Rb Clock Research Articles

Absolute frequency stabilization of a QCL at 8.6 µm by modulation transfer spectroscopy.

Modulation transfer spectroscopy is used to demonstrate absolute frequency stabilization of an 8.6-µm-wavelength quantum cascade laser against a sub-Doppler absorption of the CHF3 molecule. The obtained spectral emission properties are thoroughly characterized through a self-referenced optical frequency comb, stabilized against either a GPS-disciplined Rb clock or a 1.54-µm Er-fiber laser locked to a high-finesse ultra-low-expansion optical cavity. Fractional long-term stability and accuracy at a level of 4×10-12 (at 100 s) and 3×10-10, respectively, are demonstrated, along with an emission linewidth as narrow as 10 kHz for observation times of 0.1 s.

Analysis and experimental demonstration of underwater frequency transfer with diode green laser.

We demonstrated an underwater frequency transfer technique with a green diode laser. The characteristic of the timing fluctuation and instability for the transfer technique was analyzed and simulated. With this technique, we had transferred a highly stable 100-MHz frequency signal over an underwater link with distances of 3 m, 6 m, and 9 m for 5000 s, respectively. The experimental results involving the underwater transfer of the 100-MHz radio-frequency signal shows that the rms timing fluctuations are 5.9 ps (3-m link), 6.4 ps (6-m link), and 8.4 ps (9-m link). The calculations also show that the relative Allan deviations for the 3-m, 6-m, and 9-m transmission links are 5.6 × 10-13 at 1 s and 5.3 × 10-15 at 1000 s, 5.8 × 10-13 at 1 s and 1.1 × 10-14 at 1000, and 6.8 × 10-13 at 1 s and 1.1 × 10-14 at 1000 s, respectively. The measured instabilities were lower than Rb and Cs atomic clocks, implying that the proposed frequency transfer scheme can potentially be used to transfer the signals of these atomic clocks over underwater links.

130 W, 180 fs ultrafast Yb-doped fiber frequency comb based on chirped-pulse fiber amplification.

We report on a high-power fiber optical frequency comb consisting of a 250-MHz mode-locked fiber laser and a three-stage cascaded fiber chirped-pulse amplification system. After power scaling, the group velocity dispersion and third-order dispersion, generated in fiber stretcher and amplifiers, are compensated by a grism compressor, outputting a 132-W, 180-fs pulse train. The repetition rate and carrier-envelope offset frequency are locked to a Rb clock with the standard deviations of 1.07 and 0.87 mHz, corresponding to the fractional instability of 8.3×10-13 and 1.35×10-19, respectively. Moreover, we investigate the noise characteristics at high average powers, presenting a low-noise property of this high-power fiber OFC.

脉冲光抽运铷原子钟的Ramsey信号特性研究

脉冲光抽运铷原子钟的Ramsey信号特性研究

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.

Visible astro-comb filtered by a passively stabilized Fabry-Perot cavity.

We demonstrate a compact 29.3 GHz visible astro-comb covering the spectrum from 560 nm to 700 nm. A 837 MHz Yb:fiber laser frequency comb phase locked to a Rb clock served as the seed comb to ensure the frequency stability and high side mode suppression ratio. After the visible super-continuum generation, a Fabry-Perot cavity based on ultra-low expansion glass was utilized to filter the comb teeth. The mirrors were home-made complementary chirped mirrors pair with zero net-dispersion and high reflection to guarantee no mode skipping. Those filtered comb teeth were clearly resolved in an astronomical spectrograph of 49 000 resolution, exhibiting sharp line shape, zero noise floor, and uniform exposure amplitude.

