Frequency Stability Of Clocks Research Articles

Reduction of light shifts in a cold-atom CPT clock

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.

Laser Frequency Modulation and PM-to-AM Noise Conversion in Atomic Clocks.

Laser wavelength stability is a necessity in present-day chip-scale atomic clocks (CSACs), in next-generation atomic clocks planned for Global Navigation Satellite Systems (GNSSs), and in many other atomic devices that generate their signals with lasers. Routinely, this is accomplished by modulating the laser's frequency about an atomic or molecular resonance, which in turn induces modulated laser-light absorption. The modulated absorption then generates a correction signal that stabilizes the laser wavelength. However, in addition to creating absorption modulation for laser wavelength stabilization, the modulated laser frequency can produce a time-dependent variance in transmitted laser intensity noise because of laser phase-noise (PM) to transmitted laser intensity-noise (AM) conversion. Here, we show that the time-varying PM-to-AM conversion can have a significant influence on the short-term frequency stability of vapor-cell atomic clocks. If diode-laser enabled vapor-cell atomic clocks are to break into the [Formula: see text] frequency-stability range, the amplitude of laser frequency modulation for wavelength stabilization will need to be chosen judiciously.

An evaluation method of GPS satellite clock in-orbit with periodic terms deducted

The performance of the atomic clock in orbit is of terrific significance for the Global Navigation Satellite System (GNSS). With the rapid development of satellite navigation and atomic clock technology, the periodic error of satellite clocks caused by the environment is more prominent. This paper focuses on the analysis and quantification of the systematic periodic error in the clock offset and proposes a more accurate evaluation method for GPS satellite clocks. The fact that the J2 relativistic effect and orbit radial error are the main sources of the systematic periodic term has been revealed. Then, the Fast Fourier Transform (FFT) is employed using the sliding window to investigate the periodic influence caused by satellite orbit and the J2 relativistic effect on clock offset through six GPS satellites with different orbital planes, these satellites also cover all four types of GPS satellite blocks. The results show that there is an obvious relationship between the sun elevation and orbit radial error, clock offset fitting precision, frequency stability and amplitude. The different geometric configurations of the satellite and the varying environment make this relationship different. Based on the clock offset provided by European Space Agency (ESA), the period of clock offset is extracted and quantized, with the period of 24 h, 12 h, 8 h, 6 h, 4 h, and 3 h. According to the daily extraction results of the time-varying periodic terms, the two most noticeable terms correction on satellite clock offset has been proven to be effective in eliminating periodic errors. Compared to those without periodic correction, the fitting precision and frequency stability can improve by 48.5% and 42.6%, respectively. In addition, all GPS satellite clocks in orbit are evaluated by this periodic correction method, and the results are more approach to the actual performance of the satellite clock. Furthermore, this method can also be adapted to evaluate satellite clocks of other GNSS systems. Therefore, when we evaluate the high-precision atomic clock flying on board GNSS satellites and compare them with the manufacturers’ specifications, the periodic error cannot be neglected.

Evaluation of Stability of Higher-Order Atomic Clocks by Higher-Order Allan Variance

In this paper, we analyze a generalized version of the Allan variance, referred to as a higher-order Allan variance, that can evaluate the frequency stability of multi-dimensional atomic clocks as a function of the measurement interval. It is known that the standard Allan variance, a measure to evaluate the frequency stability of atomic clocks, has a concern that its value for third-order atomic clocks, such as hydrogen maser, is dependent not only on the sampling interval of measurement data, but also on the time of measurement. To resolve this issue, this paper introduces the higher-order Allan variance defined for the higher-order difference of clock reading deviations. The main contribution of this paper is to mathematically prove that the higher-order Allan variance depends only on the sampling interval of clock reading deviations, for which a sufficiently high order of difference is considered. Furthermore, we present numerical simulation studying the numerical stability of the higher-order Allan variance computation for time series data of clock reading deviations.

Control of the VCSEL spectrum by dual microwave frequency modulation.

We propose and investigate a method for controlling the spectrum of the vertical-cavity surface-emitting laser by simultaneous modulation of the injection current at single and doubled frequencies. We experimentally demonstrate the ability to control the power asymmetry of the first-order sidebands and to suppress the carrier by the proposed method. These possibilities are beneficial to improve frequency stability of atomic clocks based on the effect of coherent population trapping.

Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between −2×10−18 and 2×10−18 s/s2. The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is 4.0 × 10−14 s/s at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites.

Optimization of frequency shifts in optically detected magnetic-state-selection cesium beam atomic clocks

In this paper, we report a new method to suppress the AC Stark effect (light shift) in compact cesium beam atomic clocks. The clock used in experiment uses the optically detected magnetic-state-selection scheme independently proposed and developed by Peking University. This method compensates the AC Stark effect by introducing a detuned laser into the detection light. We demonstrate theoretically that the AC Stark effect can be strongly suppressed with properly chosen detuned light. In addition, we experiment this scheme and the α-coefficient (the sensitivity of the AC Stark effect to laser power fluctuation) is successfully reduced from to . We also test the long-term frequency stability with additional laser intensity noise. It is shown that the fractional Allan deviation at 20000 s is reduced from to , which reveals the suppression of the light shift with our method. These results are relevant for improving the long-term frequency stability of compact cesium beam atomic clocks.

Comparison and assessment of long-term performance of BDS-2/BDS-3 satellite atomic clocks

Recently, the performance of the new-generation BeiDou Navigation Satellite System (BDS) satellite clocks has attracted considerable attention. There are two types of BDS clocks developed in China—namely, the new rubidium (Rb-II) and passive hydrogen maser (PHM)—and these can affect positioning, navigation and timing (PNT) services. In this paper, to comprehensively evaluate and analyze the performance of BDS satellite atomic clocks, the physical characteristics are exhibited, including phase, frequency, frequency drift and noise. The physical characteristics are applied to detect the switching of satellite clocks. The frequency stability of atomic clocks is assessed by overlapping Allan deviation (ADEV) and overlapping Hadamard deviation (HDEV). The periodic characteristics of satellite clock bias data are studied through spectrum analysis. Based on 550 day precision satellite clock bias data provided by Wuhan University, China, experiments were performed, focusing on the performance of the Rb-II and PHM clocks installed on BDS-3. Some valuable conclusions are obtained: (a) the BDS-3 satellite clocks perform better than BDS-2. The root mean square value of the frequency drift of BDS-3 satellite clocks is enhanced by 41% compared to BDS-2. The noise of BDS-3 is 0.216 ns, which is 55% better than BDS-2. (b) The frequency stability of BDS-2 satellite clocks is worse than that of BDS-3. The mean daily stability of BDS-2 and BDS-3 satellite clocks by ADEV is 5.29 × 10−14 and 5.36 × 10−14, respectively, while that with HDEV is 2.35 × 10−14 and 0.70 × 10−14. For PHM clocks, the stability at 10 000 s with ADEV and HDEV is 2.29 × 10−14 and 2.25 × 10−14, respectively, while the daily stability is 0.77 × 10 −14 and 0.67 × 10−14, respectively. (c) BDS geostationary orbit (GEO) and inclined GEO satellite atomic clocks have multiple significant periodic terms while the medium earth orbit satellite clocks only own one or two, which are related to the corresponding satellite orbital periods.

Functional model modification of precise point positioning considering the time-varying code biases of a receiver

Precise Point Positioning (PPP), initially developed for the analysis of the Global Positing System (GPS) data from a large geodetic network, gradually becomes an effective tool for positioning, timing, remote sensing of atmospheric water vapor, and monitoring of Earth’s ionospheric Total Electron Content (TEC). The previous studies implicitly assumed that the receiver code biases stay constant over time in formulating the functional model of PPP. In this contribution, it is shown this assumption is not always valid and can lead to the degradation of PPP performance, especially for Slant TEC (STEC) retrieval and timing. For this reason, the PPP functional model is modified by taking into account the time-varying receiver code biases of the two frequencies. It is different from the Modified Carrier-to-Code Leveling (MCCL) method which can only obtain the variations of Receiver Differential Code Biases (RDCBs), i.e., the difference between the two frequencies’ code biases. In the Modified PPP (MPPP) model, the temporal variations of the receiver code biases become estimable and their adverse impacts on PPP parameters, such as ambiguity parameters, receiver clock offsets, and ionospheric delays, are mitigated. This is confirmed by undertaking numerical tests based on the real dual-frequency GPS data from a set of global continuously operating reference stations. The results imply that the variations of receiver code biases exhibit a correlation with the ambient temperature. With the modified functional model, an improvement by 42% to 96% is achieved in the Differences of STEC (DSTEC) compared to the original PPP model with regard to the reference values of those derived from the Geometry-Free (GF) carrier phase observations. The medium and long term (1 × 104 to 1.5 × 104 s) frequency stability of receiver clocks are also significantly improved.

