Observation of Spin Polarized Clock Transition in 87Sr Optical Lattice Clock

Atomic clocks operating at optical frequencies, with much better accuracy compared with microwave atomic clocks, have been assumed to be the next- generation time and frequency standards, Many applications will benefit from this lower frequency un- certainty of optical clocks, such as the re-definition of ＇the second＇, i.e. one of the seven base units of the international system of units （SI）, test of the time variation of fundamental physical constants and rel- ativity geodesy. Recently, the neutral atom lattice clock has achieved a lower frequency uncertainty com- pared with the optical ion clock, mainly due to the im- provement of the clock laser frequency stability refer- enced to a long high-finesse ULE cavity and the more accurate evaluation of black-body radiation shift. Strontium is an excellent candidate for the neutral atom optical clock. For the fermionic isotope of stron- tium, it has intrinsically less collision shift and the first order Zeeman shift can be removed by an inter- leaved probing approach.Recently, through the pre-cise measurement of the polarizability of strontium, the black body radiation （BBR） shift of the stron- tium lattice clock, which remains to be the limitation factor of its total frequency uncertainty, is reduced to a lower 10^-18 value.The instability of the strontium lattice clock has reached 3.1 × 10-16/√T, showing the significant advantage over the single ion optical clock. The total systematic uncertainty has reached 6.4 × 10^-18 in fractional frequency, which is the best among all optical clocks until now.     

GNSS clock corrections densification at SHAO: from 5 min to 30 s

High frequency multi-GNSS zero-difference applications like Precise Orbit Determination(POD)for Low Earth Orbiters(LEO)and high frequency kinematic positioning require corresponding high-rate GNSS clock corrections.The determination of the GNSS clocks in the orbit determination process is time consuming,especially in the combined GPS/GLONASS processing.At present,a large number of IGS Analysis Centers(AC)provide clock corrections in 5-min sampling and only a few ACs provide clocks in 30-s sampling for both GPS and GLONASS.In this paper,an efficient epoch-difference GNSS clock determination algorithm is adopted based on the algorithm used by the Center for Orbit Determination in Europe(CODE).The clock determination procedure of the GNSS Analysis Center at Shanghai Astronomical Observatory(SHAO)and the algorithm is described in detail.It is shown that the approach greatly speeds up the processing,and the densified 30-s clocks have the same quality as the 5-min clocks estimated based on a zero-difference solution.Comparing the densified 30-s GNSS clocks provided by SHAO with that of IGS and its ACs,results show that our 30-s GNSS clocks are of the same quality as that of IGS.Allan deviation also gives the same conclusion.Further validation of the SHAO 30-s clock product is performed in kinematic PPP and LEO POD.Results indicate that the positions have the same accuracy when using SHAO 30-s GNSS clocks or IGS(and its AC)finals.The robustness of the algorithm and processing approach ensure its extension to provide clocks in 5-s or even higher frequencies.The implementation of the new approach is simple and it could be delivered as a black-box to the current scientific software packages.     

Improvement of Stability of ~(40)Ca~+ Optical Clock with State Preparation

Stability is one of most important performances of an atomic clock. Here we describe our recent work on improving the stability of our 40 Ca+ optical clock. State preparation is adopted to transfer the ion to the groundstate magnetic sublevel of the clock transition, after the quenching laser transfers the ion to the ground state at each cycle. Using this method,the stability for ~(40)Ca~+ optical clock is improved to about 6.3 × 10~(-15)/τ~(1/2).Compared with 1.0 × 10~(-14)/τ~(1/2) in previous work, the averaging time is decreased to reach a given level of statistical uncertainty in a clock comparison.     

Optimization of temperature characteristics of a transportable ~(87)Rb atomic fountain clock

A high-performance transportable fountain clock is attractive for use in laboratories with high-precision time-frequency measurement requirements. This Letter reports the improvement of the stability of a transportable rubidium-87 fountain clock because of an optimization of temperature characteristics. This clock integrates its physical packaging, optical benches, microwave frequency synthesizers, and electronic controls onto an easily movable wheeled plate. Two optical benches with a high-vibration resistance are realized in this work. No additional adjustment is required after moving them several times. The Allan deviation of the fountain clock frequency was measured by comparing it with that of the hydrogen maser. The fountain clock got a short-term stability of 2.3 × 10~(-13) at 1 s and long-term stability on the order of 10~(-16) at 100,000 s.     

