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This study reports light narrowing in paraffin-coated vapor cells from room temperature 27 to 59 °C, where spin-exchange relaxation is suppressed. By means of a coating lock and eliminating the reservoir effect, an ultra-narrow magnetic resonance linewidth of 0.36 Hz and an atomic coherence lifetime of T 2 = 0.9 s are achieved. In cells free of buffer gas, the narrow linewidth over this broad temperature range is a result of enhanced spin polarization, which is facilitated by the effective suppression of radiation trapping benefiting from the stability of the vapor density. Using such cells in atomic magnetometers, the photon shot noise limit is estimated as 0.2 fT / Hz 1 / 2 and the spin-projection noise limit is estimated as 1.1 fT / Hz 1 / 2 . Also, a magnetometer system with the stable coated cell is identified, which demonstrates the potential for achieving relatively stable magnetometer sensitivity without precisely controlling the cell temperature. The long coherence lifetime and the broad operating temperature range expand the potential applications of quantum memory and other quantum sensors such as atomic clocks. [ABSTRACT FROM AUTHOR]

Stability and precision of atomic devices are closely tied to the quality and stability of the internal atmosphere of the atomic vapor cells on which they rely. Such an atmosphere can be stabilized by building the cell with low permeation materials such as sapphire or aluminosilicate glass in microfabricated devices. Recently, we have shown that permeation barriers made of Al 2 O 3 thin-film coatings deposited on standard borosilicate glass could be an alternative for buffer gas pressure stabilization. In this study, we, hence, investigate how helium permeation is influenced by the thickness, ranging from 5 to 40 nm, of such Al 2 O 3 thin films coated by atomic layer deposition. Permeation rates are derived from long-term measurements of the pressure-shifted transition frequency of a coherent population trapping (CPT) atomic clock. From thicknesses of 20 nm onward, a significant enhancement of the cell hermeticity is experienced, corresponding to two orders of magnitude lower helium permeation rate. In addition, we test cesium vapor cells filled with neon as a buffer gas and whose windows are coated with 20 nm of Al 2 O 3. As for helium, the permeation rate of neon is significantly reduced, thanks to alumina coatings, leading to a fractional frequency stability of 4 × 10 − 12 at 1 day when the cell is used in a CPT clock. These features outperform the typical performances of uncoated Cs–Ne borosilicate cells and highlight the significance of Al 2 O 3 coatings for buffer gas pressure stabilization. [ABSTRACT FROM AUTHOR]

The advancement of microcomb sources, which serve as a versatile and powerful platform for various time–frequency measurements, have spurred widespread interest across disciplines. Their uses span coherent optical and microwave communications, atomic clocks, high-precision LiDARs, spectrometers, and frequency synthesizers. Recent breakthroughs in fabricating optical micro-cavities, along with the excitation and control of microcombs, have broadened their applications, bridging the gap between physical exploration and practical engineering systems. These developments pave the way for pioneering approaches in both classical and quantum information sciences. In this review article, we conduct a thorough examination of the latest strategies related to microcombs, their enhancement and functionalization schemes, and cutting-edge applications that cover signal generation, data transmission, quantum analysis, and information gathering, processing and computation. Additionally, we provide in-depth evaluations of microcomb-based methodologies tailored for a variety of applications. To conclude, we consider the current state of research and suggest a prospective roadmap that could transition microcomb technology from laboratory settings to broader real-world applications. [ABSTRACT FROM AUTHOR]

New requirements for quantum frequency standards have emerged due to the evolving demands of global navigation satellite systems and the advancements in deep space exploration technologies. One of the quantum frequency standards that meets the new requirements is the quantum frequency standard on mercury-199 ions, which is currently one of the most promising frequency standards. We have presented a comprehensive review of current research on the quantum frequency standard on mercury-199 ions in several countries, including the USA, Russia, the European Union, and China. We have compared and analyzed the characteristics of different developments of the quantum frequency standard on mercury-199 ions. The main differences between them are the ion traps and the mercury-202 light sources. In addition, we have analyzed the Allan deviation of the quantum frequency standard on mercury-199 ions developed by different countries, and the results showed that the long-term stability (105 s) of the USA and Chinese data is an order of magnitude higher than the Russian and European Union data. [ABSTRACT FROM AUTHOR]

Atoms confined in the optical lattice can be interrogated with Doppler- and recoil-free operation. However, if not properly controlled, the optical lattice may limit clock accuracy. To improve the lattice-light-shift uncertainty, the cooling and trapping lasers' frequency stability is optimized, and the atom's signal stability is enhanced. A ring-cavity Ti:sapphire laser is locked to the optical frequency comb, which is referenced to a 578 nm ultra-stable laser, and the beat note's stability is on the order of 10−16. Using a 10 cm Fabry–Pérot cavity referenced to the Ti:sapphire laser, the optical frequency stability is transferred to the 399 nm cooling laser, creating favorable conditions for evaluating the lattice-light-shift accurately. We reevaluate lattice-light-shift in our 171Yb optical lattice clock with an uncertainty of 8.1 × 10−18, which is an order lower than our previous result, and the magic frequency is determined to be 394 798 266.6(1.3) MHz. [ABSTRACT FROM AUTHOR]

Mode‐locked ultrashort pulse sources with a repetition rate of up to several tens of gigahertz greatly facilitate versatile photonic applications such as frequency synthesis, metrology, radar, and optical communications. Dissipative Kerr soliton microcombs provide an attractive solution as a broadband, high‐repetition‐rate compact laser system in this context. However, its operation usually requires sophisticated pump laser control to initiate and stabilize the soliton microcombs, particularly in millimeter‐sized ultrahigh‐Q whispering‐gallery resonators. Here, a mechanically actuated soliton microcomb oscillator is realized with a microwave repetition rate of 15 GHz. This enables direct initiation, subsequent long‐term stabilization, and fine tuning of soliton combs without pump laser tunability that is generally required for soliton microcomb operation. The prospects for using this method with a wide range of applications are revealed that will benefit from mechanical soliton actuation such as optical clocks, spectral extension, and dual‐comb spectroscopy. [ABSTRACT FROM AUTHOR]

