Long-term Frequency Stability Research Articles

Enhancing long-term frequency stability of an actively mode-locked optoelectronic oscillator via a phase-locked loop.

A method to improve the frequency stability of microwave frequency comb (MFC) signals generated by an actively mode-locked optoelectronic oscillator (AML-OEO) is proposed and experimentally demonstrated. In the experiment, fundamental mode locking in the constructed AML-OEO is achieved, producing MFC signals with a center frequency of 2.165 GHz and a repetition rate of 396.629 kHz. By locking the MFC comb tooth to a stable reference source using a phase-locked loop (PLL), the stability of MFC's center comb tooth reaches 2.4 × 10-13@1000s and the frequency stability improves by more than two orders of magnitude on a second-level time scale compared to the free-running AML-OEO. The improved frequency stability of MFC signals makes AML-OEO suitable as high-performance microwave sources for various critical applications.

A space-borne ultra-stable laser system with an excellent long-term frequency stability for gravitational wave detection

Abstract Ultra-stable lasers are pivotal in various scientific applications, notably in space gravitational wave detection projects. We develop a space-borne ultra-stable laser system based on a home-made non-planar ring oscillator (NPRO) laser and an ultra-stable cavity laser stabilization system. The ultra-stable cavity is a vertically mounted 8 cm long cavity, with tunable zero-crossing temperature and low vibrational sensitivity. To make a cavity with any standard grade ultra-low expansion glass (ULE) material, and tune the zero-crossing temperature to the satellite platform temperature, we design three ultra-stable cavities with different configurations to unambiguously explore their thermal properties. The measurement results meet the design goals well, and the zero-crossing temperature of the cavity can be tuned from − 19 ∘ C to 16.0 °C. We measure the temperature fluctuation noise through modulation experiment, and it agrees well with the theoretical simulations. The vibrational sensitivities in three directions are measured to be around 10−11 /g–10−10 /g. The total weight of the system is 14.0 kg, with a volume of about 18 L, and the power dissipation of the electrical system is 18.6 W. Finally, the prototype of the space-borne laser shows a frequency instability of 9.5 × 10 − 16 at 0.2 s, and the frequency noise is measured to be 3.6 Hz/Hz1/2 at 6 mHz over three months, satisfying the mission targets of all current space gravitational wave detection programs.

Simplified 1.5 μm Distributed Feedback Semiconductor Laser (DFB-LD) Frequency Stabilization System Based on Gas Absorption Chamber

The classical 1.5 μm band frequency-stabilized laser using acetylene gas saturated absorption can achieve high frequency stability and reproducibility, but its system design is complex and bulky. For some practical applications, a simple, compact system containing anti-interference abilities is preferred. In this study, a low-cost and simple-structured 1.5 μm frequency-stabilized laser is constructed using digital control methods, wavelength modulation technology, and acetylene gas absorption. The fiber input and output optical devices of the system significantly simplify the optical path and reduce the volume of the system. The error signal is obtained by the first-order differential method, and a combination of the high-speed comparator circuit and the microcontroller unit (MCU) is used to detect the error signal. Through the feedback control method of coarse temperature adjustment and fine current adjustment, the second-level frequency stability of the laser is stabilized within 100 kHz, that is, the frequency stability reaches 10​−10. The designed system achieved continuous and stable operation for more than 6 h, and the long-term frequency stability reached 10​−9.

Reduction of light shifts in a cold-atom CPT clock

Light shifts induced during atom–light interactions significantly affect the medium- and long-term frequency stability of atomic clocks. Here, we employ composite laser pulse sequences to mitigate interrogation-induced light shifts in a cold-atom coherent-population-trapping clock. We obtain the anti-symmetry error signal via modulating the local oscillator phase in the free-evolution time of Ramsey interferometry. Utilizing this signal, we employ two feedback loops to simultaneously eliminate light shifts and stabilize the clock frequency using the auto-balanced Ramsey (ABR) spectroscopy scheme. Our experimental results demonstrate that this approach can reduce the clock frequency’s sensitivity to variations in light shifts by implementing four Ramsey sub-sequences. Furthermore, we show that the ABR spectroscopy scheme enhances the long-term frequency stability of the atomic clock when the averaging time τ > 5000 s.