Direct Laser Cooling Al~+ Ion Optical Clocks

The Al~+ ion optical clock is a very promising optical frequency standard candidate due to its extremely small black-body radiation shift. It has been successfully demonstrated with the indirect cooled, quantum-logic-based spectroscopy technique. Its accuracy is limited by second-order Doppler shift, and its stability is limited by the number of ions that can be probed in quantum logic processing. We propose a direct laser cooling scheme of Al~+ ion optical clocks where both the stability and accuracy of the clocks are greatly improved. In the proposed scheme,two Al~+ traps are utilized. The first trap is used to trap a large number of Al~+ ions to improve the stability of the clock laser,while the second trap is used to trap a single Al~+ ion to provide the ultimate accuracy. Both traps are cooled with a continuous wave 167 nm laser. The expected clock laser stability can reach9.0×10~(-17)/τ~(1/2). For the second trap, in addition to 167 nm laser Doppler cooling, a second stage pulsed 234 nm two-photon cooling laser is utilized to further improve the accuracy of the clock laser. The total systematic uncertainty can be reduced to about 1×10~(-18). The proposed Al~+ ion optical clock has the potential to become the most accurate and stable optical clock.     

Phase-related noise characteristics of 780 nm band single-frequency lasers used in the cold atomic clock

We propose a method to directly measure phase-related noise characteristics of single-frequency lasers in the 728–980 nm band based on a 120°phase difference interferometer.Differential phase information of the laser under test is demodulated via the interferometer.Other parameters related to the phase noise characteristics such as linewidth at different observation time, phase/frequency noise, power spectrum density of phase/frequency fluctuation, and Allan deviation are further obtained.Frequency noise as low as 1 Hz~2/Hz can be measured using our system.Then the phase-related noise characteristics of two commercial lasers frequently used in cold atomic clocks are studied systematically by the method.Furthermore, several influencing factors and their relative evolution laws are also revealed, such as the pump current and frequency-locking control parameters.This would help to optimize the laser performance, select laser sources, and evaluate the system performance for cold atomic physics applications.     

Improvements and New Evaluation of NIM4 Caesium Fountain Clock at NIM in 2005-2006

The NIM4 caesium fountain clock has been operating stably and sub-continually since August 2003. We present our improvements on NIM4 in 2005-06 and the most recent evaluation for its frequency shifts with an uncertainty of 5 × 10^-15. A 203-day comparison between NIM4 and GPS time shows an agreement of 2 × 10^-14. Finally the construction of the NIM5 transportable caesium fountain clock is briefly reported.     

100 Gb/s all-optical clock recovery based on a monolithic dual-mode DBR laser

We experimentally demonstrate all-optical clock recovery for 100 Gb/s return-to-zero on–off keying signals based on a monolithic dual-mode distributed Bragg reflector(DBR) laser, which can realize both mode spacing and wavelength tuning. By using a coherent injection locking scheme, a 100 GHz optical clock can be recovered with a timing jitter of 530 fs, which is derived by an optical sampling oscilloscope from both the phase noise and the power fluctuation. Furthermore, for degraded injection signals with an optical signal-to-noise ratio as low as4.1 d B and a 25 km long distance transmission, good-quality optical clocks are all successfully recovered.     