Characteristics of BeiDou-3 Experimental Satellite Clocks

The characteristics of the improved Atomic Frequency Standard (AFS) operated on the latest BeiDou-3 experimental satellites are analyzed from day-of-year (DOY) 254 to 281, of the year 2017, considering the following three aspects: stability, periodicity, and prediction precision. The two-step method of Precise Orbit Determination (POD) is used to obtain the precise clock offsets. We presented the stability of such new clocks and studied the influence of the uneven distribution of the ground stations on the stability performance of the clock. The results show that the orbit influence on the Medium Earth Orbit (MEO) clock offsets is the largest of three satellite types, especially from 3 × 10 3 s to 8.64 × 10 4 s. Considering this orbit influence, the analysis shows that the Passive Hydrogen Maser (PHM) clock carried on C32 is approximately 2.6 × 10 − 14 at an interval of 10 4 , and has the best stability for any averaging intervals among the BeiDou satellite clocks, which currently achieves a level comparable to that of the PHM clock of Galileo, and the rubidium (Rb) clocks of Global Positioning System (GPS) Block IIF. The stability of the improved Rb AFS on BeiDou-3 is also superior to that of BeiDou-2 from 3 × 10 2 s to 3 × 10 3 s, and comparable to that of Rb AFS on the Galileo. Moreover, the periodicity of the PHM clock and the improved Rb clock are presented. For the PHM clock, the amplitudes are obviously reduced, while the new Rb clocks did not show a visible improvement, which will need further analysis in the future. As expected, the precision of the short-term clock prediction is improved because of the better characteristics of AFS. The Root Mean Square (RMS) of 1-h clock prediction is less than 0.16 ns.

Characterization of Frequency-Doubled 1.5- m Lasers for High-Performance Rb Clocks.

We report on the characterization of two fiber-coupled 1.5- diode lasers, frequency-doubled and stabilized to Rubidium (Rb) atomic resonances at 780 nm. Such laser systems are of interest in view of their implementation in Rb vapor-cell atomic clocks, as an alternative to lasers emitting directly at 780 nm. The spectral properties and the instabilities of the frequency-doubled lasers are evaluated against a state-of-the-art compact Rb-stabilized laser system based on a distributed-feedback laser diode emitting at 780 nm. All three lasers are frequency stabilized using essentially identical Doppler-free spectroscopy schemes. The long-term optical power fluctuations at 780 nm are measured, simultaneously with the frequency instability measurements done by three beat notes established between the three lasers. One of the frequency-doubled laser systems shows at 780 nm excellent spectral properties. Its relative intensity noise <10-12 Hz-1 is one order of magnitude lower than the reference 780-nm laser, and the frequency noise <106 Hz2/Hz is limited by the laser current source. Its optical frequency instability is at s, limited by the reference laser, and better than at all timescales up to one day. We also evaluate the impact of the laser spectral properties and instabilities on the Rb atomic clock performance, in particular taking into account the light-shift effect. Optical power instabilities on long-term timescales, largely originating from the frequency-doubling stage, are identified as a limitation in view of high-performance Rb atomic clocks.

Modeling of the GPS satellite clock error and its performance evaluation in precise point positioning

The different functions, which include the polynomial and the harmonics based functions, are used to model and extrapolate the GPS satellite clock for simplifying the service mode and real-time application. The modeling accuracy decreases with the increasing modeled time, when the polynomial functions are used. The 4th order harmonics based function is used to model the one-year single day satellite clocks. The results indicate that the accuracies of the modeled Rb clocks are better than 0.30 ns, while that of the Cs clocks just are better than 0.79 ns. Meanwhile, we noticed that the daily fitted amplitudes for 16 Block IIF and Block IIR-M Rb clocks vary regularly with a 6 months periodicity. This is mostly visible for the harmonics of 6 and 12 h periods. However the initial phases of these 12 and 6 h harmonics have obvious linear variation for the 16 Block IIF and Block IIR-M Rb clocks. Additional periods of 8 h, 4.8 h, 3.43 h and 2.67 h are noticed by analyzing the modeling residuals of 4th order harmonics based function. The modeling of 8th order harmonics based function is implemented and the modeled accuracy is improved. The extrapolated results of the 4th and 8th order harmonics based functions are better than that of the broadcast ephemerides and the predicted parts of International GNSS Service (IGS) Ultra-Rapid (IGU) products. The performances of the modeled clocks in precise point positioning (PPP) show that the results of 4th and 8th order harmonics based functions reach centimeter level although their convergence times are slower than that of the IGS clock series product.

