Equipping satellites with a series of high-precision frequency references is essential; however, even advanced active hydrogen masers can often be too heavy and expensive for the current satellite payload constraints. Moreover, in geostationary Earth-orbit communication satellites lacking atomic clocks, onboard oscillators can degrade the performance of time–frequency transmission methods. To address these challenges, this study proposes a novel phase-locked transponder that leverages Einstein’s synchronization theory and real-time carrier-phase compensation to improve the transmission performance of satellite frequency transfer systems while mitigating the noise from onboard satellite oscillators. Notably, this requires only simple modifications to the existing transponder structure. By replicating the high-precision atomic frequency standards from ground stations to satellites, the proposed system achieves enhanced frequency synchronization without additional onboard clocks. The feasibility of the satellite-to-ground link was validated through both a theoretical analysis and an experimental verification. Specifically, ground experiments demonstrated a reproducibility of 6.33 ps (1σ) over a 24 h period, with a long-term frequency stability of 3.36 × 10−16 at an average time of 10,000 s under dynamic conditions, showcasing the potential of this approach for advanced frequency synchronization. This paper presents a cost-effective and scalable solution for enhancing frequency synchronization in geostationary satellites, improving communication reliability, supporting advanced scientific and navigational applications, and enabling the development of high-precision, space-air-ground integrated time–frequency synchronization networks.

As a candidate for the next generation microwave clock, microwave atomic clocks based on trapped ions are currently studied worldwide. Since 2010, our team at Tsinghua University has been committed to developing a high-performance Cd-113(+) microwave ion clock. In 2021, the laser-cooled cadmium-ion microwave clock constructed in our laboratory demonstrated remarkable performance, with a short-term instability of 4.2x10(-13)/root tau and a relative frequency uncertainty of 1.8x10(-14), improving nearly three orders of magnitude compared to the result from JPL. The ground-state hyperfine splitting of Cd-113(+) was determined to be 15199862855.02799(27) Hz, currently the most accurate measurement result for this transition frequency. Apart from that, we introduced the sympathetic cooling technology into the experiment of cadmium-ion microwave clock. Using Ca-40(+) as the coolant ion, we obtained Ramsey patterns with a free evolution time of up to 100 seconds, ultimately improving the short-term instability of the system to 3.48x10(-13)/root tau.

Absolute gravity measurement refers to the measurement of the absolute value of gravitational acceleration (g, approximately 9.8 m/s2). The precision of absolute gravity measurement is limited mainly by vibration noises. Vibration correction is a simple and feasible way to deal with vibration noises, which corrects the measurement results by detecting vibration noises with a sensor. At present, the vibration correction performance of different sensors lacks systematic analysis and evaluation. In this paper, the theoretical analysis of how the sensor characteristics affect the correction performance is carried out. The vibration correction performances of three sensors, two different seismometers and one accelerometer, are evaluated experimentally in the three cases with different vibration noises. The experimental results show that the correction precision obtained by using low-noise seismometer is limited mainly by its bandwidth and range. In case I i.e. the quiet environment, the standard deviation of corrected results obtained by using both seismometers can reach tens of μGal (1 μGal = 10–8 m/s2), which is close to that obtained by using an ultra-low-frequency vibration isolator. However, in case II i.e. the noisy environment, the standard deviation of corrected results obtained by both seismometers increase to hundreds of μGal due to the enhancement of high-frequency vibration components. This means that the correction performances of both seismometers deteriorate, and the performance of seismometer with narrower bandwidth turns even worse. Moreover, two seismometers cannot even work in case III with stronger vibration noises due to the range limitation. On the other hand, the correction precision obtained by using accelerometer is affected mainly by its resolution which is on the order of mGal (1mGal = 10–5 m/s2). Its bandwidth can reach hundreds of or even thousands of hertz and its range is generally over ±2 g, which is large enough to meet the needs for noisy and dynamic applications. In case I, the standard deviation after correction with accelerometer is larger than that before correction. This is because the intensity of vibration noises in this case is close to or even smaller than the self-noise of accelerometer so that it could not be detected effectively by accelerometer. In case II, the resolution of accelerometer is sufficient to detect the vibration noises effectively. The standard deviation of the results is reduced from 2822 μGal to 1374 μGal after correction with accelerometer, and equal to a precision of 0.1 mGal after 100 drops. In case III where the amplitude of vibration noise rises to 0.1 m/s2 and seismometer cannot work, the accelerometer could still achieve a precision of 0.3 mGal after 100 drops. The systematic deviation is corrected from –1158 mGal to –285 μGal and the standard deviation is reduced from 34 mGal to 3.3 mGal. Therefore, the low-noise seismometer is more suitable for vibration correction in a quiet environment with stable foundation, which could realize a standard deviation superior to hundreds of μGal, while the accelerometer is more appropriate for vibration correction in a complex or dynamic environment, which could achieve a standard deviation of mGal-level. Finally, the present results and analysis provide a theoretical guidance for selecting and designing the sensors in vibration correction applications.