Quantum processors and atomic clocks based on trapped ions often utilize an ion's hyperfine transition as the qubit state or frequency reference, respectively. These states are a good choice because they are insensitive in first order to magnetic field fluctuations, leading to long coherence times and stable frequency splittings. In trapped ions, however, these states are still subject to the second order AC Zeeman effect due to the necessary presence of an oscillating magnetic field used to confine the ions in a Paul trap configuration. Here, we measure the frequency shift of the 2S1/2 hyperfine transition of a 171Yb+ ion caused by the radio frequency (RF) electromagnetic field used to create confinement in several microfabricated surface trap designs. By comparing different trap designs, we show that two key design modifications significantly reduce the AC Zeeman effect experienced by the ion: (1) an RF ground layer routed directly below the entire RF electrode, and (2) a symmetric RF electrode. Both of these changes lead to better cancellation of the AC magnetic field and, thus, overall reduced frequency shifts due to the AC Zeeman effect and reduced variation across the device. These improvements enable a more homogeneous environment for quantum computing and can reduce errors for precision applications such as atomic clocks. [ABSTRACT FROM AUTHOR]

Chip-scale devices harnessing the interaction between hot atomic ensembles and light are pushing the boundaries of precision measurement techniques into unprecedented territory. These advancements enable the realization of super-sensitive, miniaturized sensing instruments for measuring various physical parameters. The evolution of this field is propelled by a suite of sophisticated components, including miniaturized single-mode lasers, microfabricated alkali atom vapor cells, compact coil systems, scaled-down heating systems, and the application of cutting-edge micro-electro-mechanical system (MEMS) technologies. This review delves into the essential technologies needed to develop chip-scale hot atomic devices for quantum metrology, providing a comparative analysis of each technology's features. Concluding with a forward-looking perspective, this review discusses the future potential of chip-scale hot atomic devices and the critical technologies that will drive their advancement. [ABSTRACT FROM AUTHOR]

The stability and accuracy of atomic devices can be degraded by the evolution of their cell inner atmosphere. Hence, the undesired entrance or leakage of background or buffer gas, respectively, that can permeate through the cell walls, should be slowed down. In this work, we investigate helium permeation in microfabricated alkali vapor cells filled with He and whose windows are made of borosilicate glass (BSG) or aluminosilicate glass (ASG). The permeation is then derived from routine measurements of the pressure-shifted hyperfine transition frequency of an atomic clock. We first confirm that ASG reduces the He permeation rate by more than two orders of magnitude, in comparison to BSG. In addition, we demonstrate that Al 2 O 3 thin-film coatings, known to avoid alkali consumption in vapor cells, can also significantly reduce He permeation. The permeation through BSG is thereby reduced by a factor up to 130, whereas the one through ASG is decreased by a factor up to 5.0 compared to uncoated substrates. These results may contribute to the development of miniaturized atomic clocks and sensors with improved long-term stability or sensitivity. [ABSTRACT FROM AUTHOR]

Measurements of the 0–0 hyperfine resonant frequencies of ground-state 85Rb atoms show a nonlinear dependence on the pressure of the buffer gases Ar, Kr, and Xe. The nonlinearities are similar to those previously observed with 87Rb and 133Cs and presumed to come from alkali-metal–noble-gas van der Waals molecules. However, the shape of the nonlinearity observed for Xe conflicts with previous theory, and the nonlinearities for Ar and Kr disagree with the expected isotopic scaling of previous 87Rb results. Improving the modeling alleviates most of these discrepancies by treating rotation quantum mechanically and considering additional spin interactions in the molecules. Including the dipolar-hyperfine interaction allows simultaneous fitting of the linear and nonlinear shifts of both 85Rb and 87Rb in either Ar, Kr, or Xe buffer gases with a minimal set of shared, isotope-independent parameters. To the limit of experimental accuracy, the shifts in He and N2 were linear with pressure. The results are of practical interest to vapor-cell atomic clocks and related devices. [ABSTRACT FROM AUTHOR]

The Aharonov–Bohm effect is a quantum mechanical phenomenon that demonstrates how potentials can have observable effects even when the classical fields associated with those potentials are absent. Initially proposed for electromagnetic interactions, this effect has been experimentally confirmed and extensively studied over the years. More recently, the effect has been observed in the context of gravitational interactions using atom interferometry. Additionally, recent predictions suggest that temporal variations in the phase of an electron wave function will induce modulation sidebands in the energy levels of an atomic clock, solely driven by a time-varying scalar gravitational potential. In this study, we consider the atomic clock as a two-level system undergoing continuous Rabi oscillations between the electron's ground and excited state. We assume the photons driving the transition are precisely frequency-stabilized to match the transition, enabling accurate clock comparisons. Our analysis takes into account, that when an atom transitions from its ground state to an excited state, it absorbs energy, increasing its mass according to the mass-energy equivalence principle. Due to the mass difference between the two energy levels, we predict that an atomic clock in an eccentric orbit experiencing a time-varying gravitational potential, will exhibit a constant frequency redshift relative to a ground clock, corresponding to the orbit's average gravitational redshift. Additionally, modulation sidebands will appear, and detecting these predicted sidebands would confirm the scalar gravitational Aharonov–Bohm effect. [ABSTRACT FROM AUTHOR]

The global positioning system (GPS) is widely known for its applications in navigation, timing, and positioning. However, its accuracy can be greatly impacted by the performance of its receiver clocks, especially for a low-cost receiver equipped with lower-grade clocks like crystal oscillators. The objective of this study is to develop a model to improve the stability of a low-cost receiver. To achieve this, a machine-learning-based linear regression algorithm is proposed to predict the differences of the low-cost GPS receiver compared to the precision timing source. Experiments were conducted using low-cost receivers like Ublox and expensive receivers like Septentrio. The model was implemented and the clocks of low-cost receivers were steered. The outcomes demonstrate a notable enhancement in the stability of low-cost receivers after the corrections were applied. This improvement underscores the efficacy of the proposed model in enhancing the performance of low-cost GPS receivers. Consequently, these low-cost receivers can be cost-effectively utilized for various purposes, particularly in applications requiring the deployment of numerous GPS receivers to achieve extensive spatial coverage. [ABSTRACT FROM AUTHOR]

