Reference Frequency Research Articles

Eccentricity Estimation for Five Binary Black Hole Mergers with Higher-order Gravitational-wave Modes

The detection of orbital eccentricity for a binary black hole system via gravitational waves is a key signature to distinguish between the possible binary origins. The identification of eccentricity has been difficult so far due to the limited availability of eccentric gravitational waveforms over the full range of black hole masses and eccentricities. Here we evaluate the eccentricity of five black hole mergers detected by the LIGO and Virgo observatories using the TEOBResumS-DALI, TEOBResumS-GIOTTO, and TEOBResumSP models. This analysis studies eccentricities up to 0.6 at the reference frequency of 5 Hz and incorporates higher-order gravitational-wave modes critical to model emission from highly eccentric orbits. The binaries have been selected due to previous hints of eccentricity or due to their unusual mass and spin. While other studies found marginal evidence for eccentricity for some of these events, our analyses do not favor the incorporation of eccentricity compared to the quasi-circular case. While lacking the eccentric evidence of other analyses, we find our analyses marginally shifts the posterior in multiple parameters for several events when allowing eccentricity to be nonzero.

Optical Frequency References at 1542 nm: Precision Spectroscopy of the R(106)50-0, R(100)49-0, R(84)47-0, R(59)45-0, P(82)47-0, and P(71)46-0 Lines of 127I2 at 514 nm

Frequency-stabilized lasers are fundamental topics in research relating to optical frequency and wavelength standards. The absolute frequencies and hyperfine structures of the R(106)50-0, R(100)49-0, R(84)47-0, R(59)45-0, P(82)47-0, and P(71)46-0 lines of molecular iodine (127I2) at 514 nm were measured using a frequency-stabilized laser based on modulation transfer spectroscopy. The hyperfine splitting of each line was fitted to a four-term Hamiltonian with an uncertainty of several kilohertz to obtain the hyperfine constants for the line. A total of 97 hyperfine transitions of the six lines were measured with an uncertainty of 5.6 kHz (fractionally 9.6 × 10−12). They can provide new optical frequency references for telecommunication and other applications.

Phase-stabilised self-injection-locked microcomb

Microresonator frequency combs (microcombs) hold great potential for precision metrology within a compact form factor, impacting a wide range of applications such as point-of-care diagnostics, environmental monitoring, time-keeping, navigation and astronomy. Through the principle of self-injection locking, electrically-driven chip-based microcombs with minimal complexity are now feasible. However, phase-stabilisation of such self-injection-locked microcombs—a prerequisite for metrological frequency combs—has not yet been attained. Here, we address this critical need by demonstrating full phase-stabilisation of a self-injection-locked microcomb. The microresonator is implemented in a silicon nitride photonic chip, and by controlling a pump laser diode and a microheater with low voltage signals (less than 1.57 V), we achieve independent control of the comb’s offset and repetition rate frequencies. Both actuators reach a bandwidth of over 100 kHz, enabling phase-locking of the microcomb to external frequency references. These results establish photonic chip-based, self-injection-locked microcombs as low-complexity yet versatile sources for coherent precision metrology in emerging applications.

A Network Approach for the Accurate Characterization of Water Lines Observable in Astronomical Masers and Extragalactic Environments.

The water molecule, crucial to the chemical composition and dynamics of the universe, is typically identified in its gas phase via radio and submillimeter transitions, with frequencies up to a few THz. To understand the physicochemical behavior of astronomical objects, accurate transition frequencies are required for these lines. From a set of 26 new and 564 previous Lamb dip measurements, utilizing our ultrasensitive laser-based spectrometers in the near-infrared region, ultrahigh-precision spectroscopic networks were set up for H2 16O and H2 18O, augmented with 40 extremely accurate frequencies taken from the literature. Based on kHz-accuracy paths of these networks, considerably improved line-center frequencies have been obtained for 35 observed or predicted maser lines of H2 16O, as well as for 14 transitions of astronomical significance of H2 18O. These reference frequencies, attached with 5-25 kHz uncertainties, may help future studies in various fields of astrochemistry and astrophysics, in particular when precise information is demanded about Doppler-velocity components, including the gas flows of galactic cores, the kinematics of planetary nebulae, or the motion in exoplanetary atmospheres.