Dynamic onboard gravimetry is essential in geophysics, geodesy, and exploration. Optical interferometry is one of the promising technologies to achieve dynamic absolute gravimetry. A vibration correction system aimed at dynamic optical absolute gravimetry is proposed in this article. Its performance is preliminarily verified in static condition on the ground and on a passive gimbal suspension, respectively. As for case on the ground, the standard deviation is reduced from 7.5 to 0.9 mGal and the systematic deviation is reduced from 1.3 to 0.3 mGal after correction. As for case on the gimbal, the amplitude of vibration noise is up to 0.1 m/s2 which is close to the intensity of vibrations onboard. The standard deviation is reduced from 43 to 1.3 mGal, and the systematic deviation is reduced from 83 to 0.2 mGal after correction. A precision of 3–4 mGal/ $\surd $ Hz could thus be achieved by proposed system. The error sources of the system are also analyzed, a combined standard uncertainty of 0.5 mGal is considered to be obtained. These results show a promise of achieving satisfying measurements for future dynamic experiments.

Accurate absolute gravimeters are important instruments in applications, such as metrology, geophysics, and geological exploration. Vibration is one of the limiting factors that cause deterioration in measurement accuracy, which includes trueness and precision. The vibration correction method, in which a seismometer is used to record the vibration, provides an effective method to deal with the disturbances. The theoretical analysis shows that the ultimate correction accuracy is limited by the inherent frequency performance of the seismometer. The correction algorithm is an optimization problem to achieve this ultimate accuracy. The selection of the optimization objectives affects the correction accuracy dramatically. Although the real gravitational acceleration is unknown before the measurement is taken, minimization of the standard deviation of the fitting residual for a single drop (SDFRSD) is proven to realize better trueness. Enhanced precision is achieved through minimization of the Type A uncertainty of gravitational accelerations for all drops (UGAAD). Simulations and experimental measurements with the T-1 absolute gravimeter verify the theoretical analysis results. In addition, the results also show that the SDFRSD correction contains the real gravitational acceleration value, while the UGAAD correction exceeds the valid range. Therefore, the SDFRSD correction approach provides better comprehensive accuracy than the UGAAD correction method.

For absolute gravimeters, which play important roles in geophysics and geological exploration, an ultra-low-frequency vertical vibration isolator is necessary to achieve the required measurement precision. A novel active vibration isolator that uses a geometric anti-spring (GAS) structure has been proposed by our team at Tsinghua University previously, but its performance is mainly limited by the large-scale drift in the detection signal of the system. In this paper, after a brief theoretical introduction to the overall system, recent improvements in this novel vibration isolator are presented. The main improvements to the isolator are the use of new blades in the GAS structure and the addition of an extra compensation circuit to eliminate the drift. The improved prototype has a resonance period of 29.2 s and a continuous working time of several days, as compared with the resonance period of 19.2 s and a working time lasting only several minutes of the previous prototype. Experiments show that the improved prototype performs well in the homemade T-1 laser-interferometry absolute gravimeter. The standard error of the mean (SEM) of a 50-drop measurement performed in Tsinghua University is reduced significantly from 404 μGal (1 μGal = 1 × 10-8 m s-2) without the vibration isolator to 10.8 μGal with the improved prototype at its best level. Additionally, the SEM of a 50-set measurement (including 800 drops) lasting for 25 h achieves 5.9 μGal with the improved prototype.

Free-fall absolute gravimeters are important classical high precision absolute gravimeters in many branches of scientific research. But its performance is always troubled by the ground vibration. Vibration correction method is used to correct the result by detecting the ground vibration with sensors. A Kalman filter based fusion method is proposed to obtain more accurate ground vibration signal by fusing the outputs of the seismometer and the accelerometer. Experiment is conducted with the homemade T-1 absolute gravimeter, the standard deviation of the corrected results using seismometer data and fused data are 586.32 mu Gal (1 mu Gal = 10(-8) m/s(2)) and 508.59 mu Gal respectively, much better than the uncorrected result's 6548.96 mu Gal. The results prove the superiority of fused data over data measured from single sensor. It is believed that the application scene of the vibration correction will be broadened and the performance of the vibration correction will also be improved by using the proposed fusion method in the future.