Evaluation of the frequency instability limited by Dick effect in the microwave ~(199)Hg~+ trapped-ion clock

In the microwave ~(199)Hg~+ trapped-ion clock, the frequency instability degradation caused by the Dick effect is unavoidable because of the periodical interrogating field. In this paper, the general expression of the sensitivity function g(t)to the frequency fluctuation of the interrogating field with Nπ-pulse(N is odd) is derived. According to the measured phase noise of the 40.5-GHz microwave synthesizer, the Dick-effect limited Allan deviation of our ~(199)Hg~+ trapped-ion clock is worked out. The results indicate that the limited Allan deviations are about 1.75 × 10~(-13)τ~(1/2) and 3.03 × 10~(-13)τ~(1/2) respectively in the linear ion trap and in the two-segment extended linear ion trap under our present experimental parameters.     

Demonstration of a Sub-Sampling Phase Lock Loop Based Microwave Source for Reducing Dick Effect in Atomic Clocks

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 final6.835 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 d Bc/Hz,-77 dBc/Hz,-104 dBc/Hz and-121 dBc/Hz at1 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~(-14)τ~(1/2) 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.     

Dick Effect in the Integrating Sphere Cold Atom Clock

The Dick effect is an important factor limiting the frequency stability of sequentially-operating atomic frequency standards. Here we study the impact of the Dick effect in the integrating sphere cold atom clock(ISCAC). To reduce the impact of the Dick effect, a 5 MHz local oscillator with ultra-low phase noise is selected and a new microwave synthesizer is built in-house. Consequently, the phase noise of microwave signal is optimized. The contribution of the Dick effect is reduced to 2.5×10~(-13)τ~(-1/2)(τ is the integrating time). The frequency stability of 4.6 × 10~(-13)τ~(-1/2) is achieved. The development of this optimization can promote the space applications of the compact ISCAC.     

Wideband Tunable Frequency-Doubling Optoelectronic Oscillator Using a Polarization Modulator and an Optical Bandpass Filter

A wideband tunable frequency-doubling optoeleetronic oscillator(FD-OEO) is proposed and experimentally demonstrated based on a polarization modulator and an optical bandpass filter(OBPF). The central frequency of the correspondingly fundamental OEO could be adjusted by tuning the bandwidth and central frequency of the OBPF, which could also be regarded as a photonic-assisted tunable microwave filter. The frequency tuning range of the FD-OEO covers from 9.5 to 32.8 GHz, and the single sideband phase noise of the fundamental signal is lower than-100 dBc/Hz at an offset of 10 kHz. Moreover, the frequency stability of the generated signal is investigated by measuring its Allan deviation. The Allan deviation of the generated fundamental signal at 10 GHz is 2.39×10~(-9).     

Ultra-Stable Rubidium-Stabilized External-Cavity Diode Laser Based on the Modulation Transfer Spectroscopy Technique

We construct an ultra-stable external-cavity diode laser via modulation transfer spectroscopy referencing on a hyperfine component of the ST Rb D2 lines at 780 nm. The Doppler-free dispersion-like modulation transfer signal is obtained with high signal-to-noise-ratio. The instability of the laser frequency is measured by beating with an optical frequency comb which is phase-locked to an ultra-stable oven controlled crystal oscillator. The Allan deviation is 3.9 × 10-13 at I s averaging time and 9.8 ×10-14 at 90s averaging time.     

Continuous Dynamic Rotation Measurements Using a Compact Cold Atom Gyroscope

We present an experimental demonstration of the rotation measurement using a compact cold atom gyroscope.Atom interference fringes are observed in the stationary frame and the rotating frame,respectively.The phase shift and contrast of the interference fringe are experimentaiiy investigated.The results show that the contrast of the interference fringe is well held when the platform is rotated,and the phase shift of the interference fringe is iineariy proportional to the rotation rate of the platform.The long-term stability,which is evaluated by the overlapped Allan deviation,is 8.5×10~(-6)rad/s over the integrating time of 1000s.     