Modeling and assessment of Galileo PPP one-way timing with RT-product

Precise point positioning (PPP) technology is widely used in positioning, navigation, and timing. In order to meet the needs of users for real-time high-precision time information, a real-time Galileo PPP one-way timing model based on existing real-time (RT) products (CAS, CNES, GMV, and WHU) was established and applied for the timing field. Experiments were designed with 8 GNSS stations with an external H-MASER clock to research Galileo PPP timing with 25 day observations. For the modified Allan deviation (MDEV) of Galileo PPP timing solutions, similar to the timing solutions of GPS, the MDEV of Galileo PPP with CAS and CNES shows worse short-term frequency stability, with 1 to 2 × 10−13 at 960 s stability, and indicates similar long-term frequency stability, with about 5–6 × 10−15 at 61 440 s stability. For Galileo PPP time transfer, the standard deviation values are about 0.01–0.49 ns for all time-links with different products. For the stability of Galileo time transfer, the similar characteristic of Galileo time transfer is comparable to that of GPS. For short-term stability, the MDEV of all time-links from Galileo PPP ranges from 2 × 10−14 to 3 × 10−14 at 960 s. For long-term stability, 1 to 2 × 10−15 levels can be reached at 61 440 s for all time-links, except for that of CNES.

BDS-3 six-frequency precise point positioning: effects of receiver-dependent inter-frequency clock bias and multi-frequency contributions

We find that there is time-varying bias at the receiver in BDS-3 multi-frequency phase observations, which will lead to receiver-dependent inter-frequency clock bias (RIFCB) and damage the rigor of BDS-3 multi-frequency precise point positioning (PPP) model. A unified RIFCB correction method compatible with uncombined and ionospheric-free combined PPP models using any BDS-3 frequencies is proposed. The contributions of multi-frequency integration to BDS-3 static and kinematic PPP performance are evaluated. The results indicate that the RIFCB amplitude can reach 1 dm. If the RIFCB correction is ignored, the phase observation residuals present a systematic bias. RIFCB has potential effects on precise time transfer, ionospheric monitoring, and fractional cycle bias estimation. Experimental results show that the long-term frequency stability of time transfer can be improved by correcting RIFCB. The joint use of all BDS-3 six-frequency signals can significantly shorten the convergence time, and the positioning accuracy can also be slightly improved.

The analysis on time transfer of GPS/Galileo /BDS PPP with integer ambiguity resolution

GPS precise point positioning (PPP) approach has been considered for achieving time transfer for a long time. By virtue of GPS/Galileo/BDS FCB products, PPP model has the possibilities for changing phase ambiguities from ‘float’ value to ‘integer’ value. In this study, PPP time/frequency transfer model has been presented and performance of seven links equipped with Hydrogen Masers (H-Masers) and cesium atomic clocks are compared in static and kinematic modes. With partial ambiguity resolution (PAR) enabled, in contrast to GPS, results show that multi-GNSS’s fixing rate is much higher and TTFF(Time To First Fixing) is much shorter. It is verified that the fixing rate and TTFF has nothing to do with the atomic clock type but has strong correlation with the quality of observation. We find that frequency stability of time link is seriously dependent on the type of atomic clock. As far as H-Masers, it has reached the order of 1E-16/1E-15 at the averaging time of 122880 s, respectively. As far as Cesium clock, it has reached the order of 1E-15/1E-14 at the averaging time of 122880 s, respectively. For H-Maser, the long-term frequency stabilities of integer PPP (IPPP) have been improved by roughly 3% at the static mode and 4% at the kinematic mode on average, respectively. For positioning, compared to PPP solutions, the stabilities of the IPPP coordinates are improved after an averaging time of 7680 s in static or kinematic mode.

Enhanced production of <sup>199</sup>Hg cold atoms based on two-dimensional magneto-optical trap