The absolute gravimeter plays an important role in metrology, geophysics, and geological exploration. Seismic and environmental vibration has been one of the most serious factors limiting its performance. Consequently, an ultralow-frequency vertical vibration isolator is required to significantly improve its measurement precision. A novel active vertical vibration isolator employing geometric antispring (GAS) structure is proposed in this paper. The payload is supported by a GAS structure fixed on an inner frame, and the inner frame is hung by coil springs from the base. The relative movement of the payload with respect to the inner frame is detected, and the inner frame is driven by a voice coil actuator controlled by a feedback circuit to track the payload's motion. The new isolator has a compact size, and it can be used for different load ranges by tuning the GAS structure. The practical closed-loop system has a resonant period of 19.2 s, compared with the period of 0.74 s in an open-loop system. Experiments showed that the new isolator has great performance in a homemade T-1 absolute gravimeter, reducing the measurement deviation by a factor of 32. It is expected to be used in both free-falling and atomic-interference absolute gravimeters. Future improvements may include optimizing the mechanical structure and integrating a temperature control subsystem.

A classical absolute gravimeter is widely used to measure the gravitational acceleration, normally known as g. It applies a Mach-Zehnder interferometer to track a free-falling retroreflector in a vacuum chamber. Theoretically, it needs a static reference retroreflector in an inertial frame. Practically, the reference retroreflector is always disturbed by the ground vibration. Vibration correction methods apply the seismometer output to calculate the motion of the reference retroreflector. Transfer function between them is hypothesized to approach the real transfer function. The error between them limits the measurement effect. A direct measurement method, which puts the reference retroreflector on the sensitive beam, is proposed. A differential parallel plate capacitance detection is used to detect the movement of the reference retroreflector relative to the ground. A closed-loop feedback controller is applied to drive the reference retroreflector tracking the ground vibration. The feedback voltage represents the ground vibration acceleration, which is the motion acceleration of the reference retroreflector. A spring, instead of another voice coil actuator in previous version, is used to balance the sensitive beam gravity. It greatly reduces the thermal noise of the seismometer. The sensitivity and acceleration resolution of the capacitance detection are respectively 3.1 V/pF and 25 μGal (1 μGal = 10 −8 m/s 2 ). In the closed-loop system, the sensitivity and resolution of the instrument are respectively 12274 V/g and 644 μGal. The bandwidth of the system is 43 Hz. The damping ratio of the system needs to be increased. In the future, it will be used for T-1 absolute gravimeter.

The ballistic free-fall absolute gravimeters are most commonly-used instruments for high-precision absolute gravity measurements in many fields, such as scientific research, resource survey, geophysics and so on. The instrumental recoil vibrations generated by the release of the test mass can cause troublesome systematic bias, because these vibrations are highly reproducible from drop to drop with coherent phase. A compound counterbalanced design of chamber using both belt-driven mechanism and cam-driven structure is proposed in this paper. This structure is designed to achieve excellent recoil compensation as well as long freefall length for high precision measurements. Simulation results show that the recoil vibration amplitude of the compound recoil-compensated structure during the drop is about 1/4 of that with only belt-driven counterbalanced structure. This confirms the feasibility and superiority of the new design. And it is believed that the absolute gravimeter based on this newly proposed chamber design is expected to obtain more precise gravity measurement results in the future.

With the development of microwave atomic clocks, black-body radiation Zeeman shifts need to be considered carefully. In this Letter, the frequency shifts of hyperfine splittings of ground state due to black-body magnetic field are investigated. The relative frequency shifts of different alkali atoms and alkali-like ions which could be candidates of microwave atomic clocks are calculated, and results are from -0.977*10^(-17) [T(K)/300]^2 to -1.947*10^(-17) [T(K)/300]^2 for different atoms. These results are consistent with previous works but with more precision, detailed derivations and clear physical pictures.

A free-fall absolute gravimeter uses a Mach-Zehnder interferometer to track the free-falling object. Theoretically, it needs an inertial reference point, which is a reference retroreflector keeping static in inertial frame for an accurate absolute gravimetry. Practically, the reference retroreflector is always disturbed by the ground vibration. Traditionally, a vibration correction method with a broadband seismometer is used to reduce the effect of the ground vibration. The transfer function between the reference retroreflector and the seismometer is hypothesized as a proportional element with time delay. The difference between the hypothesized and the real transfer function limits the effect of the vibration correction. On this basis, a modified method, replacing the sensitive element of a seismometer with the reference retroreflector, is proposed. The motion of the reference retroreflector is measured directly by differential parallel plate capacitance detection. A closed-loop control circuit produces feedback voltage to make the reference retroreflector track the ground vibration. The feedback voltage represents the reference retroreflector's motion directly. Experiments show the capacitance detecting circuit detects the displacement of the reference retroreflector relative to the ground with a resolution of 0.6 nm at 500 Hz. The acceleration resolution of the homemade vertical seismometer is about 10 mGal. The sensitivity of the seismometer is 316 V/g. The damp ratio of the homemade seismometer is little, and the natural frequency of the homemade seismometer is 104 Hz by analyzing the step response of the system. The bandwidth of the system is around 175 Hz. In the future, the homemade seismometer will be applied in absolute gravimeters for hostile measurement.

