Residual Phase Noise and Time Jitters of Single-Chip Digital Frequency Dividers

In this paper, we demonstrate the residual phase noise of a few microwave frequency dividers which usually limit the performance of frequency synthesizers. In order to compare these dividers under different operation frequencies, we calculate additional time jitters of these dividers by using the measured phase noise. The time jitters are various from -0.1 fs to 43 fs in a bandwidth from 1 Hz to 100 Hz in dependent of models and operation frequencies. The HMC series frequency dividers exhibit outstanding performance for high operation frequencies, and the time jitters can be sub-fs. The time jitters of SP8401, MC10EP139, and MC100LVEL34 are comparable or even below that of HMC series for low operation frequencies.

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).

Photonic generation of RF and microwave signal with relative frequency instability of 10^(-15)

We demonstrate the ultra-stable frequency sources aiming to improve the short-time instability of primary frequency standards. These sources are realized by using photonic generation approach, and composed of ultra-stable lasers, optical- frequency-combs, optical signal detecting parts, and synthesizers. Preliminary evaluation shows that the sources produce fixed-frequency at 9.54（/9.63） GHz, 10 MHz, and tunable-frequency around 9.192 GHz with relative frequency instability of 10^-15 for short terms.

Time Transfer in a 1839-km Telecommunication Fiber Link Demonstrating a Picosecond-Scale Stability

An implementation of high-precision time transfer over a 1839-km field fiber loop back link between two provincial capitals of China,Xi’an and Taiyuan,is reported.Time transfer stabilities of 6.5 ps at averaging time of 1 s and 4.6 ps at 40000 s were achieved.The uncertainty for the time transfer system was evaluated,showing a budget of 56.2 ps.These results stand for a significant milestone in achieving high-precision time transfer over a field fiber link spanning thousands of kilometers,signifying a record-breaking achievement for the real-field time transfer in both stability and distance,which paves the way for constructing the nationwide high-precision time service via fiber network.

Progress of the NTSC-F1 primary frequency standard

The SI "second"is realized by caesium primary frequency standards( PFSs) using laser cooled atoms in a fountain configuration. Four sub systems and operation procedure of the NTSC-F1 primary frequency standard are introduced in the paper.The frequency stability of NTSC-F1 is 3.0×10-13/ τ-1 / 2compared to hydrogen maser. Four terms of frequency shift and uncertainty including second order Zeeman frequency shift,cold collision shift,gravity shift and blackbody shift are evaluated. The improvement of NTSC-F1 is introduced.

Coherent Transfer of Optical Frequency over 112 km with Instability at the 10^(-20) Level

We demonstrate optical-carrier transfer over a 112-km single-span urban fiber link, By actively compensating the phase noise induced along the fiber link, a noise suppression of 55 dB at 1 Hz is obtained. A fractional frequency instability of 2.5× 10^-16 at i s is achieved, and reaching 7.5× 10^-20 at 10000 s. The system is stable and able to run for a long time. This work will contribute to optical frequency distribution and remote comparison among atomic clocks.

Precision frequency measurement of 1^S0–3^P1 intercombination lines of Sr isotopes

We report on frequency measurement of the intercombination（5s^2）^1S0–（5s5p）^3P1transition of the four natural isotopes of strontium, including88^Sr（82.58%）,87^Sr（7.0%）,86^Sr（9.86%）, and84^Sr（0.56%）. A narrow-linewidth laser that is locked to an ultra-low expansion（ULE） optical cavity with a finesse of 12000 is evaluated at a linewidth of 200 Hz with a fractional frequency drift of 2.8×10^-13 at an integration time of 1 s. The fluorescence collector and detector are specially designed, based on a thermal atomic beam. Using a double-pass acousto-optic modulator（AOM） combined with a fiber and laser power stabilization configuration to detune the laser frequency enables high signal-to-noise ratios and precision saturated spectra to be obtained for the six transition lines, which allows us to determine the transition frequency precisely.The optical frequency is measured using an optical frequency synthesizer referenced to an H maser. Both the statistical values and the final values, including the corrections and uncertainties, are derived for a comparison with the values given in other works.

Rabi Spectroscopy and Sensitivity of a Floquet Engineered Optical Lattice Clock

We periodically modulate the lattice trapping potential of a ^(87)Sr optical clock to Floquet engineer the clock transition.In the context of atomic gases in lattices,Floquet engineering has been used to shape the dispersion and topology of Bloch quasi-energy bands.Differently from these previous works manipulating the external(spatial)quasi-energies,we target the internal atomic degrees of freedom.We shape Floquet spin quasi-energies and measure their resonance profiles with Rabi spectroscopy.We provide the spectroscopic sensitivity of each band by measuring the Fisher information and show that this is not depleted by the Floquet dynamical modulation.The demonstration that the internal degrees of freedom can be selectively engineered by manipulating the external degrees of freedom inaugurates a novel device with potential applications in metrology,sensing and quantum simulations.