Rubidium fountain clocks are operated by a control system. In this study, first, the control requirements of a rubidium fountain clock are analyzed; then, a control system is designed and divided into a timing sequence control system, a data acquisition system, and a servo control system. Multiple boards based on PCI extensions for the instrumentation (PXI) bus and Labwindows/CVI software 2019 are adopted. The timing sequence control system outputs 16 transistor–transistor logic (TTL) signals and three arbitrary waveforms. The results show that these signals are synchronized within 380 ns. Moreover, the digital locking frequency of the master laser is triggered by one of the timing signal, sweeping the laser frequency in a wide range during polarization gradient cooling. Two time-of-flight signals are acquired, and Ramsey fringes are scanned using the data acquisition system. An error signal is obtained every two cycles, and it is feed back to the frequency synthesizer and a high resolution offset generator using the servo control system. Then the frequency synthesizer is locked to the Ramsey center resonance. The rubidium atomic fountain clock exhibited a frequency stability of 7.4 × 10−16 at 86,400 s. Moreover, the phase of the Rb fountain clock is compared with that of UTC (NTSC) in real time, demonstrating a frequency drift of 0.00044 ns/day/day. The whole control system is full-featured, robust and flexible, thus satisfying the requirements of rubidium fountain clocks. [ABSTRACT FROM AUTHOR]

GNSS spoofing has become a significant security vulnerability threatening remote sensing systems. Hardware fingerprint-based GNSS receiver identification is one of the solutions to address this security issue. However, existing research has not provided a solution for distinguishing GNSS receivers of the same specification. This paper first theoretically proves that the CSACs (Chip-Scale Atomic Clocks) used in GNSS receivers have unique hardware noise and then proposes a fingerprinting scheme based on this hardware noise. Experiments based on the neural network method demonstrate that this fingerprint achieved an identification accuracy of 94.60% for commercial GNSS receivers of the same specification and performed excellently in anomaly detection, confirming the robustness of the fingerprinting method. This method shows a new real-time GNSS security monitoring method based on CSACs and can be easily used with any commercial GNSS receivers. [ABSTRACT FROM AUTHOR]

In the geocenter motion determination using the Global Navigation Satellite Systems (GNSS), satellite clock offsets are usually estimated as white noise process. The correlation between geocenter coordinates (GCC) and the epoch-wise satellite clocks brings inferior GCC estimates, especially for the Z component. In this contribution, satellite clock offsets are described by the polynomial model, and the deviation of the model from the truth is estimated as a random parameter whose process noise is described by the variogram. Based on 3.7 years of BDS, Galileo and GPS observations from 98 global stations, we investigate the impact of the atomic clock model on GCC estimates. After employing the proposed model, the formal errors of GCC-Z component are reduced by 23–46%, 15–31% and 3–9% for BDS, Galileo and GPS, respectively. When the 7-parameter extended empirical CODE orbit model with the a priori box-wing model (BE7) is used, the atomic clock model reduces the correlation of the B1C parameter and GCC-Z component by 0.28, 0.23 and 0.07 for BDS, Galileo and GPS, respectively. Besides, a mitigation of about 60% is obtained at the 3rd and 5th BDS draconitic harmonics and a mitigation of 55% at the 3rd Galileo draconitic harmonic for the GCC-Z component. The proposed model also contributes to reduce the annual amplitudes of single BDS, Galileo and GPS solutions, improving the agreement with the Satellite Laser Ranging solutions. As an additional verification, the resulting satellite orbits are also improved by satellite clock modeling. When the BE7 model is applied, the day boundary discontinuities of daily orbits are reduced by 3.4–3.6%, and the RMS of orbit differences relative to the ESA precise orbits is reduced by 8.2–8.5% for BDS and Galileo. [ABSTRACT FROM AUTHOR]

The pulsed optically pumped (POP) atomic clock has demonstrated unexpected performance in terms of frequency stability and drift. However, it remains a huge challenge to make this type of atomic clock more compact. Herein, we report the design of a miniaturized physics package, which is equipped with a magnetron microwave cavity holding a vapor cell of 1.3 cm internal diameter. The Zeeman transition spectrum reveals that the microwave cavity resonates in TE011-like mode. Based on a low-noise testbed, we also quantitatively analyze the relaxation time, linewidth, and noise sources of the resulting POP atomic clock. The population and coherence relaxation time are measured to be 3.16(0.16) and 2.97(0.03) ms under the temperature of 333 K, which are compatible well with the theoretical calculation. The Ramsey signal shows a contrast of 35% and a linewidth of 192 Hz. The total volume of the physics package is about 44 cm3, including a layer of magnetic shielding. The short-term frequency stability is measured to be 4.8 × 10−13τ−1/2 (where τ is the averaging time), which is mainly limited by the relative intensity noise of the laser system. [ABSTRACT FROM AUTHOR]

State-of-the-art optical cavities are pivotal in pushing the envelope of laser frequency stability below 10−16. This is often achieved by extending the cavity length or cooling the system to cryogenic temperatures to reduce the thermal noise floor. In our study, we present a 30-cm-long cavity that operates at room temperature and is outfitted with crystalline coatings. The system has a predicted ultralow thermal noise floor of 4.4 × 10−17, comparable to what is observed in cryogenic silicon cavities. A 1397-nm laser is stabilized in this advanced cavity, and the stable frequency is then transferred to the clock transition in strontium optical lattice clocks via a frequency-doubling process. We have meticulously minimized and assessed the technical noise contributions through comparisons with an ultrastable reference laser that is locked to a commercially available 30-cm cavity. The frequency instability of the system is rigorously evaluated using a three-cornered-hat method. The results demonstrate that the laser frequency instability remains below 2 × 10−16 for averaging times ranging from 1 to 50 s. These findings underscore the significant potential of room-temperature cavities with crystalline coatings in high-precision metrology and pave the way for further improvements in optical lattice clocks. [ABSTRACT FROM AUTHOR]

