Cesium Clock Research Articles

Detection and identification of faults in clock ensembles with the generalized likelihood ratio test

In this paper we propose an approach for performing fault detection and identification in clock ensembles based on the generalized likelihood ratio test. We show that by applying a set of purposefully-designed statistical tests, one can successfully detect faults occurring in a clock of the ensemble, and identify which measurement in the ensemble is most likely to have triggered the detection. We first develop the theoretical framework for the characterization of the detectors and their performance, and validate the derivations via Monte Carlo simulations. Then, we apply the statistical tests to an ensemble of cesium clocks, aiming at detecting and identifying three types of non-nominal behaviors. The faulty conditions are obtained by injecting a pattern of phase steps, a phase and frequency drift, and an oscillatory phase component.

Sub-hundred-femtosecond level atmospheric transfer of microwave signal at X-band with active optical phase correction

We propose and demonstrate a scheme for atmospheric transfer of microwave signals at X-band with sub-hundred-femtosecond level precision using active optical phase correction. With the proposed scheme, we have transferred a microwave signal at 9.192 GHz over a 60-m atmospheric link. The timing fluctuations and Allan deviations are both measured and analyzed to assess the performance of our scheme. The root-mean-square timing drift of the transferred microwave signal with timing fluctuation suppression is 44 fs, and the Allan deviation is 9 × 10 − 14 at 1 s and 1 × 10 − 17 at 1000 s with optical phase correction. The transmission link achieved a lower instability than currently reported cesium fountain clocks, which means this proposed transfer scheme could be employed to transfer cesium atomic clock over the atmospheric transmission link.

UNDERWATER ACOUSTIC MODEM WITH HIGH PRECISION RANGING CAPABILITY BASED ON SECOND-LEVEL CESIUM ATOMIC CLOCK

Abstract. Equipped with a high-precision atomic clock can significantly improve the ranging accuracy of the underwater acoustic ranging system. However, the adverse characteristic of underwater acoustic channel (UAC) seriously deteriorates the ranging accuracy. In addition, as a timing device typically commercial cesium atomic clock is only designed to output second-level time reference, which cannot be applied to underwater ranging systems directly. To overcome this limitation, a new underwater acoustic modem with high precision ranging capability based on second-level cesium atomic clock is developed in this paper. The spread spectrum technology is chosen for highly reliable communication and the second-level commercial cesium atomic clock is used to ensure accurate clock synchronization. The proposed modem executes a predetermined ranging scheme based on spread spectrum technology. Specifically, at a certain specified second-level, the transmitter modem sends the ranging signal, and the receiver modem starts timing. Until the receiving modem detects the ranging signal, the propagation time is obtained and the single-item ranging capability is realized. The pool experiment shows the effectiveness of the modem, its ranging accuracy can reach cm level, and the average absolute error of ranging is 8 cm.

Development and tuning of the microwave resonant cavity of a cryogenic cesium atomic fountain clock.

A cryogenic cesium atomic fountain clock is a novel clock with the microwave cavity and atomic free flight region placed in liquid nitrogen. On the one hand, the blackbody radiation shift is reduced at cryogenic temperature. On the other hand, the vacuum in the atomic free flight region is optimized, and the background gas collision shift reduced. The microwave resonant cavity is the most important unit in a cryogenic cesium atomic fountain clock. Through theoretical and simulative investigation, this study designs the configuration and dimensions for an optimized microwave cavity. Concurrently, experiments reveal the effects of temperature, pressure, humidity, and other factors on the resonant frequency of the microwave cavity. Combining the theoretical and experimental study, we obtain the resonant frequency difference between the microwave cavity in a cryogenic vacuum and at room temperature and ambient pressure. By subtracting this frequency difference, we adjust the microwave cavity for room temperature and ambient pressure, then vacuumize and immerse it in liquid nitrogen for verification and fine tuning. Finally, we determine that the microwave cavity resonant frequency deviation from the clock transition frequency is 10 kHz with an unloaded quality factor of 25 000, which meets the application requirements of the cryogenic cesium atomic fountain clock.