Improved prediction of GPS satellite clock sub-daily variations based on daily repeat

High-precision estimates of GPS satellite clock errors reveal systematic sub-daily clock bias variations on the order of 1 ns. The low noise levels in the Rubidium Atomic Frequency Standards onboard GPS IIR, IIR-M, and IIF satellites provide visibility of these small, but systematic behaviors. Prior studies have reported on this phenomenon and sought to characterize the specific frequency components present and to identify potential causes of the observed periodic variations. Our research focuses on the repeatability of the clock variations and the potential for using observed variations directly to predict future clock behavior. Results are presented and compared to IGS Ultra-rapid and broadcast message predictions for all operating GPS satellite clocks for a 1-month period in July 2017. During this time, the accuracy of the proposed sub-daily variation prediction is better than 0.15 ns (RMS) for 8 out of 9 GPS Block IIF Rb clocks and under 0.3 ns (RMS) for most GPS IIR and IIR-M Rb clocks. This approach is complementary to existing techniques for estimating longer-term clock rates and drift and can be combined with them to improve the fidelity of predictive satellite clock models for real-time GPS position, navigation, and timing applications.

Evaluation and analysis of real-time precise orbits and clocks products from different IGS analysis centers

To meet the increasing demands from the real-time Precise Point Positioning (PPP) users, the real-time satellite orbit and clock products are generated by different International GNSS Service (IGS) real-time analysis centers and can be publicly received through the Internet. Based on different data sources and processing strategies, the real-time products from different analysis centers therefore differ in availability and accuracy. The main objective of this paper is to evaluate availability and accuracy of different real-time products and their effects on real-time PPP. A total of nine commonly used Real-Time Service (RTS) products, namely IGS01, IGS03, CLK01, CLK15, CLK22, CLK52, CLK70, CLK81 and CLK90, will be evaluated in this paper. Because not all RTS products support multi-GNSS, only GPS products are analyzed in this paper. Firstly, the availability of all RTS products is analyzed in two levels. The first level is the epoch availability, indicating whether there is outage for that epoch. The second level is the satellite availability, which defines the available satellite number for each epoch. Then the accuracy of different RTS products is investigated on nominal accuracy and the accuracy degradation over time. Results show that Root-Mean-Square Error (RMSE) of satellite orbit ranges from 3.8 cm to 7.5 cm for different RTS products. While the mean Standard Deviations of Errors (STDE) of satellite clocks range from 1.9 cm to 5.6 cm. The modified Signal In Space Range Error (SISRE) for all products are from 1.3 cm to 5.5 cm for different RTS products. The accuracy degradation of the orbit has the linear trend for all RTS products and the satellite clock degradation depends on the satellite clock types. The Rb clocks on board of GPS IIF satellites have the smallest degradation rate of less than 3 cm over 10 min while the Cs clocks on board of GPS IIF have the largest degradation rate of more than 10 cm over 10 min. Finally, the real-time kinematic PPP is carried out to investigate the effects of different real-time products. The CLK90 has the best performance and mean RMSE of 26 globally distributed IGS stations in three components are 3.2 cm, 6.6 cm and 8.5 cm. And the second-best positioning results are using IGS03 products.

Study of additive manufactured microwave cavities for pulsed optically pumped atomic clock applications

Additive manufacturing (AM) of passive microwave components is of high interest for the cost-effective and rapid prototyping or manufacture of devices with complex geometries. Here, we present an experimental study on the properties of recently demonstrated microwave resonator cavities manufactured by AM, in view of their applications to high-performance compact atomic clocks. The microwave cavities employ a loop-gap geometry using six electrodes. The critical electrode structures were manufactured monolithically using two different approaches: Stereolithography (SLA) of a polymer followed by metal coating and Selective Laser Melting (SLM) of aluminum. The tested microwave cavities show the desired TE011-like resonant mode at the Rb clock frequency of ≈6.835 GHz, with a microwave magnetic field highly parallel to the quantization axis across the vapor cell. When operated in an atomic clock setup, the measured atomic Rabi oscillations are comparable to those observed for conventionally manufactured cavities and indicate a good uniformity of the field amplitude across the vapor cell. Employing a time-domain Ramsey scheme on one of the SLA cavities, high-contrast (34%) Ramsey fringes are observed for the Rb clock transition, along with a narrow (166 Hz linewidth) central fringe. The measured clock stability of 2.2 × 10−13 τ−1/2 up to the integration time of 30 s is comparable to the current state-of-the-art stabilities of compact vapor-cell clocks based on conventional microwave cavities and thus demonstrates the feasibility of the approach.

