A Compact Direct Digital Frequency Synthesizer for the Rubidium Atomic Frequency Standard

A compact direct digital frequency synthesizer （DDFS） for system-on-chip implementation of the high precision rubidium atomic frequency standard is developed. For small chip size and low power consumption, the phase to sine mapping data is compressed using sine symmetry technique, sine-phase difference technique, quad line approximation technique,and quantization and error read only memory （QE-ROM） technique. The ROM size is reduced by 98% using these techniques. A compact DDFS chip with 32bit phase storage depth and a 10bit on-chip digital to analog converter has been successfully implemented using a standard 0.35μm CMOS process. The core area of the DDFS is 1.6mm^2. It consumes 167mW at 3.3V,and its spurious free dynamic range is 61dB.

Generation of Continuous-Wave 194 nm Laser for Mercury Ion Optical Frequency Standard

A 194-nm cw laser is an essential part in the mercury ion optical frequency standard. We report the generation of over 2mW continuous-wave radiation at 194nm in a beta barium borate crystal using a simple sum frequency mixing （SFM） system. One source beams at 718nm is resonantly enhanced with a cavity and the other at 266mn makes a single pass. Considering the walk-off effect in SFM, the source beam waists are designed to be elliptical, thus the conversion efficiency can be promoted. The 266-nm beam produced by frequency doubling of 532-nm laser is shaped close to the diffraction limit to achieve better mode matching.

Optimal Microwave Radiation Field Parameters for Mercury Ion Microwave Frequency Standards

We propose a method to determine the optimal power of the microwave resonance transition that simultaneously improves the signal-to-noise ratio and reduces line width based on saturation broadening theory and experiment. Saturation broadening spectra of the ground state hyperfine transition of trapped 199Hg＋ ions are measured and analyzed. The value of the optimal microwave power is obtained by using the proposed method and is verified. Rabi oscillations decay spectra of trapped 199Hg＋ ions are observed and the optimal microwave irradiation time for the maximum transition signal intensity is determined. This work will help to improve the short-term frequency stability of the mercury ion microwave frequency standard.

A 532 nm molecular iodine optical frequency standard based on modulation transfer spectroscopy

We report construction of an iodine-stabilized laser frequency standard at 532 nm based on modulation transfer spectroscopy(MTS)technology with good reproducibility.A frequency stability of 2.5×10^(-14)at 1 s averaging time is achieved,and the frequency reproducibility has a relative uncertainty of 3.5×10^(-13),demonstrating the great stability of our setup.The systematic uncertainty of the iodine-stabilized laser frequency standard is evaluated,especially the contribution of the residual amplitude modulation(RAM).The contribution of the RAM in MTS cannot be evaluated directly.To solve this problem,we theoretically deduce the MTS signal with RAM under large modulation depth,and prove that the non-symmetric shape of the MTS signal is directly related to the MTS effect.The non-symmetric shape factor can be calibrated with a frequency comb,and in real experiments,this value can be obtained by least-squares fitting of the MTS signal,from which we can infer the RAMinduced frequency shift.The full frequency uncertainty is evaluated to be 5.3 kHz(corresponding to a relative frequency uncertainty of 9.4×10^(-12)).The corrected transition frequency has a difference from the BIPM-recommended value of 2 kHz,which is within 1σ uncertainty,proving the validity of our evaluation.

Dual-Wavelength Bad Cavity Laser as Potential Active Optical Frequency Standard

We experimentally realize the dual-wavelength bad cavity laser for the first time. As the Cs cell temperature is kept between 118℃ and 144℃, both the 1359nm and 147Ohm lasing outputs of dual-wavelength bad cavity laser are detected. The laser output power of dual-wavelength bad cavity laser is measured when changing the 455 nm pumping laser frequency and power at 127℃ Cs cell temperature. Both the 1359 nm laser and the 1470 nm laser are working at the deep bad cavity regime, and the ratio between the linewidth of cavity mode and the laser gain bandwidth a ≈ 40 for 1359nm and 1470nm lasers. The 147Ohm laser linewidth is measured to be 407.3Hz. The dual-wavelength bad cavity laser operating on atomic transitions demonstrated here has a potential in the application as a stable optical local oscillator, even an active optical frequency standard directly in the future.

Experimental Scheme of 633 nm and 1359 nm Good-Bad Cavity Dual-Wavelength Active Optical Frequency Standard

The experimental scheme of 633 nm and 1359 nm good-bad cavity dual-wavelength active optical frequency stan- dard is proposed, where He-Ne 633nm and Cs 1359nm stimulated emissions are working at good-cavity and bad-cavity regimes, respectively. The cavity length is stabilized by locking the 633nm output frequency to a super-cavity with the Pound Drever-Hall （PDH） technique. The frequency stability of 1359 nm bad-cavity stim- ulated emission output is then expected to be further improved by at least 1 order of magnitude than the 633nm PDH system due to the suppressed cavity pulling effect of active optical clock, and the quantum limited linewidth of 1359nm output is estimated to be 72.5 mHz.