Experimental Evaluation of the Blackbody Radiation Shift in the Cesium Atomic Fountain Clock

The cesium atomic fountain clock is the world’s most accurate microwave atomic clock. The uncertainty of blackbody radiation (BBR) shift accounts for an increasingly large percentage of the uncertainty associated with fountain clocks and has become a key factor in the performance of fountain clocks. The uncertainty of BBR shift can be reduced by improving the system environment temperature. This study examined the mechanism by which the BBR shift of the transition frequency between the two hyperfine energy levels of the 133Cs ground state is generated and the calculation method for the BBR shift in the atomic fountain. Methods used to reduce the uncertainty of BBR shift were also examined. A fountain system structure with uniform temperature and good heat preservation was designed, and related technologies, such as that for measuring the temperature of the cesium fountain system, were studied. The results of 20 days of measurements, in combination with computer simulation results, showed that the temperature uncertainty of the atomic action zone is 0.12 °C and that the resulting uncertainty of BBR shift is 2.4 × 10−17.

DEVELOPMENT OF OFFICIAL INDONESIA STANDARD TIME : TEMPERATURE CONTROL SYSTEM FOR CAESIUM ATOMIC CLOCK

Every country should have an official time standard which called local coordinated universal time, UTC(k). Badan Standardisasi Nasional (BSN) has developed an official standard time, namely UTC(IDN) which is used as Indonesia Standard Time. The UTC(IDN) contributes to calculation of coordinated universal time (UTC). In order to generate the UTC(IDN), the output of 1 pulse per second signal of caesium atomic clock is utilized as the actual signals of this standard. A distribution amplifier is used to distribute the signal. Combination of time transfer system (TTS-3) and GPS are employed for comparison of UTC and UTC(IDN). TTS-3 automatically calculated the difference and it is steered by using certain algorithm. Time synchronization to the standard can be conducted through network time protocol (NTP) server, i.e., ntp.bsn.go.id. The time can be automatically synchronized using internet time or certain program at each computer or machine. The results of this work show that the time differences between UTC – UTC(IDN) vary from 43.2 ns to 1729.9 ns. UTC(IDN) has frequency and time stability of 3.6 x 10 -14 Hz/Hz per 5 days and 3.1 ns per 5 days, respectively which are in good agreement to the international time reference. A shielding chamber with temperature control system has been built to keep the ambient temperature of caesium atomic clock at (23 ± 1) ᵒC. It can be concluded that BSN has been developing and disseminating the UTC(IDN) as an Indonesia Standard Time that can support the regulation of time synchronization in Indonesia. A new temperature control system is proposed to stabilize the ambient temperature of caesium atomic clock. The temperature control system supports an accurate and stable UTC(IDN).

The Application of Low-Frequency Transition in the Assessment of the Second-Order Zeeman Frequency Shift.

Second-order Zeeman frequency shift is one of the major systematic factors affecting the frequency uncertainty performance of cesium atomic fountain clock. Second-order Zeeman frequency shift is calculated by experimentally measuring the central frequency of the (1,1) or (−1,−1) magnetically sensitive Ramsey transition. The low-frequency transition method can be used to measure the magnetic field strength and to predict the central fringe of (1,1) or (−1,−1) magnetically sensitive Ramsey transition. In this paper, we deduce the formula for magnetic field measurement using the low-frequency transition method and measured the magnetic field distribution of 4 cm inside the Ramsey cavity and 32 cm along the flight region experimentally. The result shows that the magnetic field fluctuation is less than 1 nT. The influence of low-frequency pulse signal duration on the accuracy of magnetic field measurement is studied and the optimal low-frequency pulse signal duration is determined. The central fringe of (−1,−1) magnetically sensitive Ramsey transition can be predicted by using a numerical integrating of the magnetic field “map”. Comparing the predicted central fringe with that identified by Ramsey method, the frequency difference between these two is, at most, a fringe width of 0.3. We apply the experimentally measured central frequency of the (−1,−1) Ramsey transition to the Breit-Rabi formula, and the second-order Zeeman frequency shift is calculated as 131.03 × 10−15, with the uncertainty of 0.10 × 10−15.

