A frequency servo SoC with output power stabilization loop technology for miniaturized atomic clocks

A frequency servo system-on-chip(FS-SoC)featuring output power stabilization technology is introduced in this study for high-precision and miniaturized cesium(Cs)atomic clocks.The proposed power stabilization loop(PSL)technique,incorporating an off-chip power detector(PD),ensures that the output power of the FS-SoC remains stable,mitigating the impact of power fluctuations on the atomic clock's stability.Additionally,a one-pulse-per-second(1PPS)is employed to syn-chronize the clock with GPS.Fabricated using 65 nm CMOS technology,the measured phase noise of the FS-SoC stands at-69.5 dBc/Hz@100 Hz offset and-83.9 dBc/Hz@1 kHz offset,accompanied by a power dissipation of 19.7 mW.The Cs atomic clock employing the proposed FS-SoC and PSL obtains an Allan deviation of 1.7×10^(-11) with 1-s averaging time.

Review of chip-scale atomic clocks based on coherent population trapping

Research on chip-scale atomic clocks （CSACs） based on coherent population trapping （CPT） is reviewed. The back- ground and the inspiration for the research are described, including the important schemes proposed to improve the CPT signal quality, the selection of atoms and buffer gases, and the development of micro-cell fabrication. With regard to the re- liability, stability, and service life of the CSACs, the research regarding the sensitivity of the CPT resonance to temperature and laser power changes is also reviewed, as well as the CPT resonance＇s collision and light of frequency shifts. The first generation CSACs have already been developed but its characters are still far from our expectations. Our conclusion is that miniaturization and power reduction are the most important aspects calling for further research.

Integrated physics package of a chip-scale atomic clock

The physics package of a chip-scale atomic clock （CSAC） has been successfully realized by integrating vertical cavity surface emitting laser （VCSEL）, neutral density （ND） filter, λ/4 wave plate, 87Rb vapor cell, photodiode （PD）, and magnetic coil into a cuboid metal package with a volume of about 2.8 cm3. In this physics package, the critical component, 87Rb vapor cell, is batch-fabricated based on MEMS technology and in-situ chemical reaction method. Pt heater and thermistors are integrated in the physics package. A PTFE pillar is used to support the optical elements in the physics package, in order to reduce the power dissipation. The optical absorption spectrum of 87Rb D1 line and the microwave frequency correction signal are successfully observed while connecting the package with the servo circuit system. Using the above mentioned packaging solution, a CSAC with short-term frequency stability of about 7 × 10^-10τ-1/2 has been successfully achieved, which demonstrates that this physics package would become one promising solution for the CSAC.

Stable ^(85)Rb micro vapour cells:fabrication based on anodic bonding and application in chip-scale atomic clocks

We describe the microfabrication of ^85Rb vapour cells using a glass-silicon anodic bonding technique and in situ chemical reaction between rubidium chloride and barium azide to produce Rb. Under controlled conditions, the pure metallic Rb drops and buffer gases were obtained in the cells with a few mm^3 internal volumes during the cell sealing process. At an ambient temperature of 90 ℃ the optical absorption resonance of ^85Rb D1 transition with proper broadening and the corresponding coherent population trapping （CPT） resonance, with a signal contrast of 1.5% and linewidth of about 1.7 kHz, have been detected. The sealing quality and the stability of the cells have also been demonstrated experimentally by using the helium leaking detection and the after-9-month optoelectronics measurement which shows a similar CPT signal as its original status. In addition, the physics package of chip-scale atomic clock （CSAC） based on the cell was realized. The measured frequency stability of the physics package can reach to 2.1 × 10^-10 at one second when the cell was heated to 100 ℃ which proved that the cell has the quality to be used in portable and battery-operated devices.