An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets

The satellite clocks used in the BeiDou-2 satellite navigation System (BDS) are Chinese self-developed Rb atomic clocks, and their performances and stabilities are worse than GPS and Galileo satellite clocks. Due to special periodic noises and nonlinear system errors existing in the BDS clock offset series, the GPS ultra-rapid clock model, which uses a simple quadratic polynomial plus one periodic is not suitable for BDS. Therefore, an improved prediction model for BDS satellite clocks is proposed in order to enhance the precision of ultra-rapid predicted clock offsets. First, a basic quadratic polynomial model which is fit for the rubidium (Rb) clock is constructed for BDS. Second, the main cyclic terms are detected and identified by the Fast Fourier Transform (FFT) method according to every satellite clock offset series. The detected results show that most BDS clocks have special cyclic terms which are different from the orbit periods. Therefore, two main cyclic terms are added to absorb the periodic effects. Third, after the quadratic polynomial plus two periodic fitting, some evident nonlinear system errors also exist in the model residual, and the Back Propagation (BP) neural network model is chosen to compensate for these nonlinear system errors. The simulation results show that the performance and precision using the improved model are better than that of China iGMAS ultra-rapid prediction (ISU-P) products and the Deutsches GeoForschungsZentrum GFZ BDS ultra-rapid prediction (GBU-P) products. Comparing to ISU-P products, the average improvements using the proposed model in 3 h, 6 h, 12 h and 24 h are 23.1%, 21.3%, 20.2%, and 19.8%, respectively. Meanwhile the accuracy improvements of the proposed model are 9.9%, 13.9%, 17.3%, and 21.2% compared to GBU-P products. In addition, the kinematic Precise Point Positioning (PPP) example using 8 Multi-GNSS Experiment MGEX stations shows that the precision based on the proposed clock model has improved about 16%, 14%, and 38% in the North (N), East (E) and Height (H) components.

Long distance measurement up to 1.2 km by electro-optic dual-comb interferometry

We perform a long distance measurement up to 1.2 km on the outdoor baseline by electro-optic dual-comb interferometry. A frequency comb pair is developed by phase modulating a continuous laser with a narrow linewidth, and the slightly different repetition frequencies are synchronized to the Rb clock via the signal generators. A RF electrical comb can be generated by multi-wavelength heterodyne interferometry, and thus, a series of synthetic wavelengths can be obtained, whose phases can be used to determine the distances. Compared with the reference values, the experimental results show an agreement within 379 μm in the 1180 m range. In the long-time experiments, the Allan deviation can be below 20 μm with an averaging time of 10 s, and can be further improved to be less than 600 nm when the averaging time is above 350 s at 435 m and 1180 m, respectively.

Data Timing, Time Transfer and On-board Clock Monitoring for Space Astrometry with Gaia

The paper discusses the problematic of data timing in the framework of the space astrometry mission Gaia. For various reasons related both to astrometry and to the measuring principles of the Gaia instrument it is mandatory to assign a highly stable and accurate time tag for each observational point. For this purpose Gaia has a Rb clock on board. That on-board clock is a free-running oscillator and must be regularly synchronized with TCB which is used as the underlying relativistic coordinate time scale in the whole Gaia data processing. To monitor the reading of the on-board clock with respect to TCB (or any other timescale) a one-way clock synchronization scheme is implemented. This scheme takes into account all known theoretical effects (e.g., relativity, tropospheric delay, etc.) and allows one both to monitor the health of the on-board clock and to create a clock model at the accuracy of better than 1 microsecond.