The field of chronobiology has advanced significantly since ancient observations of natural rhythms. The intricate molecular architecture of circadian clocks, their hierarchical organization within the mammalian body, and their pivotal roles in organ physiology highlight the complexity and significance of these internal timekeeping mechanisms. In humans, circadian phenotypes exhibit considerable variability among individuals and throughout the individual's lifespan. A fundamental challenge in mechanistic studies of human chronobiology arises from the difficulty of conducting serial sampling from most organs. The concept of studying circadian clocks in vitro relies on the groundbreaking discovery by Ueli Schibler and colleagues that nearly every cell in the body harbours autonomous molecular oscillators. The advent of circadian bioluminescent reporters has provided a new perspective for this approach, enabling high‐resolution continuous measurements of cell‐autonomous clocks in cultured cells, following in vitro synchronization pulse. The work by Steven A. Brown has provided compelling evidence that clock characteristics assessed in primary mouse and human skin fibroblasts cultured in vitro represent a reliable estimation of internal clock properties in vivo. The in vitro approach for studying molecular human clocks in cultured explants and primary cells, pioneered by Steve Brown, represents an invaluable tool for assessing inter‐individual differences in circadian characteristics alongside comprehensive genetic, biochemical and functional analyses. In a broader context, this reliable and minimally invasive approach offers a unique perspective for unravelling the functional inputs and outputs of oscillators operative in nearly any human tissue in physiological contexts and across various pathologies. [ABSTRACT FROM AUTHOR]

Rubidium atomic clocks have been used extensively in various fields, with applications such as a core component of Global Navigation Satellite Systems (GNSS). However, they exhibit inherently poor long-term stability. This paper presents the development of a control system for rubidium atomic clocks. It introduces an adaptive Kalman filtering algorithm for the disciplining of a rubidium atomic clock, utilizing autocovariance least squares (ALS) to estimate the clock's noise parameters. The experimental results demonstrate that the proposed algorithm achieves a high estimation accuracy. The standard deviation of the clock error between the steered rubidium atomic clock 1 Pulse Per Second (1PPS) and Coordinated Universal Time (UTC) provided by the National Time Service Center (NTSC) is better than 2.568 nanoseconds(ns), with peak-to-peak values improving to within 11.358 ns. Notably, its frequency stability is reduced to 3.06 × 10−13 @100,000 s. The results for the rubidium atomic clock demonstrate that the adaptive Kalman filtering algorithm proposed herein constitutes an accurate and effective control strategy for the rubidium atomic clock discipline. [ABSTRACT FROM AUTHOR]

We report the development of a compact, highly stable, monolithic-cavity, GaInP/AlGaInP-based vertical-external-cavity surface-emitting laser (VECSEL) with electronically tunable emission wavelength centered at 689.4425 nm for neutral strontium (Sr)-based applications. The output power reaches 40 mW (pump-power-limited) with ultra-low frequency and intensity noise performance resulting in a free-running linewidth of 720 Hz, reduced to 390 Hz when frequency locked to a reference cavity and verified via a heterodyne beat note measurement with 2 s averaging time. For shorter averaging times (0.1 ms), the free-running linewidth is as low as 40 Hz. We estimate a Lorentzian, or intrinsic, linewidth of 64 mHz from the frequency noise power spectral density at high frequencies, thus providing further evidence of the ultra-narrow fundamental linewidth of VECSELs. High frequency stability was measured via Allan deviation resulting in 1.05 × 10−12 at 2 s and 2.11 × 10−13 at 7 s averaging times when the 689 nm monolithic cavity VECSEL is free-running and locked, respectively, suitable for neutral Sr-based quantum technologies, such as optical clocks and atom interferometry. [ABSTRACT FROM AUTHOR]

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks. Scaling up the number of atoms or ions in optical atomic clocks enables better precision, but this is often accompanied by interactions that limit the accuracy. Here, the authors propose and discuss using a three dimensional Coulomb crystal of one thousand Sn2+ ions as an optical atomic clock with both high precision and high accuracy. [ABSTRACT FROM AUTHOR]

High-accuracy optical clocks have garnered increasing attention for their potential application in various fields, including geodesy. According to the gravitational red-shift effect, clocks at lower altitudes on the Earth's surface run slower than those at higher altitudes due to the differential gravitational field. Consequently, the geopotential difference can be determined by simultaneously comparing the frequency of two optical clocks at disparate locations. Here, we report geopotential difference measurements conducted using a pair of transportable 40Ca+ optical clocks with uncertainties at the 10 − 17 level. After calibrating the output frequencies of two optical clocks in the horizontal position, frequency comparison is realized by moving Clock 2 to two different positions using a high-precision optical fiber time–frequency transmission link with Clock 1. The elevation difference of the two different positions, as processed by ensemble empirical mode decomposition (EEMD), is measured as −88.4 cm ± 16.7 cm and 104.5 cm ± 20.1 cm, respectively, which is consistent with the geometric measurement results within the error range. This experimental result validates the credibility of the optical clock time–frequency comparison used in determining geopotential differences, thereby providing a novel measurement model for the establishment of a global unified elevation datum. [ABSTRACT FROM AUTHOR]

High-precision time–frequency is widely used in time measurement, satellite navigation, scientific research, and other fields. With the rapid development of optical clock technology, the fractional frequency instability and uncertainty of optical clock have reached 10−18 orders of magnitude, which is expected to contribute to generating the International Atomic Time and may even be used to redefine the "second" in the future. Therefore, the long-distance transfer of time–frequency signals between optical atomic clocks is of great significance. Free-space optical frequency transfer technology is one of the important technologies for solving the space-based optical clock comparison because of its high transfer precision and easy networking characteristics. In order to solve the long-distance space-based optical clock comparison, this paper investigates a free-space active phase noise compensation method using an Acousto-Optic Modulator (AOM), based on the traditional optical fiber phase noise compensation scheme. This new method is more flexible and scalable than the optical fiber time–frequency transfer technology. The optical frequency transfer over a 64 m free-space link is demonstrated. The fractional frequency transfer instability during free running is 9.50 × 10−16 at 1 s, and 4.44 × 10−16 at 2000 s, and the fractional frequency instability after compensation is 7.10 × 10−17 at 1 s, 3.07 × 10−19 at 2000 s, which is about 1–3 orders of magnitude better than that in free running, and provides a feasible scheme for space-based optical clock comparison. [ABSTRACT FROM AUTHOR]