Long-term performance detection and evaluation of GLONASS onboard satellite clocks

The cesium atomic clock installed on the GLObal NAvigation Satellite System (GLONASS) is a key piece of equipment. However, its performance is easily affected by the external environment and its physical characteristics. Therefore, it is essential to evaluate the long-term performance of the clock. In this study, using eight years of continuous GLONASS precise satellite clock offset products, the long-term performance of GLONASS satellite clocks is revealed for the first time. The results showed that the mean number of phase and frequency jumps for one satellite clock in one year were 0.29 and 0.19, respectively. The fitting precision, which is the standard deviation of the fitting residuals, was 0.88 nanoseconds (ns). Except for the R06 satellite clock, the first or second period was 11.24 h in the clock offset. In terms of clock stability, the short-term clock offset prediction accuracy was 0.52 ns, the frequency stability at 1000 and 10000 s was 4.03 × 10-13 and 1.01 × 10-13, respectively. Both the short-term clock offset prediction accuracy and frequency stability were inferior to those of the rubidium atomic clock of the Global Positioning System (GPS) Block IIF satellites, the second-generation BeiDou Navigation Satellite System (BDS-2), Quasi-Zenith Satellite System (QZSS), and Galileo Passive Hydrogen Maser (PHM). The mean switching number for each GLONASS satellite clock was 0.27 per year. Furthermore, the R15 satellite clock, maybe owing to its hardware noise, delivered the poorest performance among those of all the GLONASS satellite clocks.

Impact of Jason-2/T2L2 Ultra-Stable-Oscillator Frequency Model on DORIS stations coordinates and Earth Orientation Parameters

Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) is a tracking technique based on a one-way ground to space Doppler link. For Low Earth Orbit (LEO) satellites, DORIS shows a robust capability in terms of data coverage and availability, due to a wide and well-distributed ground network, where data are made available by the International Doris Service (IDS). However, systematic errors remain in the DORIS data, such as instabilities of the on-board clock due to radiation encountered in space, which limit the accurate determination of station positions.The DORIS on-board clock frequency stability is degraded by the increased radiation found in the region of the South Atlantic Anomaly (SAA) and has been shown to degrade station position estimation. This paper introduces a new model correction to the DORIS data for the frequency of the Jason-2 Ultra Stable Oscillator (USO), derived from the Time Transfer by Laser Link (T2L2) experiment (Belli and Exertier, 2018). We show that a multi-satellite DORIS solution including this T2L2-corrected data applied to the frequency modelling for The DORIS data, improves the estimation of station coordinates. We show the tie residuals with respect to collocated GPS stations are improved by several millimeters. We also demonstrate that the 117-day (Jason-2) draconitic signal in the geophysical parameters is reduced, implying that the origin of this signal is not just solar radiation pressure mis-modeling, but also radiation-induced clock perturbations on the Jason-2 DORIS Ultra-Stable-Oscillator (USO). Finally we demonstrate through comparisons with the International Earth Rotations and Reference Systems Service (IERS) C04 series for Earth Orientation Parameters (EOP), that the estimation of EOP is improved in both a Jason-2 DORIS-only and a multi-satellite DORIS solution for EOP.

Dynamical decoupling of laser phase noise in compound atomic clocks

The frequency stability of many optical atomic clocks is limited by the coherence of their local oscillator. Here, we present a measurement protocol that overcomes the laser coherence limit. It relies on engineered dynamical decoupling of laser phase noise and near-synchronous interrogation of two clocks. One clock coarsely tracks the laser phase using dynamical decoupling; the other refines this estimate using a high-resolution phase measurement. While the former needs to have a high signal-to-noise ratio, the latter clock may operate with any number of particles. The protocol effectively enables minute-long Ramsey interrogation for coherence times of few seconds as provided by the current best ultrastable laser systems. We demonstrate implementation of the protocol in a realistic proof-of-principle experiment, where we interrogate for 0.5 s at a laser coherence time of 77 ms. Here, a single lattice clock is used to emulate synchronous interrogation of two separate clocks in the presence of artificial laser frequency noise. We discuss the frequency instability of a single-ion clock that would result from using the protocol for stabilisation, under these conditions and for minute-long interrogation, and find expected instabilities of σy(τ) = 8 × 10−16(τ/s)−1/2 and σy(τ) = 5 × 10−17(τ/s)−1/2, respectively.

