Rb Atomic Clock Research Articles

On the relationship between electrical and electro-optical characteristics in vertical cavity surface emitting lasers for chip scale Rb atomic clocks

We report on a comprehensive study of the electrical and electro-optical properties of 795 nm vertical cavity surface emitting lasers (VCSELs) designed for chip scale Rb atomic clocks. We highlight several key findings including the observation that the current flow at moderate bias levels comprises several parallel paths which are identified by an analysis of the I−V characteristic also confirmed by a numerical simulation. Resistance is a key parameter in any VCSEL. We analyze it in detail at all bias levels and find that above transparency, when the VCSEL enters the high injection regime, the current flow mechanism is modified significantly from an exponential to a power law characteristic. Consequently, resistance attains a nonlinear contribution which is quadratic in the spontaneous emission regime and quasi-linear above the threshold. This nonlinear contribution is not considered in common models. The optoelectronic properties are strongly correlated with the electrical characteristics what allow to explain several peculiarities of the VCSEL performance. We designed and fabricated the VCSELs according to the requirements of miniature Rb atomic clocks, including optimal operation at high temperatures. Their minimum threshold occurs at 363 K where they emit at 794.7 nm. The modal and polarization discrimination in the bias range where these VCSELs operate in practical miniature atomic clocks is well above 30 dB.

Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Phase-shifting digital holographic microscopy for microstructure measurement by sweeping the repetition rate of femtosecond laser

This paper proposes a phase-shifting digital holographic microscopy (PSDHM) for microstructure measurement by sweeping the repetition rate of femtosecond laser, and a multiple reflection arrangement between two quasi-parallel mirrors is constructed for optical multiplication. High precision phase-shifting can be achieved by sweeping the repetition rate of the femtosecond laser referenced to a Rb atomic clock without any mechanical sweeping. Optical multiplication can shorten the spatial distance of the optical delay line used for pulses alignment, make the PSDHM structure compact and stable, and avoid certain environmental disturbances. In the experiments, a ten-step phase-shifting test was first carried out for evaluating the phase-shifting accuracy, and the phase-shifting error was calculated to be in the range of −1° to 0.25°. Then, a USAF 1951 resolution target and a microstructure standard target were measured using a four-step PSDHM, and the measurement results were compared with those from a stylus profiler and a white light interferometer, respectively. The lateral resolution of PSDHM was tested to be about 2.1 μm, and the maximum error of the longitudinal measurement was within 6 nm. Experiments verify that the PSDHM system has good performance in terms of phase-shifting accuracy, surface topography measurement and coherent noise suppression.

A Novel Method for Rubidium Bulb Bonding and Key Characterization for Future Space Clocks.

RF-discharge lamp is a key component in space- and ground-based compact and portable atomic clocks, such as rubidium atomic frequency standards (RAFSs). Precise thermal, structural design, and control of a rubidium (Rb) bulb is of crucial importance for long-term reliable operation of the onboard clocks. An important aspect is the potting material that is used to mount the Rb bulb. Potting material directly determines the thermal contact between liquid Rb pool inside glass bulb enclosure and the heating element, which is the only path to control the Rb bulb's temperature. Failure or degradation of thermal contact of the Rb bulb with its metallic base will lead to Rb clock degradation or failure. Considering this, we have successfully designed, simulated, implemented, characterized, and tested the use of indium metal as a replacement to epoxy for the Rb bulb bonding that can be implemented in future space Rb atomic clocks. Its thermal advantage over other routine space-qualified epoxies and flexibility for multiple bonding and unbonding mechanisms make it ideal for such applications. The usefulness of key properties of indium for various other space and ground applications is discussed.