Three-dimensional magneto-optical traps (3D-MOTs) are an integral component of atomic clocks, quantum computers, and other cold-atom science applications. Due to the dependence on bulk optics and lasers, conventional 3D-MOTs occupy a large volume, limiting their portability. Efforts to build 3D-MOTs using integrated photonics promise to reduce the size and weight of these systems allowing applications beyond the lab. However, the need for counterpropagating beams to facilitate 4- and 6-beam geometries necessitates free-space mirrors and quarter wave plates (QWPs) that limit integration. Replacing these mirrors and QWPs with planar retroreflecting metasurfaces provides a route to achieving a complete 3D-MOT within an integrated package. Here, we report on the design and demonstration of a retroreflecting metasurface for 3D-MOTs that operates at large angles and preserves circular polarization. Specifically, we utilize Bayesian optimization to design an amorphous silicon (a-Si) on gold metasurface for high efficiency polarization-insensitive retroreflection of 780 nm circularly polarized light at 54.7°. Numerical simulations demonstrate maintenance of circular polarization after highly efficient retroreflection ( ϵ − 1 = 1.10 , R − 1 = 0.86). Experimentally, we demonstrate similarly excellent performance at 736 nm at 50.3 ° ( ϵ − 1 = 1.04 , R − 1 = 0.73) and show that deviation from the target design is due to oxidation of the a-Si metaelements. We conclude by discussing mitigation strategies for future devices and propose a corrective optic for the currently fabricated device. This work represents a step toward the miniaturization of 3D-MOTs and expansion of cold-atom science beyond the laboratory. [ABSTRACT FROM AUTHOR]

In recent years, there has been significant interest in quantum technology, characterized by the emergence of quantum computers boasting immense processing power, ultra-sensitive quantum sensors, and ultra-precise atomic clocks. Miniaturization of quantum devices using cold atoms necessitates the employment of an ultra-high vacuum miniature cell with a pressure of approximately 10−6 Pa or even lower. In this study, we developed an ultra-high vacuum cell realized by a miniature ion pump using a high-efficiency plasma source. Initially, an unsealed miniature ion pump was introduced into a vacuum chamber, after which the ion pump's discharge current, depending on vacuum pressures, was evaluated. Subsequently, a miniature vacuum cell was fabricated by hermetically sealing the miniature vacuum pump. The cell was successfully evacuated by a miniature ion pump down to an ultra-high vacuum region, which was derived by the measured discharge current. Our findings demonstrate the feasibility of achieving an ultra-high vacuum cell necessary for the operation of miniature quantum devices. [ABSTRACT FROM AUTHOR]

Light shifts induced during atom–light interactions significantly affect the medium- and long-term frequency stability of atomic clocks. Here, we employ composite laser pulse sequences to mitigate interrogation-induced light shifts in a cold-atom coherent-population-trapping clock. We obtain the anti-symmetry error signal via modulating the local oscillator phase in the free-evolution time of Ramsey interferometry. Utilizing this signal, we employ two feedback loops to simultaneously eliminate light shifts and stabilize the clock frequency using the auto-balanced Ramsey (ABR) spectroscopy scheme. Our experimental results demonstrate that this approach can reduce the clock frequency's sensitivity to variations in light shifts by implementing four Ramsey sub-sequences. Furthermore, we show that the ABR spectroscopy scheme enhances the long-term frequency stability of the atomic clock when the averaging time τ > 5000 s. [ABSTRACT FROM AUTHOR]

Today's most precise timekeeping is based on optical atomic clocks. However, those could potentially be outperformed by a nuclear clock, based on a nuclear transition instead of an atomic shell transition. Such a nuclear clock promises intriguing applications in applied as well as fundamental physics, ranging from geodesy and seismology to the investigation of possible time variations of fundamental constants and the search for dark matter. Only one nuclear state is known so far that could drive a nuclear clock: the "Thorium Isomer" 229 m Th, i.e., the isomeric first excited state of 229 Th, representing the lowest nuclear excitation so far reported in the landscape of nuclear isotopes. Indirectly conjectured to exist already in 1976, decades of experimental efforts were dedicated to unambiguously identify this elusive nuclear state and to characterize its properties. However, for 40 years, these efforts remained inconclusive. The turning point was marked by the first direct detection of 229 m Th via its internal conversion decay branch in 2016. Since then, remarkable progress could be achieved in characterizing the properties and decay parameters. The half-life of the neutral isomer was determined, the hyperfine structure was measured via collinear laser spectroscopy, providing information on nuclear moments and the nuclear charge radius and also the excitation energy of the isomer could be directly determined with different techniques. In a recent experiment at CERN's ISOLDE facility, the long-sought radiative decay of the Thorium isomer could be observed for the first time via implantation of (β -decaying) 229 Ac into a vacuum-ultraviolet (VUV) transparent crystal and subsequent fluorescence detection in a VUV spectrometer. Thus, the excitation energy of 229 m Th could be determined with unprecedented precision to 8.338(24) eV, corresponding to a wavelength of 148.71(42) nm. These achievements, together with ongoing laser developments for the required VUV wavelength, open the door toward a laser-driven control of the isomeric transition and thus to the development of an ultra-precise nuclear frequency standard. [ABSTRACT FROM AUTHOR]