High-Precision Digital Clock Steering Method Based on Discrete Σ-Δ Modulation for GNSS

A high-precision time reference is fundamental to the positioning, navigation, and timing (PNT) of global navigation satellite systems (GNSS). The precision of clock steering determines the accuracy of practical applications that rely on the time–frequency reference. With the invention of direct digital synthesizer (DDS) technology, digital clock steering (DCS) has gradually become a mainstream technology. However, the key factor limiting DCS accuracy is the system quantization noise, which leads to a low frequency and phase adjustment accuracy. Here we propose a DCS method based on Σ-Δ modulation to address the issue of low resolution of DAC through shaping the quantization noise. A simulated GNSS time–frequency reference system experimental platform is constructed to validate the effectiveness of the proposed method. The experimental results demonstrate that this method achieves a phase adjustment accuracy of 0.48 ps and a frequency adjustment accuracy better than 0.48 pHz, which is two orders of magnitude higher than that of existing GNSS time–frequency reference systems. Thus, the proposed method offers a significant improvement in time–frequency reference systems, leading to better performance, reliability, and accuracy in a wide range of practical applications.

Multi-ion Frequency Reference Using Dynamical Decoupling.

We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on ^{40}Ca^{+}. By near-resonant magnetic coupling of the ^{2}S_{1/2} and ^{2}D_{5/2} Zeeman sublevels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2nd-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3(2) mHz/μm^{2} and coherence times of 290(20)ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.

Short-Time Variance Providing Evidential Reference Frequency for Lock-in Amplifier in Fault Diagnosis of Rolling Bearings

Short-Time Variance Providing Evidential Reference Frequency for Lock-in Amplifier in Fault Diagnosis of Rolling Bearings

Consistent Eccentricities for Gravitational-wave Astronomy: Resolving Discrepancies between Astrophysical Simulations and Waveform Models

Detecting imprints of orbital eccentricity in gravitational-wave (GW) signals promises to shed light on the formation mechanisms of binary black holes. To constrain the formation mechanisms, distributions of eccentricity derived from numerical simulations of astrophysical formation channels are compared to the estimates of eccentricity inferred from GW signals. We report that the definition of eccentricity typically used in astrophysical simulations is inconsistent with the one used while modeling GW signals, with the differences mainly arising due to the choice of reference frequency used in both cases. We also posit a prescription for calculating eccentricity from astrophysical simulations, by evolving ordinary differential equations obtained from post-Newtonian theory and using the dominant (ℓ = m = 2) mode’s frequency as the reference frequency; this ensures consistency in the definitions. On comparing the existing eccentricities of the binaries present in the Cluster Monte Carlo catalog of globular cluster simulations with the eccentricities calculated using the prescription presented here, we find a significant discrepancy at e ≳ 0.2; this discrepancy becomes worse with increasing eccentricity. We note the implications this discrepancy has for existing studies and recommend that care be taken when comparing data-driven constraints on eccentricity to expectations from astrophysical formation channels.

Twin-Field Quantum Key Distribution with Local Frequency Reference.

Twin-field quantum key distribution (TFQKD) overcomes the linear rate-loss limit, which promises a boost of secure key rate over long distance. However, the complexity of eliminating the frequency differences between the independent laser sources hinders its practical application. We analyzed and determined the frequency stability requirements for implementing TFQKD using frequency-stabilized lasers. Based on this analysis, we proposed and demonstrated a simple and practical approach that utilizes the saturated absorption spectroscopy of acetylene as an absolute reference, eliminating the need for fast frequency locking to achieve TFQKD. Adopting the 4-intensity sending-or-not-sending TFQKD protocol, we experimentally demonstrated the TFQKD over 502, 301, and 201km ultralow-loss optical fiber, respectively. We expect this high-performance scheme will find widespread usage in future intercity and free-space quantum communication networks.

