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).

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.

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.

Decreasing the uncertainty of atomic clocks via real-time noise distinguish

The environmental perturbation on atoms is a key factor restricting the performance of atomic frequency standards, especially in the long-term scale. In this Letter, we perform a real-time noise distinguish(RTND) to an atomic clock to decrease the uncertainty of the atomic clock beyond the level that is attained by the current controlling method. In RTND, the related parameters of the clock are monitored in real time by using the calibrated sensors, and their effects on the clock frequency are calculated. By subtracting the effects from the error signal, the local oscillator is treated as equivalently locked to the unperturbed atomic levels. In order to perform quantitative tests, we engineer time-varying noise much larger than the intrinsic noise in our fountain atomic clock. By using RTND, the influences of the added noises are detected and subtracted precisely from the error signals before feeding back to the reference oscillator. The result shows that the statistical uncertainty of our fountain clock is improved by an order of magnitude to 2 × 10^(-15). Besides, the frequency offset introduced by the noise is also corrected, while the systematic uncertainty is unaffected.

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.

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.

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.

An optimized ion trap geometry to measure quadrupole shifts of ^(171)Yb~＋ clocks

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the ^(171)Yb ion.This trap will minimize the quadrupole shift due to the harmonic component of the confining potential by an order of magnitude.This will be useful to reduce the uncertainties in the clock frequency measurements of the 6s ~2S_(1/2)→4f^(13)6s^2 ~2F_(7/2)and 6s ~2S_(1/2)→5d^2D_(3/2) transitions,from which we can deduce the precise values of the quadrupole moments(0s) of the 4f^(13)6s^2 ~2F_(7/2) and 5d^2D_(3/2) states.Moreover,it may be able to affirm the validity of the measured 0 value of the4f^(13)6s^2~2F_(7/2) state,for which three independent theoretical studies defer almost by one order of magnitude from the measurement.We also calculate 0s using the relativistic coupled-cluster(RCC) method.We use these 0 values to estimate the quadrupole shift that can be measured in our proposed ion trap experiment.

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.

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.

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.

Design of Atomic Time Scale Release System for Multiple Laboratories

The atomic time scale release system for multiple laboratories is completed by modular design according to the atomic clock data provided by eight domestic punctual laboratories.The system includes the three modules,the processing of atomic clock data,the calculation of atomic time scale and the release of atomic time scale data,using MATLAB for data processing and time scale calculation,and using GUI for data visualization design.The system has clear process of the algorithm,simple function modules and friendly human-machine interface.The operation results of actual data show that the time difference between the integrated atomic time scale of the system and UTC is better than±10ns,and the content of data release can meet the needs of the scientific research in related fields in China.

Cold atom clocks and their applications in precision measurements

Cold atom clocks have made remarkable progresses in the last two decades and played critical roles in precision measurements. Primary Cs fountain frequency standards have achieved a total uncertainty of a few parts in 1016, and the best optical clock has reached a type B uncertainty below 10-18. Besides applications in the metrology, navigation, etc.,ultra-stable and ultra-accurate atomic clocks have also become powerful tools in the basic scientific investigations. In this paper, we focus on the recent developments in the high-performance cold atomic clocks which can be used as frequency standards to calibrate atomic time scales. The basic principles, performances, and limitations of fountain clocks and optical clocks based on signal trapped ion or neutral atoms are summarized. Their applications in metrology and other areas are briefly introduced.

Frequency steering of spaceborne clocks based on XPNAV-1 observations

Due to high stable rotations, timing of pulsars provides a natural tool to correct the frequency deviation of spaceborne atomic clocks. Based on processing the observational data about a year of Crab pulsar given by XPNAV-1 satellite, we study the possibility of correcting the frequency deviation of spaceborne atomic clocks using pulsar timing. According to the observational data in X-ray band and the timing model parameters from radio observations, the pre-fit timing residuals with a level of 67.66 μs are obtained. By fitting the slope of the timing residuals affected by the faked frequency-biased reference clock, we estimated successfully the relative frequency deviation of the reference clock. For a satellite clock with frequency deviation of the order about 10^(-12), a calibration accuracy with relative error of about 2% can be obtained from the Crab pulsar’s data for one year.The stability of the time scale based on Crab pulsar is about 10^(-12) for an interval of one year.

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 n T deviation in space and a 0.06 n T 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).

Light-shift induced by two unbalanced spontaneous decay rates in EIT(CPT)spectroscopies under Ramsey pulse excitation

Light shift is important and inevitably affects the long-term stability of an atomic clock.In this work,considering two unbalanced branches of the spontaneous decay rate in a three-level system,we studied the frequency shifts of electromagnetically induced transparency(EIT)and coherent population trapping(CPT)clocks operating under the pulse sequence regime by numerically solving the Liouville density matrix equations.The results show that the frequency shifts are larger when the two branches of spontaneous emission rate are not equal compared to the equal case.In addition,in EIT-Ramsey,the effect of the unbalanced branches of the spontaneous decay rate and relaxations of low-energy states on the frequency shift is greater than that of Rabi frequency.In CPT-Ramsey,the relaxations of low-energy states play a dominant role in frequency shift.