A linewidth locking method to control the microwave power in optically pumped cesium-beam clocks.

In this paper, we present a linewidth locking method to control the microwave power in optically pumped cesium-beam frequency standards. The responses of optically pumped cesium-beam tubes and classical cesium-beam tubes are analyzed and compared against the power of the microwave field. Due to the wide probability distribution of atomic velocity resulting from the optical state preparation and detection, the linewidth of the Ramsey pattern is sensitive to the microwave power. The results can be used to control the microwave power instead of using the traditional extremum method. The advantages of the new method are discussed, and we named this new method the linewidth locking method. When the microwave power is well controlled at a low level by the linewidth locking method, the frequency stability of cesium-beam clocks will be improved to a certain degree for the reduction of the Ramsey pattern linewidth. In experiment, using the linewidth locking method, the Allan deviation of our optically pumped cesium-beam frequency standard is 2.64×10-12/τ and continues until the averaging time exceeds 1 × 105 s, which is 17% better than that using the traditional extremum method.

Brownian motion-induced amplitude noise in vapor-cell frequency standards

We demonstrate that the Brownian motion of alkali metal atoms in buffer gas gives rise to a significant source of frequency instability in vapor cell clocks. We consider, in particular, laser pumped cell devices working in pulsed operation and using a resonant Gaussian light beam to detect the clock transition. It is well known that the diffusion motion through the buffer gas results from many random walks performed by the atoms, as a consequence of the collisions with other atoms/molecules. Owing to this random-walk behavior, the atoms explore different intensity regions of the Gaussian laser beam, reducing the forward light transmission and causing amplitude fluctuations at the photodetector. The contribution of this so called transit noise to the clock frequency stability turns out in the low 10−14 region for a centimeter-scale cell, at the same level of other amplitude noises, like laser relative intensity noise and shot noise. As a consequence, even if it is not the main source of instability in currently used vapor cell clocks, Brownian motion-induced noise represents a novel source of frequency fluctuations and it should be accounted for in the clock stability budget. A preliminary evaluation of the transit noise is also reported for microcell devices.

Frequency-temperature effect of hydrogen maser: Theoretical analysis and temperature control optimization.

The internal temperature environment of a hydrogen maser (H maser) is one of the main factors, which limit the frequency stability of hydrogen atomic clocks (HACs). In the present study, the thermodynamic interactions between the atomic transition frequency and the cavity-bulb assembly affecting the H maser were investigated, and the cavity-pulling effect and the bulb wall frequency shift effect induced by the change in temperature were quantitatively analyzed and calculated. Moreover, the effect of the temperature gradient on the temperature sensitivity of the frequency stability (i.e., the frequency-temperature effect) was qualitatively analyzed. The precision temperature control system was optimized based on the HAC temperature stability requirement through the simulation of the temperature field for different heating pattern methods. The optimization effect was verified experimentally, and the results show that after optimizing the design, the temperature stability is improved from ±0.005 K to ±0.001 K, and the frequency deviation is decreased from 3 × 10-15 to 1 × 10-15. The research results may provide theoretical and practical references for improving the frequency stability and accuracy of HACs.

Joint Timekeeping of Navigation Satellite Constellation with Inter-Satellite Links.

As a system of ranging and positioning based on time transfer, the timekeeping ability of a navigation satellite constellation is a key factor for accurate positioning and timing services. As the timekeeping performances depend on the frequency stability and predictability of satellite clocks, we propose a method to establish a more stable and predictable space time reference, i.e., inter-satellite link time (ISLT), uniting the satellite clocks through inter-satellite links (ISLs). The joint timekeeping framework is introduced first. Based on the weighted average timescale algorithm, the optimal weights that minimize the increment of the ISLT timescale are determined and allocated to the clock ensemble to improve the frequency stability and predictability in both the long and short term. The time deviations with respect to the system time of nine BeiDou-3 satellites through multi-satellite precise orbit determination (MPOD) are used for joint timekeeping evaluation. According to the Allan deviation, the frequency of the ISLT is more stable than the nine satellite clocks in the short term (averaging time smaller than 7000 s), and its daily stability can reach 6 × 10−15. Meanwhile, the short-term (two hours) and long-term (10 h) prediction accuracy of the ISLT is 0.18 and 1.05 ns, respectively, also better than each satellite clock. Furthermore, the joint timekeeping is verified to be robust against single-satellite malfunction.