The time and frequency standard system for FAST receivers

This paper reports on the time and frequency standard system for the Five-hundred meter Aperture Spherical radio Telescope(FAST),including the system design,stability measurements and pulsar timing observations.The stability and drift rate of the frequency standard are calculated using 1-year monitoring data.The UTC-NIM Disciplined Oscillator(NIMDO)system improves the system time accuracy and stability to the level of 5 ns.Pulsar timing observations were carried out for several months.The weighted RMS of timing residuals reaches the level of less than 3.0μs.

Computed Tidal Relativistic Red-Shifts of Frequency Standards on Earth and in Space Stations

Frequencies of frequency standards are shifted by the local static gravity red shifts and also modulated by the tidal relativistic red shifts. We compute the tidal relativistic red shifts using a time-domain method and present the numerical results for the National Institute of Metrology （NIM） in Beijing, Laboratoire National de Metrologie et Essais-Systeme de References Temps-Espaee （LNE-SYRTE） in Paris and Physikalisch-Teehnische Bundesanstalt （PTB） in Braunschweig. The differences of the tidal relativistic red shift approach as large as 1.1 × 10^-16 when frequency standards at NIM are compared with those at SYRTE and PTB. Moreover, the tidal relativistic red shifts of frequency standards in space stations are also computed.

A 420nm Blue Diode Laser for the Potential Rubidium Optical Frequency Standard

We report a 42Ohm external cavity diode laser with an interference filter （IF） of 0.5am narrow-bandwidth and 79% high transmission, which is first used for Rb optical frequency standard. The IF and the cat-eye reflector are used for selecting wavelength and light feedback, respectively. The measured laser linewidth is 24 kHz when the diode laser is free running. Using this narrow-linewidth IF blue diode laser, we realize a compact Rb optical frequency standard without a complicated PDH system. The preliminary stability of the Rb optical frequency standard is 2 × 10^-13 at I s and decreases to 1.9 ×10^-14 at 1000s. The narrow-linewidth characteristic makes the IF blue diode laser a well suited candidate for the compact Rb optical frequency standard.

Dick Effect in a Microwave Frequency Standard Based on Laser-Cooled 113Cd+ Ions

The Dick effect is one of the main limits to the frequency stability of a passive frequency standard, especially for the fountain clock and ion dock operated in pulsed mode which require unavoidable dead time during interrogation. Here we measure the phase noise of the interrogation oscillator applied in the microwave frequency standard based on laser-cooled 113^Cd＋ ions, and analyze the Allan deviation limited by the Dick effect. The results indicate that the Dick effect is one of the key issues for the cadmium ion dock to reach expected frequency stability. This problem can be resolved by interrogating the local oscillator continuously with two ion traps.

Compact extended cavity diode laser system for small optically pumped cesium beam frequency standards

A compact extended cavity diode laser （ECDL） system operating at 852 nm for small optically pumped cesium （Cs） beam frequency standards was reported. ECDL and a saturated absorption spectroscopy setup were all built in an aluminum box with dimension of 10 × 10 × 7 （cm）. ECDL was based on a Littman-Metcaff configuration, whose free-running linewidth was less than 600 kHz. A digital automatic frequency lock unit （AFLU） was developed to lock the laser frequency to specify Cs absorption lines automatically and re-lock it in case of lock broken. With AFLU, the laser frequency was continuously locked for several weeks.

Second harmonic 423-nm laser generated by BIBO crystal for calcium optical frequency standard

Calcium is one prospective element for the modern optical frequency standard. The 423-nm transition line of calcium atoms has been widely used in laser slowing and laser cooling, the precise spectrum measurement, and the magnetic optical trapping （MOT）. However, there is no any available commercial diode laser working at this wavelength. We built a 423-nm laser based on extra bow-tie cavity and by using a Brewstercut uncoated BIBO （BiB306） crystal, which worked at room temperature, with conversion efficiency of 3.75%, and a potential up to 20%.