A Compact Laser System for the Pulsed Optically Pumped Rubidium Cell Atomic Clock

We describe the design and implementation of a compact laser system for the pulsed optically pumped (POP) rubidium (Rb) cell atomic clock. The laser system includes packaged optics for sub-Doppler absorption, acousto-optic modulation and light beam expansion, and dedicated electronics for laser diode reliable single-mode operation and laser frequency stabilization. With beat measurements between two identical laser systems, the laser frequency stability was found to be 3.0×10-12 for averaging times from 1 to 60 s and it reached 3.5×10-12 at 10 000 s averaging time. Based on the compact laser system, the short-term stability of the Rb cell atomic clock in pulsed regime was approximately [Formula: see text], which is in reasonable agreement with the estimated [Formula: see text]. The compact laser system is significant in terms of the development of transportable and high-performance Rb atomic clock prototypes.

A low phase noise microwave source for high‐performance CPT Rb atomic clock

Phase noise of the frequency synthesizer is one of the main limitations to the short-term stability of microwave atomic clocks. In this work, we demonstrated a low-noise, simple-architecture microwave frequency synthesizer for a coherent population trapping (CPT) clock. The synthesizer is mainly composed of a 100 MHz oven controlled crystal oscillator (OCXO), a microwave comb generator and a direct digital synthesizer (DDS). The absolute phase noises of 3.417 GHz signal are measured to be -55 dBc/Hz, -81 dBc/Hz, -111 dBc/Hz and -134 dBc/Hz, respectively, for 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, which shows only 1 dB deterioration at the second harmonic of the modulation frequency of the atomic clock. The estimated frequency stability of intermodulation effect is 4.7*10^{-14} at 1s averaging time, which is about half order of magnitude lower than that of the state-of-the-art CPT Rb clock. Our work offers an alternative microwave synthesizer for high-performance CPT Rb atomic clock.

Uncertainty evaluation of the second-order Zeeman shift of a transportable 87Rb atomic fountain clock

In this article, taking advantage of the special magnetic shieldings and the optimal coil design of a transportable Rb atomic fountain clock, the intensity distribution in space and the fluctuations with time of the quantization magnetic field in the Ramsey region were measured using the atomic magneton-sensitive transition method. In an approximately 310 mm long Ramsey region, a peak-to-peak magnetic field intensity of a 0.74 nT deviation in space and a 0.06 nT fluctuation with time were obtained. These results correspond to a second-order Zeeman frequency shift of approximately (2095.5±5.1)×10-17. This is an essential step in advancing the total frequency uncertainty of the fountain clock to the order of 10-17.

Stable mode-locked Yb-fiber laser with a 6 MHz repetition rate tuning range

For the precise measurement, a femtosecond mode-locked Yb-doped fiber laser with a 6 MHz repetition rate tuning range at a fundamental repetition rate of 26 MHz was reported, corresponding to 23% tuning ratio. With chirped fiber Bragg grating, the mode-locked fiber laser could run at different dispersion regimes. The influence of the net cavity dispersion on output characteristics and repetition rate tunability was studied. In a range of negative cavity dispersion, the mode-locked fiber laser could output the nearly same spectrum when the repetition rate was tuned, and the output spectrum was nearly Gaussian-type. Based on this result, a simple scheme, spatial optical path structure, and optimized cavity parameters was designed, which promised the large tunable range and stable mode-locking. The mode-locked fiber could stably output 3.23 mW ultrashort laser pulses with 347 fs dechirped pulse duration. Furthermore, the Yb-fiber laser was locked to the Rb atomic clock so that the repetition rate could be stabilized. The Allan deviation is 2×10−10 when the average time was 1 s.

Large-field step-structure surface measurement using a femtosecond laser.

We present a femtosecond laser-based interferometry for step-structure surface measurement with a large field of view. A height axial scanning range of 348 µm is achieved by using the method of repetition frequency scanning with reference to the Rb atomic clock and the optical path length difference design for 21 times of the pulse interval. A combined method, which includes the envelope peak positioning method for rough measurement, synthetic-wavelength interferometry for connection, and carrier wave interferometry for fine measurement, is proposed to reconstruct the surface. A three-step specimen with heights of approximately 20, 50, and 70 µm was successfully measured with a height precision of 7 nm, and the accuracy was verified by a commercial white light interferometer. The diameter of the field of view that was demonstrated was 17.3 mm, which could be much larger owing to the high spatial coherence of the femtosecond laser. The results show that the femtosecond laser system combines the step-structure measurement performance of white light interferometry and the high-precision large-field performance of phase shifting interferometry, indicating its potential for widespread use in ultra-precision manufacturing of micro/nano-devices, such as semiconductor chips, integrated circuits, and micro-electro-mechanical systems.