Microwave Pulse-Coherent Technique-Based Clock With a Novel Magnetron-Type Cavity

We report a high-performance pulsed optically pumped (POP) Rb clock based on a novel magnetron-type microwave cavity. The cavity has a volume of 30 mL, enabling a highly homogenous microwave field distribution. With the laser frequency tuning to the ground-state hyperfine level F = 2 of the D2 line, we observe a Ramsey fringe contrast of 52% in terms of optical absorption detection. The resultant shot noise limit is estimated to be [Formula: see text]. The clock frequency stability is measured as [Formula: see text] (1-100 s), which is limited by the relative intensity noise of the light.

Ramsey-coherent population trapping Cs atomic clock based on lin∥lin optical pumping with dispersion detection**Project supported by the National Key Research and Development Progress of China (Grant No. 2016YFA030210) and the Initiative Program of the State Key Laboratory of Precision Measurement Technology and Instruments, China.

A Cs vapor cell-based atomic clock that uses a lin∥lin pumping scheme with dispersion detection is reported. This atomic clock shows potential for high performance because of its high contrast pumping scheme, and for miniaturization because of its simple architecture. The experimental setup and optimal operating parameters for the clock are introduced. The current fractional frequency stability is measured to be up to 20 s and reaches at 200 s. We have thoroughly investigated the related noise sources that affect clock frequency stability at the 1 s and 100 s levels. The investigation shows that the laser frequency noise limits the clock frequency stability significantly. The clock performance can be further improved by technically upgrading the laser frequency stabilization setup.

Research on the Methods of Performance Monitoring and Evaluation for Active Hydrogen Maserstwo

Active hydrogen maser is the main frequency standard for establishing and maintaining the time scale. It has the characteristics of high short-term stability and low phase noise. At present, it plays an increasingly important role in the international atomic time (TAI) and various local time scales. Firstly, in combination with the internal state parameters of an active hydrogen maser, the correlation between the internal state parameters and the comparison data of a hydrogen maser is analyzed, and a method for the performance monitoring of a hydrogen maser is proposed. Secondly, according to the characteristics of hydrogen maser performance, a method for evaluating the performance of a hydrogen maser is given. The hydrogen maser performance includes mainly two aspects, namely the frequency stability and predictability. The performances of two types of active hydrogen masers (CH1-75 and MHM-2010) are evaluated by this method. The correlation analysis of the atomic clock state parameters and comparison data shows that the state parameter monitoring can effectively predict the variation of the hydrogen maser performance. The evaluation results of atomic clock frequency stability and predictability show that the atomic clock with a higher medium-and-long term frequency stability has a better predictability. There are two methods for the predictability evaluation, one is based on the data published by BIPM (Bureau International des Poids et Measures), and another one is based on the quadratic model. Both methods are consistent with the weights published by BIPM. Therefore, the two methods can be used as a quantitative method to evaluate the predictability of a hydrogen maser.

Time-Domain Evaluation Method for Clock Frequency Stability Based on Precise Point Positioning

The Global Navigation Satellite System (GNSS) and GNSS receivers can be used to measure the time-frequency errors of receiver clocks so as to evaluate their frequency stability. The calculation of receiver clock error by single point positioning (SPP) is not highly accurate, resulting in the limited evaluation of clock frequency stability. Therefore, this study proposes a precision point positioning (PPP) evaluation method. In this method, the receiver is driven by an external clock to be evaluated, and the receiver clock error calculated by PPP is used as the measured clock phase error to calculate the Allan variance. The frequency stability of three clocks with different grades (temperature compensated crystal oscillator [TCXO], oven controlled crystal oscillator [OCXO], and rubidium clock) are evaluated with the PPP evaluation method. The PPP evaluation method can evaluate the frequency stabilities of TCXO and OCXO for an average interval of more than 1 s, and the evaluation error of OCXO is less than 1.3 × 10 -11 . As for the rubidium clock, its frequency stability can be evaluated by the PPP evaluation method for an average interval of more than 66 s, and the error is less than 2 × 10 -13 . In general, the PPP evaluation method involves simple operations, achieves high accuracy, and is easily popularized.