The Spoofing Detection of Dynamic Underwater Positioning Systems (DUPS) Based on Vehicles Retrofitted with Acoustic Speakers

The need of precision for underwater positioning and navigation should be considered as strict as those present at the sea surface. GNSS provides 4D positioning (XYZT). Each satellite contains two rubidium and two cesium atomic clocks. They are monitored by an atomic clock on the ground, and the entire system is constantly calibrated to a universal time standard, Coordinated Universal Time (UTC). GNSS receivers determine the time T to within 100 billionths of a second without the cost of owning, operating and maintaining an atomic clock. Of particular importance is the measurement of XYZT underwater. We assume that some surface vehicles are additionally equipped with an Acoustic Speaker, which transmits the XY coordinates of the vessel with an indication of accuracy and the time T of the vessel. Submarine vehicles determine their position by help of acoustic signals from several surface acoustic sources using the Time of Arrival (ToA) algorithm. Detection of Spoofing for the Dynamic Underwater Positioning Systems (DUPS) based on vehicles retrofitted with acoustic speakers is very actual problem. Underwater spoofing works as follows: N acoustic speaker on N ships transmit the coordinates {xi,yi,ti}, i=1,N¯. GNSS signals are susceptible to interference due to their very low power (−130 dBm) and can be easily jammed by other sources, which may be accidental or intentional. The spoofer, like an underwater vehicle, receives these signals from N vessels, distorts them and transmits with increased acoustic power. All receivers into the spoofed area will calculate the same coordinates, so the indication of the coincidence of coordinates from a pair of diversity receivers is an indication of spoofing detection.

Exploring potential applications of optical lattice clocks in a plate subduction zone

Optical clocks improved the accuracy of state-of-the-art cesium clocks by more than two orders of magnitude and enabled frequency comparison with a fractional uncertainty of one part in 1018. Gravitational redshift of two such clocks allows determining their height difference with an uncertainty of 1 cm. In Europe, chronometric leveling has been extensively conducted for unifying the height reference systems. Temporal response of the leveling, which affords monitoring a cm height variation within hours of averaging time, may offer new opportunities to explore seismology and volcanology. Superb stability of optical lattice clocks will be best used for such applications. This article outlines the prospects of chronometric leveling in Japan. Combining optical lattice clocks with an existing observation network of GNSS, crustal deformations may be monitored with unprecedented accuracy in the future.

Optical state selection process with optical pumping in a cesium atomic fountain clock* *Project supported by the National Natural Science Foundation of China (Grant No. 11873044).

We propose and realize a new optical state selection method on a cesium atomic fountain clock by applying a two-laser 3–3′ optical pumping configuration to spin polarize atoms. The atoms are prepared in |F = 3, mF = 0〉 clock state with optical pumping directly after being launched up, followed by a pushing beam to push away the atoms remaining in the |F = 4〉 state. With a state selection efficiency exceeding 92%, this optical method can substitute the traditional microwave state selection, and helps to develop a more compact physical package. A Ramsey fringe has been achieved with this optical state selection method, and a contrast of 90% is obtained with a full width half maximum of 0.92 Hz. The short-term frequency stability of 6.8 × 10−14 (τ/s)−1/2 is acquired. In addition, the number of detected atoms is increased by a factor of 1.7 with the optical state selection.

Long-Distance Time Transfer in Optical Fiber Networks Using a Cascaded Taming Technology

In order to meet the time service needs of high-precision, long-distance, and multinode optical network, this paper proposes a new time synchronization solution, which combines the wavelength division multiplexing (WDM) technology with cascaded taming clock technology. The WDM technology is used for time synchronization between each pair of master-slave nodes. In the system, there are two wavelengths on the fiber link between the master node and the slave node for transmitting signals. 1 plus per second (PPS) signal, time code signal, and 10 MHz signal are, respectively, and successively, sent to the optical fiber link. By solving the one-way delay through analysis of error contribution and link characteristics of the time transmission process, time synchronization of the master-slave nodes pair is achieved. Furthermore, the authors adopt cascaded taming clock technology to ensure accurate time synchronization of each node. A 700 km long-distance time-frequency synchronization system is constructed in the laboratory. The system uses a cesium atomic clock as the reference clock source and transmits the signals through 8 small rubidium atomic clocks (RB clocks) hierarchically. Results from the experiment show that the long-term time stability is 47.5 ps/104 s. The system’s structural characteristics and the experiment results meet the requirements to allow practical use of high-precision time synchronization in networks. This proposed solution can be applied in various civil, commercial, and military fields.