Low noise operation of an all polarization-maintaining figure-9 Er:fiber laser with near-zero cavity dispersion

We demonstrate the low noise operation of a figure-9 1.5-μm Er:fiber laser constructed by all polarization-maintaining (PM) fiber and fiber components. Starting from the original rate equations and nonlinear Schrödinger equation, the cavity roundtrip evolution toward stable mode locking state is present. The radio frequency spectrum shows a 94.6-MHz fundamental repetition rate with up to 100 dB high signal-to-noise ratio. The net dispersion is tailored to near zero by incorporating and optimizing the length of PM dispersion-compensating fiber in the cavity. As a result, an integrated root-mean-square relative intensity noise of 0.0026 % [1 Hz, 1 MHz] and 10.8-fs timing jitter [100 Hz, 1 MHz] at the fundamental repetition rate are measured. We also lock the fundamental repetition frequency to a stable radio frequency reference and an in-loop relative stability of 2.1 × 10−12 at 1-s gate time is obtained.

Design and Simulation of Clock Divider using VHDL

This paper presents the diesign and simulation of clock divider circuit using VHDL(VHSIC Hardware Description Language) on an FPGA(Field Programmable Gate Array). The clock divider circuit is a fundamental component in digital system for generating lower frequency clocks from a higher frequency reference clock. The paper starts up with simple divider where the clock is divided by even numbers, odd numbers and then later expands it into non- integer dividers. Keywords:- clock divider, D flipflop, FPGA

Multiple-access ultrastable frequency dissemination based on optical frequency combs via a fiber link.

We demonstrate an optical fiber-based, multiple-access frequency transmission using two optical frequency combs. The experimental results using the Allan deviation analysis show that with the phase compensation technique, the frequency instabilities at the remote site are 8.7 × 10-15/1 s and 1.0 × 10-17/103 s, and at the accessing node along the fiber link, the frequency instabilities are 6.9 × 10-15/1 s and 1.1 × 10-17/103 s. Similarly, the power spectral density of phase noise was analyzed in the frequency domain. These experimental results demonstrate that the compensation scheme improved the performance by two to three orders of magnitude. Thus, the proposed frequency transmission technique has potential application for disseminating ultrastable frequency references in the optical fiber network.

Acoustic wave propagation and scattering in visco-acoustic medium: Integral equation representation and De Wolf approximation

A visco-acoustic medium is an approximate representation of the absorption and attenuation characteristics of the actual earth medium, which will cause energy attenuation and velocity dispersion of seismic waves. The propagation law of scattered waves in viscoelastic media can be revealed through seismic wave forward simulation. However, the numerical simulation of scattered waves in a visco-acoustic medium using the De Wolf approximation method based on the Lippmann-Schwingr (L-S) equation has not been studied. Therefore, based on the Futterman dispersion relation, the mathematical expression of the integral equation of acoustic wave propagation and scattering in the visco-acoustic medium is derived. We combine the De Wolf approximation with the quality factor Q. The thin slab approximation and screen approximation methods are two realizations of the De Wolf approximation. The thin slab approximation and the screen approximation continuation operator in the viscous-acoustic medium are constructed and applied to the numerical simulation of the scattered wave field. The research results of the concave model and complex model indicate that due to the influence of medium viscosity, the energy of the deep reflected waves is weaker in the forward modeling records of the thin slab approximation method and screen approximation method, and the dominant frequency of seismic waves moves towards the low-frequency direction; Compared with the finite difference results, they only calculate one reflection, and there are no multiple wave signals in the seismic records. Finally, We discuss the thin slab approximation and the screen approximation method for detail around the division of the thickness of the thin slab, the selection of the reference frequency, and the non-uniformity of the medium.

