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.

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.

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.

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.

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.

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.

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).

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.

Effective sideband cooling in an ytterbium optical lattice clock

Sideband cooling is a key technique for improving the performance of optical atomic clocks by preparing cold atoms and single ions into the ground vibrational state.In this work,we demonstrate detailed experimental research on pulsed Raman sideband cooling in a 171 Yb optical lattice clock.A sequence comprised of interleaved 578 nm cooling pulses resonant on the 1st-order red sideband and 1388 nm repumping pulses is carried out to transfer atoms into the motional ground state.We successfully decrease the axial temperature of atoms in the lattice from 6.5μK to less than 0.8μK in the trap depth of 24μK,corresponding to an average axial motional quantum number<nz><0.03.Rabi oscillation spectroscopy is measured to evaluate the effect of sideband cooling on inhomogeneous excitation.The maximum excitation fraction is increased from 0.8 to 0.86,indicating an enhancement in the quantum coherence of the ensemble.Our work will contribute to improving the instability and uncertainty of Yb lattice clocks.

Calculations of dynamic multipolar polarizabilities of the Cd clock transition levels

The pursuit of a systematic frequency uncertainty beyond 10^(-18) clock has triggered a multitude of investigations on the multipolar and higher-order lattice light shifts.The Cd atom has been proposed as a new candidate for the development of a lattice clock because of its smaller blackbody radiation shift at room temperature.Here,we apply an improved combined method of the Dirac-Fock plus core polarization and relativistic configuration interaction methods to calculate the dynamic multipolar polarizabilities of the Cd clock states.The effects of the high-order core-polarization potentials on the energies,reduced matrix elements,and multipolar polarizabilities have been evaluated systematically.The detailed comparison with available literature demonstrates that taking into account of the high-order core-polarization potentials is a simple and effective approach to improve the results of atomic properties for heavy atoms.

Rubidium-beam microwave clock pumped by distributed feedback diode lasers

A rubidium-beam microwave clock, optically pumped by a distributed feedback diode laser, is experimentally investigated. The clock is composed of a physical package, optical systems, and electric servo loops. The physical package realizes the microwave interrogation of a rubidium-atomic beam. The optical systems, equipped with two 780-nm distributed feedback laser diodes, yield light for pumping and detecting. The servo loops control the frequency of a local oscillator with respect to the microwave spectrum. With the experimental systems, the microwave spectrum, which has an amplitude of 4 n A and a line width of 700 Hz, is obtained. Preliminary tests show that the clock short-term frequency stability is 7 × 10^-11 at 1 s, and 3 × 10^-12 at 1000 s. These experimental results demonstrate the feasibility of the scheme for a manufactured clock.