Efficient preparation of cold atoms plays an important role in realizing precision measurement including optical lattice clocks (OLCs). Fast preparation of cold atoms reduces Dick noise by shortening dead time in a clock interrogation cycle, which improves the stability of OLCs. Here, we increase the loading rate of the three-dimensional magneto-optical trap (3D-MOT) in the ultra-high vacuum environment by utilizing the two-dimensional magneto-optical trap (2D-MOT) with a push beam, reduce the temperature of cold atoms with the compression-MOT technique which is implemented by reducing the detuning of 3D-MOT rapidly at the end of atom preparation, and realize the enhanced production of cold atoms for <sup>199</sup>Hg OLCs. To achieve 3D-MOT and 2D-MOT of mercury atoms, a deep ultraviolet laser (DUVL) system composed of three DUVLs is developed with one working in lower power for frequency locking and the other two in high power for laser cooling. Such a configuration improves the long-term frequency stability and shows greater robustness than our previous system consisting of two DUVLs. To maximize the 3D-MOT loading rate, we orderly optimize the detuning and the magnetic field gradient of 3D-MOT and those of 2D-MOT as well as the detuning and the power of the push beam. After all parameters are optimized, we measure the maximum loading rate of 3D-MOT to be 3.1×10<sup>5</sup> s<sup>–1</sup> and prepare cold atoms of 1.8×10<sup>6</sup> in 9 s. The loading rate is greatly enhanced by a factor of 51 by using 2D-MOT and the push beam. In order to improve the efficiency of transferring cold atoms from 3D-MOT to optical lattice, we use compression-MOT technique to reduce the temperature of cold atoms and produce cold <sup>199</sup>Hg atoms which are about 45 μK, lower than the expected temperature of Doppler cooling theory. By achieving the high gain of the 3D-MOT loading rate under the ultra-high vacuum and reducing the temperature of cold atoms, this enhanced preparation of cold atoms based on 2D-MOT effectively shortens the preparation time of cold atoms and improves the transfer efficiency of optical lattice, which provides a significant scheme for efficiently preparing cold mercury atoms in other experiments.

Light shift of Ramsey coherent population trapping resonance using drive current modulation

We investigated the light shift of Ramsey coherent population trapping (CPT) resonance by drive current modulation (DCM), which can be realized with low power consumption in a small system, to improve the performance of a CPT atomic clock. The light shift makes the greatest contribution to the degradation of long-term frequency stability of a CPT atomic clock. We also devised digitizer-based DCM to reduce the uncertainty in the frequency of light shift due to wavelength variation at the time of observation. The results show that light shift with DCM is reduced compared with cw excitation and is consistent with theoretical calculations. The estimated frequency uncertainty of the light shift due to wavelength variation using the proposed method is 2.1 × 10−13, which is approximately 165 times better than that of the conventional method without a digitizer, thus demonstrating the effectiveness of the proposed method for future small atomic clocks.

Enhancing long-term frequency stability of a single-mode optoelectronic oscillator based on phase conjugation.

We propose and experimentally demonstrate what we believe to be a novel single-mode optoelectronic oscillator (OEO) with low frequency drift based on phase conjugation. The long-term frequency stabilization of the OEO is achieved by using photonic microwave phase-conjugate passive compensation. Besides, since there happens to be a nonlinear coupled double loop structure in the OEO, single-mode oscillation can be achieved. The experimental results show that the side mode suppression ratio (SMSR) of the radio frequency (RF) signal from the OEO at 9.93 GHz is enhanced from 5 dB to 68 dB after side mode suppression, and the maximum frequency drift within 600 s reduced from 1.51 ppm to 0.04 ppm, optimized by a factor of about 40. The OEO has a simple structure, no external injection, and the phase noise is not limited by the injected signal.

A GPS-Referenced Wavelength Standard for High-Precision Displacement Interferometry at λ = 633 nm.

Since the turn of the millennium, the development and commercial availability of optical frequency combs has led to a steadily increase of worldwide installed frequency combs and a growing interest in using them for industrial-related metrology applications. Especially, GPS-referenced frequency combs often serve as a "self-calibrating" length standard for laser wavelength calibration in many national metrology institutes with uncertainties better than u = 1 × 10-11. In this contribution, the application of a He-Ne laser source permanently disciplined to a GPS-referenced frequency comb for the interferometric measurements in a nanopositioning machine with a measuring volume of 200 mm × 200 mm × 25 mm (NPMM-200) is discussed. For this purpose, the frequency stability of the GPS-referenced comb is characterized by heterodyning with a diode laser referenced to an ultrastable cavity. Based on this comparison, an uncertainty of u = 9.2 × 10-12 (τ = 8 s, k = 2) for the GPS-referenced comb has been obtained. By stabilizing a tunable He-Ne source to a single comb line, the long-term frequency stability of the comb is transferred onto our gas lasers increasing their long-term stability by three orders of magnitude. Second, short-term fluctuations-related length measurement errors were reduced to a value that falls below the nominal resolving capabilities of our interferometers (ΔL/L = 2.9 × 10-11). Both measures make the influence of frequency distortions on the interferometric length measurement within the NPMM-200 negligible. Furthermore, this approach establishes a permanent link of interferometric length measurements to an atomic clock.