The engineering face-lift of the 32m dish: technical upgrades of Ghana Radio Astronomy Observatory (GRAO)

Ghana's 32-meter radio telescope, inaugurated in August 2017, was once a redundant telecommunications dish that underwent conversion. Prior to this transformation, feasibility studies were conducted to assess the dish's structural integrity, technical compatibility, and economic viability. These studies aimed to determine if the conversion project could be technically achieved given the available technology, expertise, and resources. This paper delves into the engineering considerations surrounding structural, mechanical, software, control and monitoring, radio frequency, and timing frequency reference requirements that distinguish the operation of a radio telescope from its former role as a satellite earth station. Significant components such as the azimuth bearing, sub-reflector support, cable wrap, and electrical motors underwent replacement. Additionally, a new C-band receiver, radio frequency controller, active hydrogen maser timing frequency, and software were developed. Testing protocols to meet science requirements for both single-dish observations and Very Long Baseline Interferometry (VLBI) are also discussed. The conversion process proved to be lengthy and encountered numerous unforeseen circumstances, yet it provided invaluable learning experiences for a developing country like Ghana.

Amplification factors for extreme sea level frequency have problematic features as a metric of coastal hazard

Abstract The future projected frequency of a specified baseline extreme sea level (ESL), often called the amplification factor (AF), is extensively used as a metric of evolving coastal flood hazard with sea level rise (SLR). The baseline ESL is typically analyzed using extreme value analysis, and the SLR is added to the resulting distribution. In the presence of SLR uncertainty, it is natural to analyze AFs probabilistically. I derive probability density functions (PDFs) of AF, given uncertainty distributions of SLR. If the ESL distribution is modeled as Gumbel and the SLR distribution as normal, then the AF distribution is log normal. However, in active tropical cyclone regions, ESL often has a longer tail than Gumbel, and a Frechet (Type-II) Generalized Extreme Value (GEV) is more appropriate. In this case, I show that the AF distribution has a divergent mean, preventing its use as a hazard metric. In addition, I show that for Frechet ESL, the AF cannot even be defined for SLR above a threshold β / ξ f 0 − ξ , where f 0 is the specified baseline frequency (e.g., f 0 = 0.01 yr−1 for the 100-year exceedance), β is the GEV scale parameter and ξ the shape parameter. This SLR threshold can be as low as 0.5 m in the southeast US and Caribbean, within reach mid to late century. Above the threshold, ESL at all frequencies exceeds the baseline reference frequency, preventing the calculation of AF. The resulting probabilistic distribution of AF is insensitive to SLR above the threshold. These features detrimentally impact the utility of AF as a hazard metric. Frechet distributions are appropriate and commonly used for ESL in tropical cyclone regions, but AFs applied to such distributions must interpreted with caution. In such regions, coastal risk managers should consider other flood hazard metrics, such as probabilistic estimates of flood depth.

A metaheuristic algorithm for regulating virtual inertia of a standalone microgrid incorporating electric vehicles

AbstractModern electrical networks, particularly microgrids, have seen a sharp rise in acquiring non‐conventional sources. The inertia of the microgrid decreases drastically because RESs have been used in place of traditional synchronous generators. The reduced inertia negatively impacts the dynamics and performance of the microgrid with RESs, which decreases the microgrid's stability, especially in operation on an island. The primary purpose of this research study is to enhance the dynamic security of an island microgrid by merging an electric vehicle with a frequency control technique based on virtual inertia control. A Proportional Integral Derivative Filter Constant (PIDFN) controller optimally created using the Modified Differential Evolution (MDE) method served as the foundation for control in the virtual inertia control loop. The effectiveness of the MDE‐based PIDFN controller was examined considering the diverse operational scenarios are compared and contrasted with those of traditional methods Differential Evolution (DE) and Teaching Learning Based Optimization (TLBO)‐based PIDFN controllers. Real‐time wind and solar power statistics and random load fluctuations were incorporated to provide realistic simulation settings. The outcomes demonstrate that the MDE‐based PIDFN controller performs better in reference frequency tracking and reducing frequency disturbances than the other optimization strategies.