Free-fall absolute gravimeters are widely employed to measure the gravitational acceleration, commonly known as g. It applies an interferometer to measure the trajectory of a free-falling object. The measurement precision of the absolute gravimeters is limited by the ground vibration. A vibration correction method is often applied in a noisy environment including a moving platform, sometimes it is required to get the g value quickly. It takes much time about 6 min to calculate the g value for one set measurement (no less than 25 drops). In order to quickly and accurately obtain the g value in hostile environments, there are two modifying methods including applying a lower sampling rate than original sampling rate of the vibration signal, and applying a division on trajectory data method. An equally spaced in distance division method is used. The results show, when applying the sampling rate of the vibration signal 1 MHz and the division factor 14, the total consumption time is reduced to one quarter of the time, from about 6 min to 1.5 min. Meanwhile, the error between the corrected results with and without the modifying methods is below 10 μGal, and the standard deviation of the g value has no significant change. In the future, promisingly it will be used to quick and precise dynamic absolute gravity measurement in hostile environments.

The rapid development of high-precision time and frequency transfer techniques allow the real-time comparison of remote hydrogen masers (H-masers). Since the year of 2013, we have been working on building a fiber-based frequency synchronization network in Beijing, using our homemade frequency transfer devices and buried city fiber links. So far, frequency signals of 3 Hmasers from 2 different institutes are transferred to our laboratory in Tsinghua University and are compared with the local Hmaser in real time, forming up a clock ensemble of 4 clocks from 3 places. Using this frequency network, we studied the correlation of the pair of co-located H-masers. With our measurement we found that the correlation is at the magnitude of 10?30 and only shows up after the averaging time is larger than 103s.

We demonstrate a compact signal transmission delay measurement system in optical fibers. The frequency of a microwave signal is locked to the signal transmission delay which can be obtained in frequency domain. With a frequency-scanning ambiguity resolving system, the signal transmission delay can be precisely determined. The system delay fluctuation is monitored in real-time and subtracted from the measurement result. This method achieves sub-picosecond uncertainty.

Vibration isolators have been widely used to keep the target object from the ground vibration in order to improve the measurement accuracy. Nowadays, the ultra-low frequency vibration isolator based on a two-stage structure shows the best performance. Traditionally, vertically suspended springs are usually applied as the second-stage. As the requirement of the low stiffness, the springs need to be long, which brings the disadvantages of relatively large size and small allowable load. A novel ultra-low frequency active vertical vibration isolator is proposed in this paper, which applies geometric anti-spring (GAS) instead of the second-stage suspended springs. The isolated object (the second stage) is supported by GAS fixed on an inner frame (the first stage), and the inner frame is hung with supporting springs from the base of the vibration isolator. The inner frame is driven by a voice coil to track the motion of the isolated object according to the relative motion signal detected by a photoelectric detector. Ideally, GAS provides zero restoring force for the object, thus realizing a long natural resonance period. Experimental results show that the isolator can achieve a resonance period of 14.7 s, compared with a simulated result of 20.7 s. Therefore, it is accessible to reduce the isolator’s volume and increase the allowable load by replacing the traditional second-stage suspended springs with GAS, without harming the vibration isolation effect. Promisingly it will be applied in free-falling and atomic-interference absolute gravimeters, and other precise measurements.

Design of the active region and analysis of temperature sensitivity of high-temperature operating 795-nm special VCSELs for Chip-Scale Atomic Clock (CSAC) are presented. Composition and thickness of the InAlGaAs multiple quantum wells (MQWs) are optimized at room and elevated temperatures. Temperature sensitivity of the threshold current is analyzed by calculating the temperature dependence of cavity-mode gain over a broad temperature range (25 o C-150 o C). A self-consistent VCSEL model based on quasi 3D finite element analysis is employed to investigate self-heating effects and temperature distribution in the proposed structure. Output power of 2.5mW is expected from 10µm aperture VCSELs at 10mA current at ambient temperature of 358K.

This paper introduces the formation of a physical real-time time scale using data of remote clocks from different time laboratories in Beijing region linked via fiber-based high-precision frequency transfer network.