Time transfer with BDS-3 signals: CV, PPP and IPPP

The third phase of BeiDou navigation satellite system (BDS-3) was officially commissioned on 31 July 2020. In this study, we make a comprehensive evaluation of BDS-3 time transfer with the B1I, B3I, B1C and B2a measurements. The multi-path (MP) errors and noises of different BDS-3 ranging signals are analyzed to illustrate characteristic of the code observations firstly. Then dual-frequency ionosphere-free linear combinations of BDS-3 B1I&B3I and B1C&B2a measurements are used to achieve time transfer. Using Multi-GNSS Experiment station observations, we evaluate the performance of BDS-3 time transfer with common-view (CV), precise point positioning (PPP) and integer ambiguity PPP (IPPP) techniques. Analysis results show that BDS-3 B1C&B2a CV time transfer links show a better performance than GPS L1P&L2P links, whereas BDS-3 B1I&B3I links are worse than GPS links. For the PPP time transfer, GPS links show the best performance, followed by BDS-3 B1C&B2a links and B1I&B3I links. Furthermore, frequency stability of BDS-3 IPPP time transfer is more stable than PPP solutions at the long average interval time. And the long-term frequency stability of BDS-3 IPPP is comparable with GPS IPPP.

All-fiber-based ultrastable laser with long-term frequency stability of 1.1 × 10-14

We demonstrate an ultrastable miniaturized transportable laser system at 1550 nm by locking it to an optical fiber delay line (FDL). To achieve optimized long-term frequency stability, the FDL was placed into a vacuum chamber with a five-layer thermal shield, and a delicate two-stage active temperature stabilization, an optical power stabilization, and an RF power stabilization were applied in the system. A fractional frequency stability of better than 3.2×10-15 at 1 s averaging time and 1.1×10-14 at 1000 s averaging time was achieved, which is the best long-term frequency stability of an all-fiber-based ultrastable laser observed to date.

Mitigation of lamp oven and cavity oven temperature-induced frequency variation in rubidium atomic clock.

The long-term frequency stability of the rubidium atomic clock is primarily affected by temperature variations in the lamp oven and the cavity oven, which cause changes in light intensity, which are then converted into frequency variations. Therefore, we propose using light intensity variations to actively improve the cavity oven and lamp oven temperature sensitivity of the rubidium atomic clock. This is accomplished through research into the theory of the rubidium atomic frequency standard, specifically the effect of light intensity, lamp oven temperature, and cavity oven temperature on the frequency deviation. In previous work, we discovered the relationship between the light intensity and frequency deviation by combining this with our engineering expertise. Furthermore, some related experiments show that the method is feasible with the lamp oven and cavity oven temperature sensitivity of the rubidium atomic clock greatly improved, providing an effective way to improve the rubidium atomic clock's long-term frequency stability.

Stable terahertz wave dissemination over underground fiber network with optical phase correction

We report a phase-stabilized photonic terahertz wave distribution over an urban underground fiber network. The optical carriers of the terahertz signal are generated by filtering out optical spectral lines of an optical frequency comb (OFC). The phase fluctuation due to the optical carriers separation link and fiber link is compensated by an optical phase actuation network, which employs a high-precision voltage-controlled oscillator (VCO) in the phase-locked loop to drive the acousto-optic frequency shifter (AOFS) for fast phase correction We demonstrated the stabilized transfer of a 1000.04 GHz terahertz signal over a 42 km urban telecom fiber link, and achieved residual phase noise of -37 dBc/Hz at 1 Hz offset frequency, and the long-term frequency stability at 4000 s averaging time reaches 2 × 10−16. The factors that cause the performance limitations of the photonic terahertz wave distribution system are further analyzed.

Modelling and Assessment of BDS-3 Real-time Precise Point Positioning Time Transfer Based on PPP-B2b Service

In 2020, users in and around China had access to a new real-time precise point positioning (RTPPP) service with the BeiDou global navigation satellite system (BDS-3) B2b (PPP-B2b) signal. In this study, the quality of PPP-B2b products is first assessed and compared with the CNAV1 broadcast ephemeris. Then a mode of BDS-3 PPP time transfer with PPP-B2b (B2b-RTPPP) is developed and evaluated in static and kinematic modes. The results demonstrate that the discontinuity of orbit is improved by applying the PPP-B2b, and its root mean square errors (RMSEs) are 0.081 m, 0.165 m, and 0.107 m in the radial, along-track, and cross-track components, respectively. The standard deviation (STD) of the PPP-B2b clock offset is 0.08 ns, greatly better than that of the broadcast clock offset. For time transfer, the type A uncertainty of the B2b-RTPPP solution is approximately 0.1 ns in static mode, and approximately 0.3 ns in kinematic mode. The B1I/B3I B2b-RTPPP time transfer solution performs better than the B1C/B2a solution. For frequency stability, the modified Allan deviation (MDEV) of the B2b-RTPPP solution is comparable to that of the post-processing solution. The B1C/B2a combination has better short-term frequency stability than B1I/B3I, while the long-term frequency stability of B1C/B2a is worse. In addition, the contribution of the differential code bias (DCB) to B2b-RTPPP time transfer is also investigated. The type A uncertainty of the B2b-RTPPP solution without DCB correction is worse than that of the B2b-RTPPP solution with DCB correction. The B1C/B2a B2b-RTPPP solution without DCB correction has better frequency stability than the B1I/B3I B2b-RTPPP solution.