A preliminary experiment of determining the geopotential difference using two hydrogen atomic clocks and TWSTFT technique

General relativity theory(GRT)concludes that a precise clock ticks at different running rates if it is under the influence of different geopotentials.Therefore,by comparing the running rates of clocks at arbitrary two stations,the geopotential difference between them can be determined.In this study,with the help of two hydrogen atomic clocks(noted as H-masers),using the two-way satellite time and frequency transfer(TWSTFT)technique,we carried out experiments of the geopotential difference determination at the China Aerospace Science&Industry Corporation(CASIC),Beijing.Here the ensemble empirical mode decomposition(EEMD)method is adopted to remove periodic signals included in the original observations.Finally,the clock-comparison-determined geopotential difference in the experiments is determined.Results show that the difference between the geopotential difference determined by GRT and that determined by measuring tape is about 1316.1±931.0 m2s-2,which is equivalent to 134.3±95.0 m in height,and in consistence with the stability of the H-masers applied in the experiments(at the level of10-15/day).With the rapid improvement of atomic clocks’accuracy,the geopotential determination by accurate clocks is prospective,and it is promising to realize the unification of the world vertical height system(WVHS).

Theoretical analysis of suppressing Dick effect in Ramsey-CPT atomic clock by interleaving lock

For most pulsed atomic clocks, the Dick effect is one of the main limits to reach its frequency stability limitation due to quantum projection noise. In this paper, we measure the phase noise of the local oscillator in the Ramsey-CPT atomic clock and calculate the Dick effect induced Allan deviation based on a three-level atomic model, which is quite different from typical atomic clocks. We further present a detailed analysis of optimizing the sensitivity function and minimizing the Dick effect by interleaving lock. By optimizing the duty circle of laser pulses, average time during detection and optical intensity of laser beam, the Dick effect induced Allan deviation can be reduced to the level of 10 14.

Ramsey-CPT spectrum with the Faraday effect and its application to atomic clocks

A method that obtains the Ramsey-coherent population trapping （CPT） spectrum with the Faraday effect is investi- gated. An experiment is implemented to detect the light polarization components generated from the Faraday effect. The experimental results agree with the theoretical calculations based on the Liouville equation. By comparing with the method without using the Faraday effect, the potential of this method for a CPT-based atomic clock is assessed. The results indicate that this method should improve the short-term frequency stability by several times.

Physics package based on intracavity laser cooling ^(87)Rb atoms for space cold atom microwave clock

This article proposes a new physics package to enhance the frequency stability of the space cold atom clock with the advantages of a microgravity environment. Clock working processes, including atom cooling, atomic state preparation,microwave interrogation, and transition probability detection, are integrated into the cylindrical microwave cavity to achieve a high-performance and compact physics package for the space cold atom clock. We present the detailed design and ground-test results of the cold atom clock physics package in this article, which demonstrates a frequency stability of 1.2×10^(-12) τ^(-1/2) with a Ramsey linewidth of 12.5 Hz, and a better performance is predicted with a 1 Hz or a narrower Ramsey linewidth in microgravity environment. The miniaturized cold atom clock based on intracavity cooling has great potential for achieving space high-precision time-frequency reference in the future.

A Yb optical clock with a lattice power enhancement cavity

We construct a power enhancement cavity to form an optical lattice in an ytterbium optical clock.It is demonstrated that the intra-cavity lattice power can be increased by about 45 times,and the trap depth can be as large as 1400Er when laser light with a power of only 0.6 W incident to the lattice cavity.Such high trap depths are the key to accurate evaluation of the lattice-induced light shift with an uncertainty down to~1×10-18.By probing the ytterbium atoms trapped in the power-enhanced optical lattice,we obtain a 4.3 Hz-linewidth Rabi spectrum,which is then used to feedback to the clock laser for the close loop operation of the optical lattice clock.We evaluate the density shift of the Yb optical lattice clock based on interleaving measurements,which is-0.46(62)mHz.This result is smaller compared to the density shift of our first Yb optical clock without lattice power enhancement cavity mainly due to a larger lattice diameter of 344μm.