The weak frequency anomaly detection method of atomic clocks based on Kalman filter and extrapolation-accumulation

A new method based on the innovation of Kalman filter and extrapolation-accumulation is proposed to detect weak frequency anomalies in atomic clocks with short detection time and high detection probability. In this method, the detection statistics of the innovation extrapolation method in several epochs are accumulated. It avoids the influence of outliers, increases the noncentrality parameter of chi-square distribution, and realizes more effective detection of weak frequency anomalies. The simulation results show that compared with the innovation method and the innovation extrapolation method, the new method has a higher detection probability for micro frequency anomalies, and the detection time is shortened. The new method is used to analyze the real data of the cesium atomic clock, and the results are consistent with the simulation results.

ВЛИЯНИЕ МАГНИТНОГО ЗАРЯДА НА ЭФФЕКТ САНЬЯКА В ПРОСТРАНСТВЕ-ВРЕМЕНИ БАРДИНА

This paper investigates one of the most interesting effects associated with the rotation of astrophysical objects (the Sagnac effect). The effect was first confirmed in laboratory experiments by Georges Sagnac with a rotating ring interferometer in 1913. Later, the effect was also confirmed within the framework of the Earth in the "Around-the-World" experiment conducted by J. Hafele and R. Kitting, in which they twice circled the Earth with an atomic cesium clock on board and compared the "flying" clock with those remaining static on the Earth. As a result, a non-zero difference in the clock rate was found as a confirmation of the Sagnac effect. Subsequently, more precise satellite experiments have been carried out to measure the Sagnac effect within the Earth. The effect was also considered in general relativity and modified theories of gravity, where many works were carried out to study the influence of such parameters as angular momentum, cosmological constant, Ricci scalar, etc. on the Sagnac effect. An interesting task is to study the influence of a magnetic charge on the effect, since the solution with rotation described by a black hole with mass M and magnetic charge g is the Bardeen nonsingular black hole. The work will calculate the Sagnac effect in the space-time of the rotating Bardeen black hole for both geodesic and non-geodesic circular orbits of the light source / receiver (assuming that the light source and receiver are defined at the same point). Two types of circular orbits describe the opposing influence on the Sagnac effect: the Sagnac delay increases with an increase in the magnetic charge in the case of non-geodesic circular orbits and decreases in the case of geodesic circular orbits. However, the farther is the orbit of the light source / receiver, the less the magnetic charge affects the Sagnac delay. It is also assumed that the gravity of the Earth and the Sun near the surface is well described by the Bardeen metric.

Peculiarities of Constructing a Scheme for Formation of a Microwave Excitation Signal in a Cesium Atomic Clock

In this paper, we determine the formation peculiarities of a microwave excitation signal in the quantum frequency standard on cesium-133 atoms. To improve the characteristics of the microwave excitation signal, a method for optimizing the parameters of blocks and schemes of a quantum frequency standard with allowance for the established features is proposed. The studies showed that the use of this method can improve the spectral characteristics of the microwave excitation signal and reduce the step of tuning its output frequency. The experimental results allowed establishing that the use of this method improves the output frequency stability of the quantum standard by 20%. The established peculiarities create conditions for new research aimed at developing methods and techniques for improving the characteristics of the microwave excitation signal.

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.

Evaluation of second-order Zeeman frequency shift in NTSC-F2* *Project supported by the National Key R&D Program of China (Grant No. 2016YFF0200202), the Maintenance and Reformation Program for the Major Science and Technology Fundamental Devices of the Chinese Academy of Sciences (Grant No. DSS-WXGZ-2020-0005), and the Foundation for Western Young Scholars, China (Grant No. XAB2018A06).

Caesium atomic fountain clock is a primary frequency standard, which realizes the duration of second. Its performance is mostly dominated by the frequency accuracy, and the C-field induced second-order Zeeman frequency shift is the major effect, which limits the accuracy improvement. By applying a high-precision current supply and high-performance magnetic shieldings, the C-field stability has been improved significantly. In order to achieve a uniform C-field, this paper proposes a doubly wound C-field solenoid, which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift. Based on the stable and uniform C-field, we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition |F = 3, mF = –1〉 → |F = 4, mF = –1〉 central frequency, obtaining this frequency shift as 131.03 × 10−15 and constructing the C-field profile (σ = 0.15 nT). Meanwhile, during normal operation, we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition |F = 3, mF = –1〉 → |F = 4, mF = –1〉 fringe for ten consecutive days and record this frequency fluctuation in time domain. The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10 × 10−15. The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6 × 10−17. Compared with NTSC-F1, NTSC-F2, there appears a significant improvement.

