High-precision optical time and frequency transfer

Optical two-way time and frequency transfer (O-TWTFT) is an enabling technology that has applications ranging from fundamental investigations of relativity to the operation of global navigation satellite systems. Linear-optical-sampling (LOS) between optical frequency combs has been used to create very stable optical two-way time and frequency transfer links over free-space. Here, we demonstrate two-way time and frequency transfer using LOS between electro-optic frequency combs. This two-way electro-optic time and frequency transfer system demonstrated instabilities as low as 15 fs at 1 s of averaging time. These results show a pathway to highly stable, frequency agile, and low SWaP-C time transfer networks.

Platform motion poses significant challenges to high-precision optical time and frequency transfer. We give a detailed description of these challenges and their solutions in comb-based optical two-way time and frequency transfer (O-TWTFT). Specifically, we discuss the breakdown in reciprocity due to relativity and due to asynchronous sampling, the impact of optical and electrical dispersion, and velocity-dependent transceiver calibration. We present a detailed derivation of the equations governing comb-based O-TWTFT in the presence of motion. We describe the implementation of real-time signal processing algorithms based on these equations and demonstrate active synchronization of two sites over turbulent air paths to below a femtosecond time deviation despite effective velocities of +/-25 m/s, which is the maximum achievable with our physical setup. With the implementation of the time transfer equation derived here, we find no velocity-dependent bias between the synchronized clocks to within at two-sigma statistical uncertainty of 330 attoseconds.

In a high-precision optical fiber time transfer system, in order to solve the scientific problem of time transfer dispersion deviation caused by the inconsistency of the two-way laser wavelengths, a high-precision time transfer method based on laser wavelength tracking is proposed in this paper. In the two-way time comparison, the laser emitted by the local site is used as a reference, and other lasers in the system track the reference, and the difference between the two-way laser wavelengths is small enough and stable for a long time, thereby greatly reducing the time transfer deviation caused by the inconsistency of the two-way laser wavelengths. In order to verify the performance of laser wavelength tracking, a double-layer temperature controlled externally modulated laser is designed, an experimental device for automatic laser wavelength tracking is designed, and laser wavelength tracking experimental modules are developed. The results show that the standard deviation of wavelength jitter is 55 fm, and the long-term relative stability of laser wavelength tracking is better than 5 fm@1×10<sup>4</sup> s, which ensures that the two laser wavelengths can remain relatively stable for a long time. In the case of long-distance fiber time transfer, by optimizing the setting value of the wavelength difference between each laser and the reference light on the link, the dispersion deviation of time transfer can be further reduced. In order to verify the feasibility of the high-precision optical fiber time transfer method based on laser wavelength tracking, a long-distance multi-station optical fiber time transfer experimental setup is built in our laboratory. The experiment is carried out in the laboratory by using 0.005, 250, 500, 750 km optical fiber links. The experimental results obtained on 750 km link show that the time transfer deviation is better than 5 ps, the stability is 4.7 ps@1 s, 0.4 ps@4×10<sup>4</sup> s, and the uncertainty is 8.4 ps. In the engineering application of optical fiber time transfer, by optimizing the working sequence of the system, the holding time length of the remote site clock can be reduced, and the accuracy of optical fiber time transfer can be further improved, which lays a foundation for realizing high-precision long-haul optical fiber time transfer.