Molecular spin qubits have demonstrated immense potential in quantum information science research due to the addressability of electron spins using microwave frequencies, and the scalability and tunability of molecular systems. Exemplary in this regard is the holmium polyoxometalate, [Na9Ho(W5O18)2]·35H2O (HoW10), which features an accessible atomic clock transition at 9.4 GHz; however, the coherence time of this molecule is limited by spin-phonon coupling driven decoherence processes. To limit these decoherence pathways, materials need to be designed to reduce energy overlap between spin and phonon states, and this necessitates developing a better understanding on how structural modifications impact the vibrational landscape for classes of complexes. Herein we conducted a full investigation into the fundamental structural and vibrational properties of the lanthanide Lindqvist polyoxometalate series, [Na9Ln(W5O18)2]·xH2O (Ln = La(III)–Lu(III), except Pm(III)) (LnW10), to assess how structural changes effect vibrational characteristics and to elucidate pathways to improve the coherence properties of HoW10. Single crystal X-ray diffraction results revealed four distinct structural polymorphs in complexes 1–14 wherein first coordination spheres were identical, and differences manifested as changes in lattice packing. Interestingly, the subtle changes in packing exhibited by the four polymorphs were found to impact distortions away from ideal D4d symmetry for each of the LnW10 complexes. Raman and far-infrared (FIR) spectra of complexes 1–14 were collected to identify vibrational modes present in low energy regions and peak fitting assignments were made according to literature precedents. Qualitative and Partial least squares (PLS) analysis show correlations between complex structural parameters with the low energy Raman and FIR vibrational modes of interest. Overall, this investigation shows that the second coordination sphere plays an integral role in modulation of the structural and vibrational characteristics of LnW10 complexes, which makes it a viable route for tuning spin and vibrational manifolds of species within this series. [ABSTRACT FROM AUTHOR]

Space-based Radio Occultation (RO) experiments currently require the tracking of signals from the Global Navigation Satellite System (GNSS) by a Low-Earth-Orbit (LEO) satellite as the signals travel through different layers of the atmosphere. The orbit and clock solutions for the GNSS constellations affect these experiments in two ways: They are needed to obtain a zero-differencing GNSS-based orbit and clock solution for the LEO, and they enter directly the processing of each single radio occultation profile, where the orbit and clock information for the transmitter (GNSS satellite) and receiver (LEO) is required. In this work, we investigate how different GLONASS and GPS orbit and clock solutions affect the statistical properties of RO profiles by comparing our results with forward-modelled bending angle profiles obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) short-range forecasts. Given that GNSS orbits are relatively smooth, the focus will be on the effect of different transmitter clock data rates, and we tested the range from 1 to 30 seconds. The analysis is based on the reprocessing of Sentinel-6A data (four months in 2021, or about 110k occultations) and of a smaller sample of recent COSMIC-2/FORMOSAT-7 data (about 9k occultations). We find that at impacts heights above about 35 km GLONASS bending angles statistics markedly improve with the use of high-rate clock information. For GPS, not much is gained by using rates higher than 30 s, and the statistics are better for more recent GPS blocks. These results are likely the manifestation of the different short-timescale behaviour of the atomic clocks onboard the GPS and GLONASS constellations. [ABSTRACT FROM AUTHOR]

Atomic clocks with higher frequency stability and accuracy than traditional space-borne atomic clocks are the cornerstone of long-term autonomous operation of space-time-frequency systems. We proposed a space cold atoms clock based on an intracavity cooling scheme, which captures cold atoms at the center of a microwave cavity and then executes in situ interactions between the cold atoms and microwaves. As a result of the microgravity environment in space, the cold atoms can interact with the microwaves for a longer time, which aids in realizing a high-precision atomic clock in space. This paper presents the overall design, operational characteristics, and reliability test results of the space atomic clock based on the intracavity cooling scheme designed for the operation onboard the China space station. In addition, the engineering prototype performance of the space cold atoms microwave clock is also presented. The ground test results for the clock show a fractional frequency stability of 1.1 × 10−12 τ−1/2 reaching 2.5 × 10−15 at 200,000 s, providing solid technical and data support for its future operation in orbit. [ABSTRACT FROM AUTHOR]

Optical resonators are indispensable tools in optical metrology that usually benefit from an evacuated and highly-isolated environment to achieve peak performance. Even in the more sophisticated design of Fabry-Perot (FP) cavities, the material choice limits the achievable quality factors. For this reason, monolithic resonators are emerging as promising alternative to traditional designs, but their design is still at preliminary stage and far from being optimized. Here, we demonstrate a monolithic FP resonator with 4.5 cm3 volume and 2 × 105 finesse. In the ambient environment, we achieve 18 Hz integrated laser linewidth and 7 × 10−14 frequency stability measured from 0.08 s to 0.3 s averaging time, the highest spectral purity and stability demonstrated to date in the context of monolithic reference resonators. By locking two separate lasers to distinct modes of the same resonator, a 96 GHz microwave signals is generated with phase noise -100 dBc/Hz at 10 kHz frequency offset, achieving orders of magnitude improvement in the approach of photonic heterodyne synthesis. The compact monolithic FP resonator is promising for applications in spectrally-pure, high-frequency microwave photonic references as well as optical clocks and other metrological devices. ©2024. All rights reserved. Optical resonators are essential tools for high precision metrology and applications where the spectral purity is highly demanded. Here, the authors demonstrate a monolithic resonator made of fused silica to support 18 Hz integrated laser linewidth in the ambient environment, and W-band microwave generation with low phase noise of -100 dBc/Hz at 10 kHz frequency offset. [ABSTRACT FROM AUTHOR]

Coordinated Universal Time (UTC) is calculated using the time data of hundreds of remote atomic clocks. These time data are generated by comparing the atomic clocks to another standard clock through time transfer. One-way time transfer using the Global Navigation Satellite Systems (GNSS) is one of the most essential and widely used time transfer techniques. The stability of the transferred time may be degraded due to many phenomena that affect GNSS signals during their path from the transmitter to the receiver. Multipath reflections are one of these phenomena that considerably degrade one way time transfer stability. It is a common notion that the fewer multipath reflections there are, the better the time transfer stability will be. This can be achieved by limiting the reception of GPS signals to high elevation satellites. In this paper, the author studied the effect of satellite elevation on time transfer stability for both GPS and Galileo. The results of this study suggest that the old shape of the relation between the elevation mask and the time transfer stability may have changed. Therefore, the author proposed a new technique for mitigating the effect of multipath on time transfer stability. The proposed technique was applied to real timing data generated from the Golden receiver of the Physikalisch-technische Bundesanstalt (PTB), which is the German national metrology institute. [ABSTRACT FROM AUTHOR]