Improvement of the short- and long-term stability of high performance portable optically pumped cesium beam atomic clock

The research of optically pumped cesium beam atomic clock (OPCB) at Peking University has lasted for decades. At present, the short-term frequency stability is 3×10−12/τ and the long-term (5-day) frequency stability can reach 7 × 10−15. The optimization methods of the short-term frequency stability are using laser induced beam spectrum to stabilize the laser frequency, using cyclic transition to detect the atomic state and using a cesium oven with a collimator to generate the cesium atomic beam. The methods of obtaining the good long-term frequency stability are controlling the microwave power based on the atomic transition probability, controlling the C-field intensity based on Zeeman frequency and controlling the laser power using fluorescence. The compact optically pumped cesium beam atomic clock of Peking University is expected to contribute to the field of timing, positioning, navigation and high speed digital communication.

Frequency stabilization of multiple wavelength lasers based on a broadband spectrum

We report on frequency stabilization of multiple wavelength lasers operating at 1389 and 1695 nm simultaneously on a broadband spectrum. These lasers are implemented in ytterbium optical lattice clock experiments, which need to have a narrow enough linewidth and maintain high long-term frequency stability. A 1560 nm femtosecond mode-locked laser with a narrow mode spacing of 250 MHz is used as a master laser, which is referenced to a local ultrastable optical cavity with the instability better than 1 × 10−15 at 1 s averaging time. Through the combination of erbium-doped fiber amplifier and high nonlinear fiber, the spectral width of the maser laser is broadened from 10 nm to more than 300 nm. The range of the broadened spectrum can cover 1389 and 1695 nm. Meanwhile, the spectral intensity at the corresponding wavelength can ensure that the signal-to-noise ratio of the beat signals between the two lasers and the broadened spectrum is about 30 dB at a resolution bandwidth (RBW) of 100 kHz. After phase locking the 1389 and 1695 nm lasers on the broadband spectrum, the residual linewidths are obtained to be about 0.8 Hz at 1 Hz RBW, and the stabilities are 3.5 × 10−16 and 4.7 × 10−16 at 1 s averaging time respectively, improving about six orders of magnitude. Our result can be conducive to obtaining the stabilized laser sources for the atomic optical clock, and will be of great significance for simplifying and miniaturizing the optical clock system.

Numerical analysis and optimization of radio-frequency ion trap potential

The trap of multi-ion frequency standard is an ideal candidate for a new generation of ground and space-borne timekeeping systems, which has high signal-to-noise ratio, low frequency drift rate and excellent long-term frequency stability. The non-ideal characteristic of radio-frequency potential is one of the dominant factors that restrict the performance of ion frequency standard. In this study, the finite element numerical analysis method is used to quantitatively analyse and optimize the electrical potential field of ion trap, and an analytical model of ideal trapping potential is established. The typical transient numerical potential surface of trapping potential is used for decoupling analysis of various electrical potential effects. Based on the optimal structure parameters, the numerical model and analytical model of non-standard ion trap are established to verify the validity and accuracy of the numerical analysis method. This method can provide a quantitative solution for the high precision reconstruction of the trapping potential model of heterotype ion traps.

Absolute Frequency Readout of Cavity against Atomic Reference

Future space-based geodesy missions such as the Mass Change Mission and the Next Generation Gravity Mission are expected to rely on laser ranging as their primary instrument. Short-term laser frequency stability has previously been achieved on the GRACE Follow On mission by stabilizing the lasers to an optical cavity. The development of a technique to provide long-term laser frequency stability is expected to be required. We have previously demonstrated a technique to track long-term frequency changes by using measurements of the optical cavity’s free spectral range. In this paper, we calibrate this technique to absolute frequency by using an atomic reference. We have also validated an approach for on-ground calibration to allow the absolute frequency to be determined whilst in orbit.