206.6(2.0)  MHz/T^{2}, and 655 058 646 691(101) kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.

An open source digital servo for atomic, molecular, and optical physics experiments

We describe a general purpose digital servo optimized for feedback control of lasers in atomic, molecular, and optical physics experiments. The servo is capable of feedback bandwidths up to roughly 1 MHz (limited by the 320 ns total latency); loop filter shapes up to fifth order; multiple-input, multiple-output control; and automatic lock acquisition. The configuration of the servo is controlled via a graphical user interface, which also provides a rudimentary software oscilloscope and tools for measurement of system transfer functions. We illustrate the functionality of the digital servo by describing its use in two example scenarios: frequency control of the laser used to probe the narrow clock transition of (27)Al(+) in an optical atomic clock, and length control of a cavity used for resonant frequency doubling of a laser.

Compact field programmable gate array-based pulse-sequencer and radio-frequency generator for experiments with trapped atoms

We present a compact field-programmable gate array (FPGA) based pulse sequencer and radio-frequency (RF) generator suitable for experiments with cold trapped ions and atoms. The unit is capable of outputting a pulse sequence with at least 32 transistor-transistor logic (TTL) channels with a timing resolution of 40 ns and contains a built-in 100 MHz frequency counter for counting electrical pulses from a photo-multiplier tube. There are 16 independent direct-digital-synthesizers RF sources with fast (rise-time of ∼60 ns) amplitude switching and sub-mHz frequency tuning from 0 to 800 MHz.

Deceleration, precooling, and multi-pass stopping of highly charged ions in Be⁺ Coulomb crystals

Preparing highly charged ions (HCIs) in a cold and strongly localized state is of particular interest for frequency metrology and tests of possible spatial and temporal variations of the fine structure constant. Our versatile preparation technique is based on the generic modular combination of a pulsed ion source with a cryogenic linear Paul trap. Both instruments are connected by a compact beamline with deceleration and precooling properties. We present its design and commissioning experiments regarding these two functionalities. A pulsed buncher tube allows for the deceleration and longitudinal phase-space compression of the ion pulses. External injection of slow HCIs, specifically Ar(13+), into the linear Paul trap and their subsequent retrapping in the absence of sympathetic cooling is demonstrated. The latter proved to be a necessary prerequisite for the multi-pass stopping of HCIs in continuously laser-cooled Be(+) Coulomb crystals.

High accuracy measurement of the ground-state hyperfine splitting in a ¹¹³Cd⁺ microwave clock

A microwave frequency standard based on laser-cooled (113)Cd(+) ions has been developed in recent years, and the short-term frequency instability is measured to be 6.1×10(-13)/√τ. By comparing the Cd(+) clock to a superior frequency reference, the ground-state hyperfine splitting of (113)Cd(+) is measured precisely to be 15199862855.0192(10) Hz with a fractional precision of 6.6×10(-14). This result is consistent with previous results, and the measurement precision is improved by nearly one order more than the best result reported before.

Square Kilometre Array Telescope--Precision Reference Frequency Synchronisation via 1f-2f Dissemination

The Square Kilometre Array (SKA) project is an international effort to build the world's largest radio telescope, with a one-square-kilometre collecting area. In addition to its ambitious scientific objectives, such as probing cosmic dawn and the cradle of life, the SKA demands several revolutionary technological breakthroughs, such as ultra-high precision synchronisation of the frequency references for thousands of antennas. In this report, with the purpose of application to the SKA, we demonstrate a frequency reference dissemination and synchronisation scheme in which the phase-noise compensation function is applied at the client site. Hence, one central hub can be linked to a large number of client sites, thus forming a star-shaped topology. As a performance test, a 100-MHz reference frequency signal from a hydrogen maser (H-maser) clock is disseminated and recovered at two remote sites. The phase-noise characteristics of the recovered reference frequency signal coincide with those of the H-maser source and satisfy the SKA requirements.

Invited Article: A compact optically coherent fiber frequency comb

We describe the design, fabrication, and performance of a self-referenced, optically coherent frequency comb. The system robustness is derived from a combination of an optics package based on polarization-maintaining fiber, saturable absorbers for mode-locking, high signal-to-noise ratio (SNR) detection of the control signals, and digital feedback control for frequency stabilization. The output is phase-coherent over a 1-2 μm octave-spanning spectrum with a pulse repetition rate of ∼200 MHz and a residual pulse-to-pulse timing jitter <3 fs well within the requirements of most frequency-comb applications. Digital control enables phase coherent operation for over 90 h, critical for phase-sensitive applications such as timekeeping. We show that this phase-slip free operation follows the fundamental limit set by the SNR of the control signals. Performance metrics from three nearly identical combs are presented. This laptop-sized comb should enable a wide-range of applications beyond the laboratory.