Measurements of Majorana transition frequency shift in caesium atomic fountain clocks

The caesium atomic fountain clock is a primary frequency standard.During its operation,a Majorana transition frequency shift will occur once a magnetic field at some special locations along the atomic trajectory is singular.In this study,by developing a physical model,we analyzed the magnetic field requirements for atomic adiabatic transition and calculated the influence of the Majorana atomic transition on the atomic state via a quantum method.Based on the simulation results for the magnetic field in the fountain clock,we applied the Monte Carlo method to simulate the relationship between the Majorana transition frequency shift and the magnetic field at the entrance of the magnetic shielding,as well as the initial atomic population.Measurement of the Majorana transition frequency shift was realized by state-selecting asymmetrically populated atoms.The relationship between the Majorana transition frequency shift and the axial magnetic field at the entrance of the magnetic shielding was obtained.The measured results were essentially consistent with the calculated results.Thus,the magnetic field at the entrance of the magnetic shielding was configured,and the Majorana transition frequency shift of the fountain clock was calculated to be 4.57×10^(-18).

Analysis of error sources on orbital atomic clocks’stability

As a rule,stability calculation of atomic clock requires observations with equivalent sampling interval.Apart from atomic clocks in laboratory,orbital atomic clock stability calculations are impacted of raw data sampling intervals,noncontinuous time series,non-data segment,frequency drift,and other factors.So,the calculated stability results are not so exact.In this article,the impacts of kinds of error sources on Allan and Hadamard variances are analyzed using global positioning system satellite precise clock offset data.And the laws of variety are summarized.

Miniaturized optical system for atomic fountain clock

Using modularized components, we have built a miniaturized optical system for 87Rb atomic fountain clock that is fitted on an 80 cm × 60 cm optical breadboard. Compared with the conventional optical setup on the table, our system is more compact, more robust and miniaturized. Taking advantage of this system, laser beams are transmitted through eight optical fibre patch cords from the optical breadboard to an ultra high vacuum system. This optical setup has operated for five months in our fountain system and required no alignment.

Efforts towards a low-temperature-sensitive physics package for vapor cell atomic clocks

Strong environmental dependence is an intractable problem for vapor cell clocks,for which the high-temperature sensitivity of the physics package is considered one of the dominant reasons.In this paper,we report the design and realization of a low-temperature-sensitive physics package for vapor cell clocks.The physics package comprises three layers of magnetic shields,three layers of heating ovens,and the cavity-cell assembly.The cavity-cell assembly employs a compact magnetron-type cavity and a Rb vapor cell sealed with N2-Ar mixed buffer gas.The dependence of the clock frequency on temperature fluctuation is evaluated to be 2×10^(−11)/℃.In pursuit of the stable temperature,a three-stage temperature regulator is implemented on the physics package.It adopts a combination of open andclosed-loop control to address the problem of significant thermal coupling between the heating ovens.Under a laboratory environment,the measured Hadamard deviation of the temperature variation is 4×10^(−5)℃in 1 day of averaging.

Recent improvements on the atomic fountain clock at SIOM

We report the recent advance in our rubidium atomic fountain clock（AFC）. The parameters of the Ramsey cavity are optimized by balancing the coupling from the two ports. The temperature control system of the Ramsey interaction region is renovated, and the resonant temperature of the Ramsey cavity is regulated to be slightly above the room temperature.The quality of magnetic environment in the Ramsey interaction region is also improved. A new digital-to-analog converter（DAC） circuit that controls the local oscillator is adopted to decrease the noise of the oven-controlled crystal oscillator output. As a result, the short-term fractional frequency stability of 2.7 × 10^-13τ^-1/2τand the long-term fractional frequency stability of 1.6 × 10^-15 at the average time of 32800 s are achieved.

Improvement of the short-term stability of atomic fountain clock with state preparation by two-laser optical pumping

To improve the signal to noise ratio(SNR)and the short-term stability of cesium atomic fountain clocks,the work of two-laser optical pumping is presented theoretically and experimentally.The short-term stability of the NIM6 fountain clock has been improved by preparing more cold atoms in the|F=4,m_(F)=0>clock state with a shortened cycle time.Two π-polarized laser beams overlapped in the horizontal plane have been applied after launching,one is resonant with|F=4>→|F′=4>transition and the other is resonant with|F=3>→|F′=4>transition.With optical pumping,the population accumulated in the|m_(F)=0>clock state is improved from 11%to 63%,and the detection signal is increased by a factor of 4.2,the SNR of the clock transition probability and the short-term stability are also improved accordingly.