An Accurate Frequency Control Method and Atomic Clock Based on Coherent Population Beating Phenomenon

An accurate frequency control method and atomic clock based on the coherent population beating(CPB) phenomenon is implemented.In this scheme,the frequency difference of an rf and an atomic transition frequency can be digitally obtained by measuring the CPB oscillation frequency.The frequency measurement resolution of several milli-hertz can be achieved by using a 10 MHz oven controlled crystal oscillator as the reference.The expression of the Allan deviation of the CPB clock is theoretically deduced and it is revealed that the Allan deviation is inversely proportional to the signal-to-noise ratio and proportional to the line-width of coherent population trapping spectrum.We also approve that the CPB atomic clock has a large toleration of the drift of the local oscillator.In our CPB experimental system,a frequency instability of 3.0×10~(-12) at 1000 s is observed.The important feature of high frequency measurement resolution of the CPB method may also be used in magnetometers,atomic spectroscopy,and other related research.     

Uncertainty principle in larmor clock

It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency. The connection between the dwell time and the Larmor time has also been confirmed. Moreover, the results show that the behavior of the Larmor time depends on the height and width of the barrier.     

Microwave frequency transfer over a 112-km urban fiber link based on electronic phase compensation

We demonstrate the transmission of a microwave frequency signal at 10 GHz over a 112-km urban fiber link based on a novel simple-architecture electronic phase compensation system. The key element of the system is the low noise frequency divider by 4 to differentiate the frequency of the forward signal from that of the backward one, thus suppressing the effect of Brillouin backscattering and parasitic reflection along the link. In terms of overlapping Allan deviation,the frequency transfer instability of 4.2 × 10~(-15) at 1-s integration time and 1.6 × 10~(-18) at one-day integration time was achieved. In addition, its sensitivity to the polarization mode dispersion in fiber is analyzed by comparing the results with and without laser polarization scrambling. Generally, with simplicity and robustness, the system can offer great potentials in constructing cascaded frequency transfer system and facilitate the building of fiber-based microwave transfer network.     

Precision spectroscopy with a single ~(40)Ca~+ ion in a Paul trap

Precision measurement of the 4s2S1/2–3d2D5/2clock transition based on40Ca+ion at 729 nm is reported. A single40Ca+ion is trapped and laser-cooled in a ring Paul trap, and the storage time for the ion is more than one month. The linewidth of a 729 nm laser is reduced to about 1 Hz by locking to a super cavity for longer than one month uninterruptedly.The overall systematic uncertainty of the clock transition is evaluated to be better than 6.5×10-16. The absolute frequency of the clock transition is measured at the 10-15 level by using an optical frequency comb referenced to a hydrogen maser which is calibrated to the SI second through the global positioning system(GPS). The frequency value is 411 042 129776 393.0(1.6) Hz with the correction of the systematic shifts. In order to carry out the comparison of two40Ca+optical frequency standards, another similar40Ca+optical frequency standard is constructed. Two optical frequency standards exhibit stabilities of 1×10-14τ-1/2with 3 days of averaging. Moreover, two additional precision measurements based on the single trapped40Ca+ion are carried out. One is the 3d2D5/2state lifetime measurement, and our result of 1174(10) ms agrees well with the results reported in [Phys. Rev. A 62 032503(2000)] and [Phys. Rev. A 71 032504(2005)]. The other one is magic wavelengths for the 4s2S1/2–3d2D5/2clock transition; λ|m j|=1/2= 395.7992(7) nm and λ|m j|=3/2=395.7990(7) nm are reported, and it is the first time that two magic wavelengths for the40Ca+clock-transition have been reported.     

An Yb-fiber frequency comb phase-locked to microwave standard and optical reference

We present a fully stabilized Yb-fiber frequency comb locked to a microwave standard and an optical reference separately. The carrier-envelope offset frequency is generated by a standard f–2f interferometer with 40 dB signal-tonoise ratio. The offset frequency and the repetition rate are stabilized simultaneously to the radio frequency reference for more than 30 hours, and the fractional Allan deviation of the comb is the same as the microwave standard of 10^-12 at 1 s.Alternatively, the comb is locked to an ultra-stable optical reference at 972 nm using an intracavity electro-optic modulator,exhibiting a residual integrated phase noise of 458 mrad(1 Hz–10 MHz) and an in-loop tracking stability of 1.77× 10^-18 at 1 s, which is significantly raised by six orders comparing to the case locked to the microwave frequency standard.