Ground-State Cooling of a Trapped Ion Using Long-Wavelength Radiation

We demonstrate ground-state cooling of a trapped ion using radio-frequency (rf) radiation. This is a powerful tool for the implementation of quantum operations, where rf or microwave radiation instead of lasers is used for motional quantum state engineering. We measure a mean phonon number of n[over ¯]=0.13(4) after sideband cooling, corresponding to a ground-state occupation probability of 88(7)%. After preparing in the vibrational ground state, we demonstrate motional state engineering by driving Rabi oscillations between the |n=0⟩ and |n=1⟩ Fock states. We also use the ability to ground-state cool to accurately measure the motional heating rate and report a reduction by almost 2 orders of magnitude compared with our previously measured result, which we attribute to carefully eliminating sources of electrical noise in the system.

Search for Ultralight Scalar Dark Matter with Atomic Spectroscopy

We report new limits on ultralight scalar dark matter (DM) with dilatonlike couplings to photons that can induce oscillations in the fine-structure constant α. Atomic dysprosium exhibits an electronic structure with two nearly degenerate levels whose energy splitting is sensitive to changes in α. Spectroscopy data for two isotopes of dysprosium over a two-year span are analyzed for coherent oscillations with angular frequencies below 1  rad s-1. No signal consistent with a DM coupling is identified, leading to new constraints on dilatonlike photon couplings over a wide mass range. Under the assumption that the scalar field comprises all of the DM, our limits on the coupling exceed those from equivalence-principle tests by up to 4 orders of magnitude for masses below 3×10(-18)  eV. Excess oscillatory power, inconsistent with fine-structure variation, is detected in a control channel, and is likely due to a systematic effect. Our atomic spectroscopy limits on DM are the first of their kind, and leave substantial room for improvement with state-of-the-art atomic clocks.

Motion and gravity effects in the precision of quantum clocks

We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and show that its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.

Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty

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. Here we take an important step towards realizing the full potential of a many-particle clock with a state-of-the-art stable laser. Our (87)Sr optical lattice clock now achieves fractional stability of 2.2 × 10(-16) at 1 s. With this improved stability, we perform a new accuracy evaluation of our clock, reducing many systematic uncertainties that limited our previous measurements, such as those in the lattice ac Stark shift, the atoms' thermal environment and the atomic response to room-temperature blackbody radiation. Our combined measurements have reduced the total uncertainty of the JILA Sr clock to 2.1 × 10(-18) in fractional frequency units.

Broadband, unpolarized repumping and clearout light sources for Sr(+) single-ion clocks

Future transportable optical clocks require compact and reliable light sources. Here, broadband, unpolarized repumper and state clearout sources for Sr⁺ single-ion optical clocks are reported. These turn-key devices require no frequency stabilization or external modulators. They are fiber based, inexpensive, and compact. Key characteristics for clock operation are presented, including optical spectra, induced light shifts, and required extinction ratios. Tests with an operating single-ion standard show a clearout efficiency of 100%. Compared to a laser-based repumper, the achievable fluorescence rates for ion detection are a few tens of percent lower. The resulting ion kinetic temperature is 1-1.5 mK, near the Doppler limit of the ion system. Similar repumper light sources could be made for Ca⁺ (866 nm) and Ba⁺ (650 nm) using semiconductor gain media.

Observation of motion-dependent nonlinear dispersion with narrow-linewidth atoms in an optical cavity

As an alternative to state-of-the-art laser frequency stabilization using ultrastable cavities, it has been proposed to exploit the nonlinear effects from coupling of atoms with a narrow transition to an optical cavity. Here, we have constructed such a system and observed nonlinear phase shifts of a narrow optical line by a strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multiphoton scattering events (Dopplerons) that affect the cavity field transmission and phase. By varying the number of atoms and the intracavity power, we systematically study this nonlinear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple system opens new possibilities for alternative routes to laser stabilization at the sub-100 mHz level and superradiant laser sources involving narrow-line atoms. The understanding of relevant motional effects obtained here has direct implications for other atomic clocks when used in relation to ultranarrow clock transitions.