The CIPM list ‘Recommended values of standard frequencies’: 2021 update

This paper gives a detailed account of the analysis underpinning the 2021 update to the list of standard reference frequency values recommended by the International Committee for Weights and Measures. This update focused on a subset of atomic transitions that are secondary representations of the second (SRS) or considered as potential SRS. As in previous updates in 2015 and 2017, methods for analysing over-determined data sets were applied to make optimum use of the worldwide body of published clock comparison data. To ensure that these methods were robust, three independent calculations were performed using two different algorithms. The 2021 update differed from previous updates in taking detailed account of correlations among the input data, a step shown to be important in deriving unbiased frequency values and avoiding underestimation of their uncertainties. It also differed in the procedures used to assess input data and to assign uncertainties to the recommended frequency values, with previous practice being adapted to produce a fully consistent output data set consisting of frequency ratio values as well as absolute frequencies. These changes are significant in the context of an anticipated redefinition of the second in terms of an optical transition or transitions, since optical frequency ratio measurements will be critical for verifying the international consistency of optical clocks prior to the redefinition. In the meantime, the reduced uncertainties for optical SRS resulting from this analysis significantly increases the weight that secondary frequency standards based on these transitions can have in the steering of International Atomic Time.

Energy Management Strategy for a Net Zero Emission Islanded Photovoltaic Microgrid-Based Green Hydrogen System

Investing in green hydrogen systems has become a global objective to achieve the net-zero emission goal. Therefore, it is seen as the primary force behind efforts to restructure the world’s energy, lessen our reliance on gas, attain carbon neutrality, and combat climate change. This paper proposes a power management for a net zero emission PV microgrid-based decentralized green hydrogen system. The hybrid microgrid combines a fuel cell, battery, PV, electrolyzer, and compressed hydrogen storage (CHSU) unit aimed at power sharing between the total components of the islanded DC microgrid and minimizing the equivalent hydrogen consumption (EHC) by the fuel cell and the battery. In order to minimize the EHC and maintain the battery SOC, an optimization-based approach known as the Equivalent Consumption Minimization Strategy (ECMS) is used. A rule-based management is used to manage the power consumed by the electrolyzer and the CHSU by the PV system in case of excess power. The battery is controlled by an inverse droop control to regulate the dc bus voltage and the output power of the PV system is maximized by the fuzzy logic controller-based MPPT. As the hybrid microgrid works in the islanded mode, a two-level hierarchical control is applied in order to generate the voltage and the frequency references. The suggested energy management approach establishes the operating point for each system component in order to enhance the system’s efficiency. It allows the hybrid system to use less hydrogen while managing energy more efficiently.

Optical cavity reaching 10-16 frequency stability with compact optical circulator based in-coupling optics

Future space missions will benefit from highly stable and compact optical frequency references. While many promising technologies are currently under investigation, optical cavities are a well-suited technique for applications in which relative references are required. To improve the frequency stability of optical cavities, a key step in combining high performance with compactness and robustness is the further development of in-coupling optics. Here, we present our work of using a fiber-coupled circulator based in-coupling for a high-finesse optical cavity. Implementing the new, to the best of our knowledge, in-coupling board to an extensively characterized crossed cavity set-up allows us to identify possible differences to the commonly used free-beam technique. With a frequency stability of 5.5×10−16Hz−1/2 at 1 Hz and with only a slight degradation in frequency stability below the mHz range, no circulator-caused instabilities were observed.

Proposal for a realtime Einstein-synchronization-defined satellite virtual clock

Abstract The realization of high performance satellite onboard clock is vital for various PNT applications. For further improvement of the synchronization-based satellite time and frequency references, this paper proposes a geosynchronous (GEO) satellite virtual clock concept based on ground–satellite synchronization and presents a beacon transponder structure for its implementation (scheduled for launch in 2025), which does not require atomic clocks to be mounted on the satellite. Its high performance relies only on minor modifications to the existing transponder structure of GEO satellites. We carefully modeled the carrier phase link and analyzed the factors causing link asymmetry within the special relativity. Considering that the performance of such synchronization-based satellite clocks is primarily limited by the link’s random phase noise, which cannot be adequately modeled, we designed a closed-loop experiment based on commercial GEO satellites for pre-evaluation. This experiment was aimed at extracting the zero-means random part of the ground-satellite Ku-band carrier phase via a feedback loop. Ultimately, we obtained a 1σ value of 0.633 ps (two-way link), following the Gaussian distribution. From this result, we conclude that the proposed real-time Einstein-synchronization-defined satellite virtual clock can achieve picosecond-level replication of onboard time and frequency.