Analysis and Design of an Improved Servo System for Rubidium Atomic Frequency Standard

In this paper, we analyze and design a new type of servo system with noninteger voltage controlled crystal oscillator （VCXO） for rubidium atomic frequency standard （RAFS）, which does not require fractional frequency synthesizer. By the estab- lishment of the loop equations with noises and drifts, we prove that all the components of the loop can affect its performance in- dex, and in which, RAFS long-term frequency stability is mainly determined by frequency multiplier, quantum system, and servo amplifier; the short-term one is mostly decided by VCXO. Owing to the elimination of the frequency synthesizer and its additive mixing unit, we can reduce phase noise and stray of the servo sys- tem, and it is favorable for miniaturizing the RAFS system. In addition, we adopt some targeted optimization measures to im- prove the frequency stability index. The good short-term fre- quency stability index is also validated by the test results.

Improvement of Laser Frequency Stabilization for the Optical Pumping Cesium Beam Standard

A method is presented to improve the laser frequency stabilization for the optical pumping cesium clock. By comparing the laser frequency stabilization of different schemes, we verify that the light angle is an important factor that limits the long-term frequency stability. We minimize the drift of the light angle by using a fiber- coupled output, and lock the frequency of a distributed-feedback diode laser to the fluorescence spectrum of the atomic beam. The measured frequency stability is about 3.5 ×10^-11 at i s and reaches 1.5 × 10^-12 at 2000s. The Allan variance keeps going down for up to thousands of seconds, indicating that the medium- and long-term stability of the laser frequency is significantly improved and perfectly fulfills the requirement for the optical pumping cesium clock.

A diode laser spectrometer at 634 nm and absolute frequency measurements using optical frequency comb

This paper reports that two identical external-cavity-diode-laser （ECDL） based spectrometers are constructed at 634nm referencing on the hyperfine B-X transition R（80）8-4 of 127I2. The lasers are stabilized on the Doppler-free absorption signals using the third-harmonic detection technique. The instability of the stabilized laser is measured to be 2.8 × 10^-12 （after 1000 s） by counting the beat note between the two lasers. The absolute optical frequency of the transition is, for the first time, determined to be 472851936189.5 kHz by using an optical frequency comb referenced on the microwave caesium atomic clock. The uncertainty of the measurement is less than 4.9 kHz.

Decreased vibrational susceptibility of Fabry-Perot cavities via designs of geometry and structural support

Ultra-stable optical cavities are widely used for laser frequency stabilization. In these experiments the laser performance relies on the length stability of the Fabry-Perot cavities. Vibration-induced deformation is one of the dominant factors that affect the stability of ultra-stable optical cavities. We have quantitatively analysed the elastic deformation of Fabry-Perot cavities with various shapes and mounting configurations. Our numerical result facilitates a novel approach for the design of ultra-stable cavities that are insensitive to vibrational perturbations. This approach can be applied to many experiments such as laser frequency stabilization, high-precision laser spectroscopy, and optical frequency standards.

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

Precision measurement of the 4s2 S1/2-3d2 D5/2 clock transition based on 40Ca＋ ion at 729 nm is reported. A single 40Ca＋ 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 411 042 129 776 393.0（1.6） Hz with the correction of the systematic shifts. In order to carry out the comparison of two 40Ca＋ optical frequency standards, another similar 40Ca＋ optical frequency standard is constructed. Two optical frequency standards exhibit stabilities of 1 × 10^-14 T-1/2 with 3 days of averaging. Moreover, two additional precision measurements based on the single trapped 40Ca＋ ion are carried out. One is the 3d2Ds/2 state 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 4s2S1/2-3d2Ds/2 clock transition; λ ｜mj｜=1/2= 395.7992（7） nm and λ｜m｜=3/2 = 395.7990（7） nm are reported, and it is the first time that two magic wavelengths for the 40Ca＋ clock-transition have been reported.

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.

Transferring the stability of iodine-stabilized diode laser at 634 nm to radio frequency by an optical frequency comb

An optical flequency comb phase-locked on an iodine frequency stabilized diode laser at 634 nm is constructed to transfer the accuracy and stability from the optical domain to the radio frequency domain. An external-cavity diode laser is frequency-stabilized on the Doppler-free absorption signals of the hyperfine transition R（80）8-4 using the third-harmonic detection technique. The instability of the ultra-stable optical oscillator is determined to be 7 ×10^-12 by a cesium atomic clock via the optical frequency comb＇s mass frequencv dividing technique.

Residual frequency drift in an atomic fountain clock

We report a locking mode in which the local oscillator （LO） is locked to an atomic fountain and calibration of the residual frequency drift （RFD）. In this running mode, the locked LO outputs a standard frequency signal, and a short-term fractional frequency stability of 2.7 × 10-13-1/2 is achieved. Due to the frequency drift of the LO in free running mode, a systematic frequency bias, or RFD, exists after being locked by the atomic fountain. We analyze and measure the RFD with a value of -3（2） × 10-16. A sectionalized post-process method is adopted to calibrate the RFD.