In this paper, we present a high-precision optical frequency noise detection and comparison technique using a two-way transfer method over a 260 km field fiber link. This method allows for the comparison of optical frequencies between remote optical references without the need for data transfer through communication. We extend a previously established two-way comparison technique to obtain all data at the local site. Two optical carrier signals are injected into the bidirectional fiber from both ends, and one carrier is reflected back from the remote end. This enables the phase comparison of the two carrier signals at a single site without the need to transmit experimental data. The common-mode frequency noise induced by the bidirectional fiber link is detected and effectively suppressed without the need for sophisticated active fiber noise control. Our demonstration system, which uses a 260 km field fiber link and a common laser source, achieves a fractional instability of 2.5 × 10 − 17 at 1 s averaging time and scales down to 3.5 × 10 − 21 at 8000 s. This scheme offers the distinct advantage of completing the comparison at a single site, eliminating the need for remote data transfer via communication. This method is expected to enhance reliability for high-precision frequency comparisons between remote optical clocks and advanced atomic clocks. [ABSTRACT FROM AUTHOR]

The system time of the four major navigation satellite systems is mainly maintained by multiple high-performance atomic clocks at ground stations. This operational mode relies heavily on the support of ground stations. To enhance the high-precision autonomous timing capability of next-generation navigation satellites, it is necessary to autonomously generate a comprehensive space-based time scale on orbit and make long-term, high-precision predictions for the clock error of this time scale. In order to solve these two problems, this paper proposed a two-level satellite timing system, and used multiple time-keeping node satellites to generate a more stable space-based time scale. Then this paper used the sparse sampling Long Short-Term Memory (LSTM) algorithm to improve the accuracy of clock error long-term prediction on space-based time scale. After simulation, at sampling times of 300 s, 8.64 × 104 s, and 1 × 106 s, the frequency stabilities of the spaceborne timescale reach 1.35 × 10–15, 3.37 × 10–16, and 2.81 × 10–16, respectively. When applying the improved clock error prediction algorithm, the ten-day prediction error is 3.16 × 10–10 s. Compared with those of the continuous sampling LSTM, Kalman filter, polynomial and quadratic polynomial models, the corresponding prediction accuracies are 1.72, 1.56, 1.83 and 1.36 times greater, respectively. [ABSTRACT FROM AUTHOR]

In recent years, there has been a dramatically increasing demand for high-performance narrow-linewidth lasers for optical atomic clock and quantum applications. In this paper, we report on a single-frequency distributed Bragg reflector fiber laser operating at 871 nm that can be used to produce a 435.5 nm narrow-linewidth laser for a Yb+ clock via second-harmonic generation. Linearly polarized single-longitudinal-mode laser output with a power of 6.7 mW and a polarization extinction ratio of 29 dB was obtained by using a 3-cm long 1 wt. % neodymium (Nd3+)-doped phosphate fiber as the gain fiber. [ABSTRACT FROM AUTHOR]

It is believed that cores of neutron stars provide a natural laboratory where exotic high baryon density phases of quantum chromo dynamics (QCD) may exist. In fact, the theoretically well-established neutron superfluid phase is also believed to be found only inside neutron stars. Focus on neutrons stars has tremendously intensified in recent years with the direct detection of gravitational waves (GWs) by LIGO/Virgo from binary neutron star (BNS) merger events which has allowed the possibility of directly probing the properties of the interior of a neutron star. A truly remarkable phenomenon manifested by rapidly rotating neutron stars is in their avatar as Pulsars. The accuracy of pulsar timing can reach the level of one part in 10 1 5 , comparable to that of atomic clocks. Indeed, it was such a great accuracy which had allowed the first indirect detection of GWs from a BNS system. Such an incredible accuracy of pulse timings points to a very interesting possibility. Any deformation of the pulsar, even if it is extremely tiny, has the potential of leaving its imprints on the pulses through introduction of tiny perturbations in the entire moment of inertia (MI) tensor. While, the diagonal components of perturbed MI tensor affect the pulse timings, the off-diagonal components lead to wobbling of pulsar, directly affecting the pulse profile. This opens up a new window of opportunity for exploring various phase transitions occurring inside a pulsar core, through induced density fluctuations, which may be observable as perturbations in the pulse timing as well as its profile. Such perturbations also naturally induce a rapidly changing quadrupole moment of the star, thereby providing a new source of GW emission. Another remarkable possibility arises when we consider the effect of an external GW on neutron star. With the possibility of detecting any minute changes in its configuration through pulse observations, the neutron star has the potential of performing as a Weber detector of GW. This brief review will focus on these specific aspects of a pulsar. Specifically, the focus will be on the type of physics which can be probed by utilizing the effect of changes in the MI tensor of the pulsar on pulse properties. [ABSTRACT FROM AUTHOR]

The experimental comparison of two thulium optical lattice clocks in a time interval of up to one hour has been carried out. The synchronous comparison of a clock transition in two independent atomic ensembles using a single ultrastable laser has allowed us to eliminate fluctuations of the laser frequency from the measured frequency difference and to reach a relative measurement error of 10–16 after 500-s averaging, which corresponds to a relative instability of . The successful demonstration of the long-term operation of two systems using the synchronous comparison of clock transitions opens the possibility of studying systematic shifts in thulium optical clocks with an uncertainty of 10–17. [ABSTRACT FROM AUTHOR]

General relativity predicts that two counter-orbiting clocks around a spinning mass differ in the time required to complete the same orbit. The difference in these two values for the orbital period is generally referred to as the gravito-magnetic (GM) clock effect. It has been proposed to measure the GM clock effect using atomic clocks carried by satellites in prograde and retrograde orbits around the Earth. The precision and stability required for satellites to accurately perform this measurement remains a challenge for current instrumentation. One of the most accurate clocks in the Universe is a millisecond pulsar, which emits periodic radio pulses with high stability. Timing of the pulsed signals from millisecond pulsars has proven to be very successful in testing predictions of general relativity and the GM clock effect is potentially measurable in binary systems. In this work, we derive the generic GM clock effect by considering a slowly spinning binary system on an elliptical orbit, with both arbitrary mass ratio and arbitrary spin orientations. The spin–orbit interaction introduces a perturbation to the orbit, causing the orbital plane to precess and nutate. We identify several different contributions to the clock effects: the choice of spin supplementary condition and the observer-dependent definition of a full revolution and 'nearly identical' orbits. We discuss the impact of these subtle definitions on the formula for GM clock effects and show that most of the existing formulae in the literature can be recovered under appropriate assumptions. [ABSTRACT FROM AUTHOR]