This paper presents recent time keeping and time transfer research activities at National Institute of Metrology (NIM). In 2018, 4 more Hydrogen masers joined the NIM clock ensemble, the total relative weight of NIM clocks has been increased, and correspondingly the algorithm of UTC (NIM) has also been modified based on the new clock ensemble. With the modification of the algorithm, the performance of UTC (NIM) has been improved continuously, the deviation of UTC (NIM) from UTC has been kept within ±5 ns, and its stability has also been improved. For GNSS time and frequency transfer, NIM has done some research work based on Beidou Navigation Satellite System(BDS), BDS time transfer experiment with the NIM-made GNSS receivers on multiple baselines has been carried out in order to promote the implementation of BDS time transfer in the calculation International Atomic Time(TAI). The experiment has shown that BDS and GPS time transfer results are consistent, and less than 1 ns time stability could be achieved at some thousand seconds averaging time. For Two Way Satellite Time and Frequency Transfer(TWSTFT), NIM started to join the Europe-Asia links with satellite ABS-2a from March 2018, the very first results of NIM-PTB showed a time stability of 0.1 ns/d. NIM has operated Software-Defined Radio (SDR)Receiver since 2017 in parallel with Satre Modem, some beneficial results could be seen . For time transfer system calibration, as one of the GNSS “Group 1” (G1) laboratories designated by BIPM, NIM has organized several calibration campaigns with the NIM-made transportable calibrator. Two Way Optical fiber Time and Frequency Transfer (TWOTFT) has also been carried out continuously at NIM.

Gravitational redshift (GRS), a fundamental prediction of general relativity (GR), serves as a critical test of the Einstein Equivalence Principle (EEP) by comparing time flow rates between differing gravitational potentials. Over the decades, GRS experiments in astronomical observations, terrestrial measurements, and space-based investigations have achieved precision levels as fine as 10-5. However, most GRS experiments depend on microwave links for time and frequency transfer, with only a few exploring optical time and frequency transfer methods. Optical time transfer links provide a transformative alternative, offering superior resistance to atmospheric perturbations and higher modulation bandwidths, which enable sub-picosecond synchronization and exceptional time transfer precision. In 1975, Professor Carroll Alley (1927–2016) and his team at the University of Maryland (UMD), USA, demonstrated the feasibility of the optical time transfer method for GRS testing, achieving 10-2 accuracy using cesium clocks with 2×10-14 stability per day and laser pulses of 0.5 mJ energy, 0.1 ns duration, and 10 pulses per second. Modern advancements in optical timing experiments, such as the Chinese Laser Timing (CLT) on the China Space Station (CSS) mission, launched in October 2022, and the European Laser Timing (ELT), part of the upcoming Atomic Clock Ensemble in Space (ACES) mission aboard the International Space Station (ISS), promise unprecedented precision in future GRS experiments.This study investigates GRS testing by simulating ELT data. The ACES mission features atomic clocks with instabilities of about 2×10-16, including a hydrogen maser achieving 1.5×10-15 after 10,000 seconds and a cesium clock with stability of 1.1×10-13​√τ, where τ is the integration time in seconds. Additionally, the ELT payload is equipped with a novel single photon detector with a timing stability of < 3 ps @ 300 s and an event timer with precision of < 1 ps. Our simulation results indicate that using the two-way laser time transfer (TWLTT) link via the ELT experiment achieves precision levels 3–4 orders of magnitude higher than those obtained in the Alley experiment 50 years ago, thanks to the advanced atomic clocks aboard the ACES mission. This study is supported by the National Natural Science Foundations of China (NSFC) (Grant Nos. 42030105, 42388102, and 42274011) and the Space Station Project (2020-228).

Free-space optical time and frequency transfer techniques can synchronize fixed ground stations at the femtosecond level, over distances of tens of kilometers. However, optical time transfer will be required to span intercontinental distances in order to truly unlock the performance of optical frequency standards and support an eventual redefinition of the SI second. Fiber dispersion and Sagnac uncertainty severely limit the performance of long-range optical time transfer over fiber networks, so satellite-based free-space time transfer is a promising solution. In pursuit of ground-to-space optical time transfer, previous work has considered a number of systematic shifts and concluded that all of them are manageable. One systematic effect that has not yet been substantially studied in the context of time transfer is the effect of excess optical path length due to atmospheric refraction. For space-borne objects, orbital motion causes atmospheric refraction to be imperfectly canceled even by two-way time and frequency transfer techniques, and so will require a temperature-, pressure-, and humidity-dependent correction. This systematic term may be as large as a few picoseconds at low elevations and remains significant at elevations up to ~35°. It also introduces biases into previously-studied distance- and velocity-dependent corrections.