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.

Evaluation of the radial inhomogeneity of a magnetic field by magnetic-sensitive Ramsey interference fringes at 87Rb atomic fountain clock

This paper demonstrates the evaluation of the radial inhomogeneity of the magnetic field of an atomic fountain clock, which affects the Ramsey interference fringe visibility. Based on the simplified inhomogeneous magnetic field model, the relationship between the fringe visibility and the inhomogeneity of the magnetic field is obtained; a magnetic field broadening limit of 70 pT for the fountain clock is observed when the interference fringes disappear. Magnetic field broadening of 100 pT in the local interaction region of the atomic fountain clock is measured by a special magnetic-sensitive Ramsey interference method. It is verified that the non-uniform widening of the magnetic field is the cause of the absence of interference fringes of adjacent lines.

Stability properties of an Rb CPT atomic clock with buffer-gas-free cells under dynamic excitation

This work presents a study of the short-term stability properties of Rb atomic clocks based on coherent population trapping (CPT) under dynamic excitation of a CPT resonance in cells without buffer gas. It is demonstrated that in an optical cell with anti-relaxation coating of its inner walls, the best stability is achieved at the scanning frequency of the frequency difference of the bichromatic pump field equal to 2 kHz at the resonance width of 450 Hz. In cells without a wall coating, the optimal scanning frequency range is found to be 1.2–2.8 kHz at the resonance width of 29 kHz. Examination of the slope of the stabilization system’s discriminant curve at zero error signal for buffer-gas-free cells uncovered an amount of correlation between the discriminant curve slope and atomic clock stability. It is demonstrated that the highest stability of atomic clocks in dynamic excitation mode is achieved at a ratio of scanning frequency and amplitude around 1.

Real-time clock prediction of multi-GNSS satellites and its application in precise point positioning

With the development of Global Navigation Satellite System (GNSS), multi-GNSS is expected to greatly benefit precise point positioning (PPP), especially during the outage of real time service (RTS). In this paper, we focus on the performance of multi-GNSS satellite clock prediction and its application in real-time PPP. Based on the statistical analysis of multi-system satellite clock products, a model consisting of polynomial and periodic terms is employed for multi-system satellite clock prediction. To evaluate the method proposed, both post-processed and real-time satellite clock products are employed in simulated real-time processing mode. The results show that the accuracy of satellite clock prediction is related to atomic clock type and satellite type. For GPS satellites, the average standard deviations (STDs) of Cs atomic clocks will reach as high as 0.65 ns while the STD of Rb atomic clocks is only about 0.15 ns. As for BDS and Galileo, the average STD of 2-hour satellite clock prediction are 0.30 ns and 0.06 ns, respectively. In addition, it is validated that real-time PPP can still achieve positioning accuracy of one to three decimeters by using products of 2-hour satellite clock prediction. Moreover, compared to the results of GPS-only PPP, multi-system can greatly enhance the accuracy of real-time PPP from 12.5% to 18.5% in different situations.

Demonstration of a Sub-Sampling Phase Lock Loop Based Microwave Source for Reducing Dick Effect in Atomic Clocks**Supported by the National Key Research and Development Program of China under Grant No 2017YFA0304400, and the National Natural Science Foundation of China under Grant Nos 91336213, 11703031, U1731132 and 11774108.

We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop (PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator (OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer (DDS) which is also referenced to the 100 MHZ OCXO to generate the final 6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are −47 dBc/Hz, −77 dBc/Hz, −104 dBc/Hz and −121 dBc/Hz at 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than 5.0 × 10−14τ1/2 when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.

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.