We report on the development and performance evaluation of an ultra-stable laser for an 27Al+ optical clock. After a series of noise suppressions, especially the vibrational and temperature fluctuation noise, the 30 cm long cavity stabilized laser obtains a frequency instability of 1.3 × 10−16 @1 s. This result is predicted by noise summation and confirmed by the three-cornered hat method. The 27Al+ optical clock transition is also used to characterize the laser frequency noise, and consistent results are yielded. This is the first reported instance of using single ion optical clocks to measure the frequency noise of ultra-stable lasers, as far as we know. With the implementation of the ultra-stable clock laser, an ultra-narrow linewidth clock transition of 2.8 Hz is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we presented a 47.5 in. 8K2K AMOLED MNT employing a low temperature poly‐silicon (LTPS) backplane, top emissive inkjet printing (IJP) OLED devices, and gate driver on array (GOA) supporting independent 32 * 9 zone control and internal compensation driving. By combining printed RGB units with a common evaporative blue stack, we proposed the hybrid tandem IJP devices that improved both device efficiency and operation load balance. In the local boosting GOA design, a novel architecture for independent display partition control was developed. The GOA cascading and timing scheme was carefully considered by reusing several clock signals to support both TFT internal compensation and display zone control. It is so far the first prototype AMOLED MNT integrating inkjet printing process and local high frame rate (up to 960 Hz) driving. Thanks to the 8K2K high resolution, local frame rate data processing, and IJP OLED EL reaching HDR brightness up to 580 nits with superior optical performance, it shows a brand‐new approach to deliver a premium display. [ABSTRACT FROM AUTHOR]

One of the most effective ways to advance the performance of quantum computers and quantum sensors is to increase the number of qubits or quantum resources in the system. A major technical challenge that must be solved to realize this goal for trapped-ion systems is scaling the delivery of optical signals to many individual ions. In this paper we demonstrate an approach employing waveguides and multi-mode interferometer splitters to optically address multiple 171Yb+ ions in a surface trap by delivering all wavelengths required for full qubit control. Measurements of hyperfine spectra and Rabi flopping were performed on the E2 clock transition, using integrated waveguides for delivering the light needed for Doppler cooling, state preparation, coherent operations, and detection. We describe the use of splitters to address multiple ions using a single optical input per wavelength and use them to demonstrate simultaneous Rabi flopping on two different transitions occurring at distinct trap sites. This work represents an important step towards the realization of scalable integrated photonics for atomic clocks and trapped-ion quantum information systems. A promising strategy for scaling trapped-ion-based quantum technologies is to use fully integrated optical waveguides to deliver light to numerous ions at multiple sites. Here, the authors. optically address three ions using on-chip waveguides to deliver three distinct wavelengths per ion, and perform Rabi flopping on each ion simultaneously. [ABSTRACT FROM AUTHOR]

A new epitaxial layer design with a double mode expander layer, high refractive index claddings, and an aluminum-free active area has been used to demonstrate distributed feedback lasers operating at 778.1 nm wavelength with reduced Lorentzian linewidth aimed at miniature atomic clock applications. The design also reduces the vertical beam divergence to improve the modal matching with optical fibers as well as maintain the high power output and reduce the emission linewidth. The lasers demonstrate single-mode operation with an over 35 dB side-mode suppression ratio, a power output ≤58 mW, a coupling efficiency to tapered fibers ≤40%, and a Lorentzian linewidth of 3.7 kHz. The performance allowed the free-running distributed feedback lasers to demonstrate spectroscopy of Rb vapor, which resolved the 85Rb and 87Rb two-photon transitions. [ABSTRACT FROM AUTHOR]

What time does a clock tell after quantum tunneling? Predictions and indirect measurements range from superluminal or instantaneous tunneling to finite durations, depending on the specific experiment and the precise definition of the elapsed time. Proposals and implementations use the atomic motion to define this delay, although the inherent quantum nature of atoms implies a delocalization and is in sharp contrast to classical trajectories. Here, we rely on an operational approach: We prepare atoms in a coherent superposition of internal states and study the time read-off via a Ramsey sequence after the tunneling process without the notion of classical trajectories or velocities. Our operational framework (i) unifies definitions of tunneling delay within one approach, (ii) connects the time to a frequency standard given by a conventional atomic clock that can be boosted by differential light shifts, and (iii) highlights that there exists no superluminal or instantaneous tunneling. [ABSTRACT FROM AUTHOR]

To ensure the long-term stable and uninterrupted service of satellite navigation systems, the robustness and reliability of time–frequency systems are crucial. Integrity monitoring is an effective method to enhance the robustness and reliability of time–frequency systems. Time–frequency signals are fundamental for integrity monitoring, with their time differences and frequency biases serving as essential indicators. These indicators are influenced by the inherent characteristics of the time–frequency signals, as well as the links and equipment they traverse. Meanwhile, existing research primarily focuses on only monitoring the integrity of the time–frequency signals' output by the atomic clock group, neglecting the integrity monitoring of the time–frequency signals generated and distributed by the time–frequency signal generation and distribution subsystem. This paper introduces a time–frequency signal integrity monitoring algorithm based on the temperature compensation frequency bias combination model. By analyzing the characteristics of time difference measurements, constructing the temperature compensation frequency bias combination model, and extracting and monitoring noise and frequency bias features from the time difference measurements, the algorithm achieves comprehensive time–frequency signal integrity monitoring. Experimental results demonstrate that the algorithm can effectively detect, identify, and alert users to time–frequency signal faults. Additionally, the model and the integrity monitoring parameters developed in this paper exhibit high adaptability, making them directly applicable to the integrity monitoring of time–frequency signals across various links. Compared with traditional monitoring algorithms, the algorithm proposed in this paper greatly improves the effectiveness, adaptability, and real-time performance of time–frequency signal integrity monitoring. [ABSTRACT FROM AUTHOR]