According to TWSTFT, two way optical fiber time and frequency transfer(TWOTFT) was designed.TWOTFT in real time based on the instant exchange of time transfer data via optical fiber was implemented. One kind of time and frequency standard disciplined by UTC(NIM) (National Metrology Primary Standard of China), called NIMDO, was constructed using TWOTFT for accurate and precise time synchronization, whose time difference from UTC(NIM) could be less than 1 ns, which is much better than NIMDO via GNSS (Global Navigation Satellite System) time transfer method (based on GPS (Global Positioning System) time transfer).

Time and frequency transfer is of great value in satellite navigation, communication and others fields. The existing link of time and frequency transfer based on laser pulse is mainly used for time transfer, it is unable to achieve the optical frequency transfer. In this paper, a method of satellite-ground time and frequency transfer based on ultra narrow linewidth laser and optical frequency comb is proposed. This method not only can implement the time transfer but also can implement the frequency transfer, which has the very high application value.

In the time and frequency transfer and dissemination field, it is important to provide cost effective remote frequency calibration services with an uncertainty of around 10-12 for end users. It is also required to develop ultra precise transfer methods with an order of 10-15 or better uncertainty for the comparison between ultra stable frequency standards which are under developing. This study shows two methods using optical fiber networks to satisfy these demands. First, it is an economical remote calibration method using existing synchronous optical fiber communication networks. The measured frequency stability (the Allan deviation) of the transmission clock is 2times10-13 for an averaging time of one day. The result indicates the method is promising for the simple remote frequency calibration service. Second, it is an ultra precise two-way optical fiber time and frequency transfer method using a newly proposed bi-directional optical amplifier. In this method, wavelength division multiplexing (WDM) signals are transmitted along a single optical fiber. The preliminary measured frequency stability is less than 1015 (tau =104 s) for a 100-km-long fiber with the bi-directional amplifier. It suggests that the method has capability for improving TAI (International Atomic Time) and UTC (Coordinated Universal Time)

Research on time and frequency transfer between stations through Global Navigation Satellite System (GNSS) carrier-phase observation data has been a hot topic for many years. However, the estimation of ambiguity has always been a challenge. Unlike Global Positioning System (GPS), BeiDou System (BDS) is a hybrid constellation with GEOstationary (GEO) satellites included. By virtue of the stationary characteristics of BDS GEO satellites, the method of precise common-view time and frequency transfer is proposed in this paper. With this method, high-precision time and frequency transfer can be achieved by utilizing the carrier-phase observation data from BDS GEO satellites and the precise products of the International GNSS Monitoring and Assessment System (iGMAS). The advantages are as follows. 1) Unlike traditional GNSS Medium Earth Orbit (MEO) satellites, BDS GEO satellites are always visible within their coverage area. Therefore, there will only be one ambiguity for this method over long periods of 1 month or more, which can be calibrated as a systematic error; 2) By using BDS GEO satellites, the time transfer results will not be affected by the phase wind-up effect. With sites in Europe and China, experiments based this method are performed, and the results show that: 1) For zero and ultra-short baselines, the Root Mean Square (RMS) values of the proposed method are better than 0.1ns; 2) For the short baseline (33 km), the performance of the proposed method is comparable to Two Way Optical Time and Frequency Transfer; 3) For the long baseline (700 km and 1750 km), the performance of the proposed method is better than Two Way Satellite Time and Frequency Transfer; 4) For inter-continental baselines (over 7000 km), the RMS value of the residuals with respect to Precise Point Positioning time transfer is at the sub-nanosecond level.