Spectral emission from the alkali inductively-coupled plasma: Theory and experiment

The weakly-ionized, alkali inductively-coupled plasma (ICP) has a long history as the light source for optical pumping. Today, its most significant application is perhaps in the rubidium atomic frequency standard (RAFS), arguably the workhorse of atomic timekeeping in space, where it is crucial to the RAFS’ functioning and performance (and routinely referred to as the RAFS’ “rf-discharge lamp”). In particular, the photon flux from the lamp determines the signal-to-noise ratio of the device, and variations in ICP brightness define the long-term frequency stability of the atomic clock as a consequence of the ac-Stark shift (i.e., the light-shift). Given the importance of Rb atomic clocks to diverse satellite navigation systems (e.g., GPS, Galileo, BeiDou) – and thereby the importance of alkali ICPs to these systems – it is somewhat surprising to find that the physical processes occurring within the discharge are not well understood. As a consequence, researchers do not understand how to improve the spectral emission from the lamp except at a trial-and-error level, nor do they fully understand the nonlinear mechanisms that result in ICP light instability. Here, we take a first step in developing an intuitive, semi-quantitative model of the alkali rf-discharge lamp, and we perform a series of experiments to validate the theory’s predictions.

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.

Optically-detected spin-echo method for relaxation times measurements in a Rb atomic vapor

We introduce and demonstrate an experimental method, optically-detected spin-echo (ODSE), to measure ground-state relaxation times of a rubidium (Rb) atomic vapor held in a glass cell with buffer-gas. The work is motivated by our studies on high-performance Rb atomic clocks, where both population and coherence relaxation times (T1 and T2, respectively) of the ‘clock transition’ (52S1/2 ) are relevant. Our ODSE method is inspired by classical nuclear magnetic resonance spin-echo method, combined with optical detection. In contrast to other existing methods, like continuous-wave double-resonance (CW-DR) and Ramsey-DR, principles of the ODSE method allow suppression of decoherence arising from the inhomogeneity of the static magnetic field across the vapor cell, thus enabling measurements of intrinsic relaxation rates, as properties of the cell alone. Our experimental result for the coherence relaxation time, specific for the clock transition, measured with the ODSE method is in good agreement with the theoretical prediction, and the ODSE results are validated by comparison to those obtained with Franzen, CW-DR and Ramsey-DR methods. The method is of interest for a wide variety of quantum optics experiments with optical signal readout.

Double-resonance spectroscopy in Rubidium vapour-cells for high performance and miniature atomic clocks

We report our studies on using microwave-optical double-resonance (DR) spectroscopy for a high-performance Rb vapour-cell atomic clock in view of future industrial applications. The clock physics package is very compact with a total volume of only 0.8 dm3. It contains a recently in-house developed magnetron-type cavity and a Rb vapour cell. A homed-made frequency-stabilized laser system with an integrated acousto-optical-modulator (AOM) – for switching and controlling the light output power– is used as an optical source in a laser head (LH). The LH has the overall volume of 2.5 dm3 including the laser diode, optical elements, AOM and electronics. In our Rb atomic clock two schemes of continuous-wave DR and Ramsey-DR schemes are used, where the latter one strongly reduces the light-shift effect by separation of the interaction of light and microwave. Applications of the DR clock approach to more radically miniaturized atomic clocks are discussed.

Imaging Microwave and DC Magnetic Fields in a Vapor-Cell Rb Atomic Clock

We report on the experimental measurement of the DC and microwave magnetic field distributions inside a recently-developed compact magnetron-type microwave cavity, mounted inside the physics package of a high-performance vapor-cell atomic frequency standard. Images of the microwave field distribution with sub-100 $\mu$m lateral spatial resolution are obtained by pulsed optical-microwave Rabi measurements, using the Rb atoms inside the cell as field probes and detecting with a CCD camera. Asymmetries observed in the microwave field images can be attributed to the precise practical realization of the cavity and the Rb vapor cell. Similar spatially-resolved images of the DC magnetic field distribution are obtained by Ramsey-type measurements. The T2 relaxation time in the Rb vapor cell is found to be position dependent, and correlates with the gradient of the DC magnetic field. The presented method is highly useful for experimental in-situ characterization of DC magnetic fields and resonant microwave structures, for atomic clocks or other atom-based sensors and instrumentation.