Optical state selection process with optical pumping in a cesium atomic fountain clock

We propose and realize a new optical state selection method on a cesium atomic fountain clock by applying a two-laser 3-3'optical pumping configuration to spin polarize atoms.The atoms are prepared in|F=3,mF=0>clock state with optical pumping directly after being launched up,followed by a pushing beam to push away the atoms remaining in the|F=4>state.With a state selection efficiency exceeding 92%,this optical method can substitute the traditional microwave state selection,and helps to develop a more compact physical package.A Ramsey fringe has been achieved with this optical state selection method,and a contrast of 90%is obtained with a full width half maximum of 0.92 Hz.The short-term frequency stability of 6.8×10^(-14)(τ/s)^(-1/2) is acquired.In addition,the number of detected atoms is increased by a factor of 1.7 with the optical state selection.

Integrated, reliable laser system for an ^(87)Rb cold atom fountain clock

We designed, assembled, and tested a reliable laser system for ^(87)Rb cold atom fountain clocks. The laser system is divided into four modules according to function, which are convenient for installing, adjusting, maintaining, and replacing of the modules. In each functional module, all optical components are fixed on a baseplate with glue and screws, ensuring the system's structural stability. Mechanical stability was verified in a 6.11g RMS randomvibration test, where the change in output power before and after vibration was less than 5%. Thermal stability was realized by optimizing of the structure and appropriate selection of component materials of the modules through thermal simulation. In the laser splitting and output module, the change in laser power was less than 20% for each fiber in thermal cycles from 5℃ to 43℃. Finally,the functionality of the laser system was verified for a rubidium fountain clock.

The time and frequency system of the Tianma 65 m radio telescope

A time and frequency system is a critical component of Very Long Baseline Interferometry(VLBI)stations,providing stable and reliable standards that directly impact data processing quality.At the Tianma 65 m radio telescope(TMRT),this system has been meticulously designed to ensure long-term reliability and high performance.It incorporates high-performance hydrogen atomic clocks,high-precision time standards,automatic signal switching,and robust system software.This comprehensive approach has enabled the system to achieve long-term reliable operation,successfully supporting both major national engineering tasks and daily scientific observations.The effectiveness of the system is evidenced by its consistent delivery of the precision and stability required for radio astronomy.This article provides an in-depth exploration of the design and operation of the time and frequency system at the Tianma 65 m telescope,examining various aspects of its architecture,implementation,and performance.By sharing these insights,we aim to contribute knowledge that could benefit similar systems at other VLBI stations,greatly advancing radio astronomy infrastructure.

Physical Space Is Finite

Metrological analysis shows that any clock in inertial motion in infinite space shall not have time dilation, due to relativity of such motion in such space. On the other hand, atomic clock in inertial motion in finite space shall exhibit time dilation, due to alteration of momentum of clock-defining particle caused by nonzero curvature of trajectory of such motion in such space. Therefore, time dilation experiment of atomic clock in inertial motion in physical space provides a direct and decisive way of determining geometry of physical space in real-time. Phenomenon of time dilation of atomic clock in inertial motion in physical space has long been observed and confirmed experimentally. Therefore, extent of physical space has to be finite, consistent with result of high precision experiment of free particle in high-speed motion conducted a decade ago.Keywords Geometry of Physical Space, Time Dilation, Atomic Clock, Special Relativity Theory.

High-performance coherent population trapping clock based on laser-cooled atoms

We present a coherent population trapping clock system based on laser-cooled^(87)Rb atoms.The clock consists of a frequency-stabilized CPT interrogation laser and a cooling laser as well as a compact magneto-optical trap,a highperformance microwave synthesizer,and a signal detection system.The resonance signal in the continuous wave regime exhibits an absorption contrast of~50%.In the Ramsey interrogation method,the linewidth of the central fringe is31.25 Hz.The system achieves fractional frequency stability of 2.4×10^(-11)/(√τ),which goes down to 1.8×10^(-13)at 20000 s.The results validate that cold atom interrogation can improve the long-term frequency stability of coherent population trapping clocks and holds the potential for developing compact/miniature cold atoms clocks.