We report on the evaluation of the performance of optical time transfer links connecting a facility of Deutsche Telekom in Bremen with the Physikalisch-Technische Bundesanstalt in Braunschweig. In the current configuration three links have been established, two via a hub in Hannover and one using an independent alternate route. They are equipped with electronically stabilized fiber optic time and frequency transfer systems and parallel operation is maintained since December 2016. A novel method of link calibration, composed of two steps (one performed in the laboratory and the second one in the field), to accurately determine the influence of fiber chromatic dispersion is discussed in detail, and a thorough analysis of the uncertainty budget is given. We show that the time transfer performance achieved is difficult to characterize based on measurements with time interval counters that are the standard equipment in timing laboratories and in the telecommunications sector. In our experiments, values of TDEV at the low ps-level at averaging times between 104 to 106 s have been achieved. The uncertainty of time transfer (including all kinds of delays) is of the order of 50 ps in a cascade of links. The results obtained show that such a kind of link is capable to deliver signals to a remote end with an instability being at least two orders of magnitude below the current requirements included in relevant Recommendations of the International Telecommunication Union—Telecommunication Sector (ITU-T). Moreover, the current implementation would allow primary Cs fountain clocks to be compared at the level of their performance, that is characterized by an uncertainty at the low 10−16 level and a frequency instability of the same order of magnitude at 1 d averaging.

Two-way Satellite Time and Frequency transfer (TWSTFT) is a primary technique for UTC generation [1]. Only the direct link, the so called UTC link between a Lab(k) and PTB, is used for UTC generation. The numerous redundant links are measured but never used. The concept of the TWSTFT network time transfer has been discussed by several authors [2,3,4,10]. [5,6] are examples of the very first use of redundancy (Triangle Closure Calibration) in the TW network for the time link calibrations. It is based on using all the direct UTC and redundant links (Fig. 1) and the hypothesis that the TWSTFT measurement errors obey the normal distribution with an homogeneous distribution over the whole network. However [7,8] proved that the hypothesis may not be held. Considerable biases exist, such as the diurnals, which cannot be fully averaged out by increasing the measurement quantity or eliminated in a simple least square (LSQ) network adjustment [3]. The maximised gains in uncertainty depend on the optimal use of the redundancy in the TWSTFT network but the maximum number of the measurements to be used. We first discussed the weak points of the equal-weight network time transfer and then proposed our solutions: (1) Weighting each link according to its uncertainty estimate; (2) Using the GPSPPP to strengthen or replace the errored TWSTFT links in the network adjustment. Obviously, unequal weighting is necessary; (3) The above solutions can be extended to use all types of observations, such as the TWOTFT (Two-Way Optical fibre Time and Frequency Transfer) etc. The global network adjustment takes the link measurement to establish its observation equation. Therefore, there are theoretically not limits in the types and the numbers of the observations (GPS, GLONASS, GALILEO, BEIDOU, TWOTFT, TWSTFT/SDR [13] etc.) on any baseline in the network T/F transfer. Such all the redundancy is used. This is called the multi-technique network T/F transfer [9].

Bi-directional methods are widely used in scientific and productive measurements. By the symmetric principle, systematic errors are largely cancelled. The technique of Two-Way Satellite Time and Frequency Transfer (TWSTFT) is a typical example. Using the reciprocated radio signals emitted at two Earth laboratories and exchanged through a geostationary telecommunication satellite, the atmosphere delay effects are greatly reduced in the combination of the up and down signals. Applications to time transfer of the optical fibre technique, here under the acronym TWOTFT (Two-Way Optical fiber Time and Frequency Transfer) developed rapidly. The reciprocity of the signal in both the directions allows balancing the propagation path delays in the fibre since they average out almost entirely by employing the two-way method. Based on historical documents and the latest developments and in view of metrology, we briefly review and preview the two-way techniques for application in accurate time transfer for UTC.

Mitigation of the multipath effect in BDS-based time transfer using a wave-absorbing shield

Residual timing jitter in the free-space optical two-way time and frequency transfer caused by atmospheric turbulence