Sub-picosecond timing fluctuation suppression in laser-based atmospheric transfer of microwave signal using electronic phase compensation

We demonstrated a timing fluctuation suppression in outdoor laser-based atmospheric radio-frequency transfer over a 110 m one-way free-space link using an electronic phase compensation technique. Timing fluctuations and Allan Deviation are both measured to characterize the instability of transferred frequency incurred during the transfer process. With transferring a 1 GHz microwave signal over a timing fluctuation suppressed transmission link, the total root-mean-square (rms) timing fluctuation was measured to be 920 femtoseconds in 5000 s, with fractional frequency instability on the order of 1×10−12 at 1 s, and order of 2×10−16 at 1000 s. This atmospheric frequency transfer scheme with the timing fluctuation suppression technique can be used to fast build an atomic clock-based frequency free-space transmission link since its stability is superior to a commercial Cs and Rb clock.

Enhancement of the performance of a fiber-based frequency comb by referencing to an acetylene-stabilized fiber laser.

We demonstrate a significant improvement in the performance of a fiber-based frequency comb when a GPS-disciplined Rb clock is replaced with an acetylene-stabilized laser as the frequency reference. We have developed a compact, maintenance-free acetylene-stabilized fiber laser with a sub-kHz short-term linewidth and an Allan deviation below 3×10-13 for integration times above 1 s. Switching the comb reference from the Rb clock to the acetylene-stabilized laser improves both comb tooth linewidth and Allan deviation by about two orders of magnitude. Furthermore, long-term measurements of the acetylene-stabilized laser frequency with reference to the GPS-disciplined clock indicate a potential relative frequency uncertainty of 2 × 10-12.

High-Performance Coherent Population Trapping Clock with Polarization Modulation

We demonstrate a vapor cell atomic clock prototype based on continuous-wave (CW) interrogation and double-modulation coherent population trapping (DM-CPT) technique. The DM-CPT technique uses a synchronous modulation of polarization and relative phase of a bi-chromatic laser beam in order to increase the number of atoms trapped in a dark state, i.e. a non-absorbing state. The narrow resonance, observed in transmission of a Cs vapor cell, is used as a narrow frequency discriminator in an atomic clock. A detailed characterization of the CPT resonance versus numerous parameters is reported. A short-term frequency stability of $3.2 \times 10^{-13} \tau^{-1/2}$ up to 100 s averaging time is measured. These performances are more than one order of magnitude better than industrial Rb clocks and comparable to those of best laboratory-prototype vapor cell clocks. The noise budget analysis shows that the short and mid-term frequency stability is mainly limited by the power fluctuations of the microwave used to generate the bi-chromatic laser. These preliminary results demonstrate that the DM-CPT technique is well-suited for the development of a high-performance atomic clock, with potential compact and robust setup due to its linear architecture. This clock could find future applications in industry, telecommunications, instrumentation or global navigation satellite systems.

Frequency Measurement System of Optical Clocks Without a Flywheel Oscillator.

We developed a system for the remote frequency comparison of optical clocks. The system does not require a flywheel oscillator at the remote end, making it possible to evaluate optical frequencies even in laboratories, where no stable microwave reference, such as an Rb clock, a Cs clock, or a hydrogen maser exists. The system is established by the integration of several systems: a portable carrier-phase two-way satellite frequency transfer station and a microwave signal generation system by an optical frequency comb from an optical clock. The measurement was as quick as a conventional method that employs a local microwave reference. We confirmed the system uncertainty and instability to be at the low 10-15 level using an Sr lattice clock.

Pulsed Optically Pumped Rb clock

INRIM demonstrated a Rb vapour cell clock based on pulsed optical pumping (POP) with unprecedented frequency stability performances, both in the short and in the medium-long term period. In the frame of a EMRP project, we are developing a new clock based on the same POP principle but adopting solutions aimed at reducing the noise sources affecting the INRIM clock. At the same time, concerning possible technological applications, particular care are devoted in the project to reduce the size and the weight of the clock, still keeping the excellent stability of the INRIM clock. The paper resumes the main results of this activity.