Optical phase cloning by an integrated dual-parallel Mach-Zehnder modulator

The use of a dual-parallel Mach-Zehnder modulator in a feed-forward configuration is shown to serve the purpose of cloning the optical phase of a master oscillator on a distributed-feed-back (DFB) slave laser exhibiting a multi-MHz-wide frequency noise spectrum. A residual phase error of 113 mrad is obtained together with an extremely high control bandwidth of hundreds of megahertz and a gigahertz-level capture and tuning range. Besides offering a dramatic improvement over feedback loops, this approach is susceptible of hybrid integration in a cost-effective compact device benefiting from the wide tunability of DFB lasers.

Subhertz linewidth laser by locking to a fiber delay line

An ultralow-noise, subhertz 1.55 μm erbium-doped fiber laser that is locked on an all-fiber-based Michelson interferometer is presented in this paper. The interferometer uses 500 m SMF-28 optical fiber and an acousto-optic modulator to allow heterodyne detection. By comparing two identical laser systems, a 0.67 (0.21) Hz linewidth beat-note signal is achieved and we obtain fractional frequency instability of 7×10(-15) at short timescales (0.1-1 s). The frequency noise power spectral density of two identical lasers is below -1  dB Hz(2)/Hz at 1 Hz and it reaches -18  dB Hz(2)/Hz from 200 Hz to 1 kHz.

Effect of soil temperature on optical frequency transfer through unidirectional dense-wavelength-division-multiplexing fiber-optic links

Results of optical frequency transfer over a carrier-grade dense-wavelength-division-multiplexing (DWDM) optical fiber network are presented. The relation between soil temperature changes on a buried optical fiber and frequency changes of an optical carrier through the fiber is modeled. Soil temperatures, measured at various depths by the Royal Netherlands Meteorology Institute (KNMI) are compared with observed frequency variations through this model. A comparison of a nine-day record of optical frequency measurements through the 2×298  km fiber link with soil temperature data shows qualitative agreement. A soil temperature model is used to predict the link stability over longer periods (days-months-years). We show that optical frequency dissemination is sufficiently stable to distribute and compare, e.g., rubidium frequency standards over standard DWDM optical fiber networks using unidirectional fibers.

Magnetic-dipole transitions in highly charged ions as a basis of ultraprecise optical clocks

We evaluate the feasibility of using magnetic-dipole (M1) transitions in highly charged ions as a basis of an optical atomic clockwork of exceptional accuracy. We consider a range of possibilities, including M1 transitions between clock levels of the same fine-structure and hyperfine-structure manifolds. In highly charged ions these transitions lie in the optical part of the spectra and can be probed with lasers. The most direct advantage of our proposal comes from the low degeneracy of clock levels and the simplicity of atomic structure in combination with negligible quadrupolar shift. We demonstrate that such clocks can have projected fractional accuracies below the 10^{-20}-10^{-21} level for all common systematic effects, such as blackbody radiation, Zeeman, ac-Stark, and quadrupolar shifts.

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

Singly ionized ytterbium, with ultranarrow optical clock transitions at 467 and 436 nm, is a convenient system for the realization of optical atomic clocks and tests of present-day variation of fundamental constants. We present the first direct measurement of the frequency ratio of these two clock transitions, without reference to a cesium primary standard, and using the same single ion of 171Yb+. The absolute frequencies of both transitions are also presented, each with a relative standard uncertainty of 6×10(-16). Combining our results with those from other experiments, we report a threefold improvement in the constraint on the time variation of the proton-to-electron mass ratio, μ/μ=0.2(1.1)×10(-16)  yr(-1), along with an improved constraint on time variation of the fine structure constant, α/α=-0.7(2.1)×10(-17)  yr(-1).

Searching for topological defect dark matter via nongravitational signatures

We propose schemes for the detection of topological defect dark matter using pulsars and other luminous extraterrestrial systems via nongravitational signatures. The dark matter field, which makes up a defect, may interact with standard model particles, including quarks and the photon, resulting in the alteration of their masses. When a topological defect passes through a pulsar, its mass, radius, and internal structure may be altered, resulting in a pulsar "quake." A topological defect may also function as a cosmic dielectric material with a distinctive frequency-dependent index of refraction, which would give rise to the time delay of a periodic extraterrestrial light or radio signal, and the dispersion of a light or radio source in a manner distinct to a gravitational lens. A topological defect passing through Earth may alter Earth's period of rotation and give rise to temporary nonzero electric dipole moments for an electron, proton, neutron, nuclei and atoms.