Improvement of the short-term stability of atomic fountain clock with state preparation by two-laser optical pumping* *Project supported by the National Natural Science Foundation of China (Grant No. 11873044).

To improve the signal to noise ratio (SNR) and the short-term stability of cesium atomic fountain clocks, the work of two-laser optical pumping is presented theoretically and experimentally. The short-term stability of the NIM6 fountain clock has been improved by preparing more cold atoms in the | F = 4, mF = 0〉 clock state with a shortened cycle time. Two π-polarized laser beams overlapped in the horizontal plane have been applied after launching, one is resonant with | F = 4〉 → | F′ = 4〉 transition and the other is resonant with | F = 3〉 → | F′ = 4〉 transition. With optical pumping, the population accumulated in the | mF = 0〉 clock state is improved from 11% to 63%, and the detection signal is increased by a factor of 4.2, the SNR of the clock transition probability and the short-term stability are also improved accordingly.

A cesium atomic clock frequency anomaly detection algorithm based on clock prediction and its performance analyses

A cesium atomic clock frequency anomaly detection algorithm based on clock prediction and its performance analyses

Nonlinear Autoregressive Model With Exogenous Input Recurrent Neural Network to Predict Satellites’ Clock Bias

The prediction of Satellites’ Clock Bias (SCB) plays an important role in optimizing the clock bias parameters in navigation messages, meeting the requirements of real-time dynamic precise point positioning and providing the prior information required for satellite autonomous navigation. Satellite-borne atomic clocks are often affected by many factors in space, which makes it difficult to describe the clocks’ bias and behavior with fixed model to achieve reliable high-precision prediction. The composition and characteristics of clock bias for satellite-borne atomic clock are described and analyzed, a clock bias prediction algorithm based on Nonlinear autoregressive model with exogenous input (NARX) recurrent neural network is proposed, the advantages of this model in SCB and other time series prediction are introduced in detail. The SCB data from four different clock types are selected for calculation and analysis. The comparative results show that, for both 6h and 24h forecasts, the accuracy and stability of NARX model are significantly better than three commonly used models, especially in the prediction of satellite cesium atomic clock.

Experimental Verification of the Neural Network Predicting Procedure Applied for UTC(PL)

The article presents and summarizes the research results of the UTC-UTC(PL) differences predicting procedure for the Polish Time Scale UTC(PL) developed at the Institute of Metrology, Electronics and Computer Science of the University of Zielona Gora. The research has been conducted in close cooperation with the Time and Frequency Laboratory of Central Office of Measures, responsible for the realization of the UTC(PL). The planned experiment covered a 50-month period, in which the UTC(PL) timescale has been carried out using, as a master clock, atomic clocks with different properties: commercial cesium atomic clock 5071A Opt. 001 (first case) and VCH-1003M hydrogen maser (second and third cases). In case of the developed predicting procedure by means of group method of data handling (GMDH)-type neural network (NN), the transitional period (second case) in which the master clock had been replaced by the new clock, is also very important. For GMDH-type NN, input data as a TS1 and TS2 time series have been prepared, based on the already-known differences of UTC(PL) from UTC and UTC rapid timescales and on determined differences between UTC(PL) and the master clock steering the UTC(PL). The method of preparing TS1 and TS2 time series is an important part of the developed procedure for predicting UTC(PL) differences from UTC, before they will be calculated and published by fr. Bureau International des Poids et Mesures (BIPM). The obtained research results confirmed that the developed predicting procedure by means of GMDH-type NN ensures a proper quality of maintaining the national timescale. The best quality of UTC(PL) predicting has been achieved for the third case, both for data prepared according to the TS1 and TS2 time series. This is confirmed by the calculated values of the prediction quality measures and the Modified Allan deviation. On the other hand, the second case confirmed the possibility of using the proprietary development of the TS2 time series to predict UTC-UTC(k) differences. This time series is a very good alternative for the TS1 time series, when the amount of data in this series is insufficient due to replacement of the clock or its failure.