Interrogation of optical Ramsey spectrum and stability study of an ^(87)Sr optical lattice clock

The optical Ramsey spectrum is experimentally realized in an ^(87)Sr optical lattice clock, and the measured linewidth agrees well with theoretical expectation. The coherence time between the clock laser and the atoms, which indicates the maximum free evolution period of using Ramsey detection to measure the atom-laser phase information, is determined as 340(23) ms by measuring the fringe contrasts of the Ramsey spectrum as a function of the free evolution period. Furthermore, with the same clock duty cycle of about 0.1, the clock stability is measured by using the Ramsey and Rabi spectra,respectively. The experimental and theoretical results show approximately the same stability as the two detection methods, which indicates that Ramsey detection cannot obviously improve the clock stability until the clock duty cycle is large enough. Thus, it is of great significance to choose the detection method of a specific clock.

Wiener Filtration Algorithm of an Ensemble Pulsar Timescale Based on a Power-law Model of Pulsar Power Spectrum

An ensemble pulsar timescale derived from the traditional Wiener filtration still contains some high level noise.To improve this situation we developed a Wiener filtration algorithm of the ensemble pulsar timescale based on a power-law model of power spectrum for pulsars.Our algorithm has three strengths:(1)mitigating spectral leakage between frequency bins for Fourier techniques;(2)using a power-law model for power spectrum;(3)signal realization in original residuals of data set by the power-law model.According to improved algorithm we constructed an ensemble pulsar timescale EPT-TAI using timing data with respect to International Atomic Time(TAI)about 16 yr time span of ten pulsars from International Pulsar Timing Array second data release(version A).The results show that EPT-TAI detected correctly the differences TT(BIPM2015)-TAI between terrestrial time TT(BIPM2015)and TAI.Fractional frequency stabilityσzanalysis shows that EPT-TAI does not indicate red noise for 16 yr time interval,and fractional frequency stability for 8 yr and longer time intervals is slightly better than that of TT(BIPM2015)-TAI.Stability for short time intervals of TT(BIPM2015)-TAI is better than that of EPT-TAI,but TT(BIPM2015)-TAI shows red noise for longer time intervals.Using the same algorithm we also derived an ensemble pulsar timescale EPT-TT(BIPM2015)with respect to TT(BIPM2015).The fractional frequency stability curve of EPT-TT(BIPM2015)shows similar characteristics as that of EPT-TAI but with slightly lower values.

Simulation and Design of Fluorescence Collector

Fluorescence collector is a critical component in optically pumped Cs beam frequency standards. We design a new fluorescence collector by means of a new method. By means of two simulation methods, a smaller fluorescence collector with the same collection efficiency is achieved. It can be applied to almost all fluorescence detection systems in atom-light interaction experiments. We select the practical fluorescence collector studied by comparing three designing schemes. Its structure is very plain. Moreover, its fluorescence collection efficiency is very high. The collection efficiency of the practical fluorescence collector we designed is over 33% by means of two different ways.

Evaluation of second-order Zeeman frequency shift in NTSC-F2

Caesium atomic fountain clock is a primary frequency standard,which realizes the duration of second.Its performance is mostly dominated by the frequency accuracy,and the C-field induced second-order Zeeman frequency shift is the major effect,which limits the accuracy improvement.By applying a high-precision current supply and high-performance magnetic shieldings,the C-field stability has been improved significantly.In order to achieve a uniform C-field,this paper proposes a doubly wound C-field solenoid,which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift.Based on the stable and uniform C-field,we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition|F=3,mF=-1→|F=4,mF=-1 central frequency,obtaining this frequency shift as 131.03×10^(-15)and constructing the C-field profile(σ=0.15 n T).Meanwhile,during normal operation,we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition|F=3,mF=-1→|F=4,mF=-1 fringe for ten consecutive days and record this frequency fluctuation in time domain.The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10×10^(-15).The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6×10^(-17).Compared with NTSC-F1,NTSC-F2,there appears a significant improvement.

Ground state of rotating ultracold quantum gases with anisotropic spin orbit coupling and concentrically coupled annular potential

MotiVated by recent experimental realization of synthetic spin-orbit coupling in neutral quantum gases, we consider the quasi-two-dimensional rotating two-component Bose-Einstein condensates with anisotropic Rashba spin-orbit cou- pling subject to concentrically coupled annular potential. For experimentally feasible parameters, the rotating condensate exhibits a variety of rich ground state structures by varying the strengths of the spin-orbit coupling and rotational frequency. Moreover, the phase transitions between different ground state phases induced by the anisotropic spin-orbit coupling are obviously different from the isotropic one.

The application of co-integration theory in ensemble pulsar timescale algorithm

Employing multiple pulsars and using an appropriate algorithm to establish ensemble pulsar timescale can reduce the influences of various noises on the long-term stability of pulsar timescale,compared to a single pulsar.However,due to the low timing precision and significant red noises of some pulsars,their participation in the construction of ensemble pulsar timescale is often limited.Inspired by the principle of solving non-stationary sequence modeling using co-integration theory,we put forward an algorithm based on co-integration theory to establish an ensemble pulsar timescale.It is found that this algorithm can effectively suppress some noise sources if a co-integration relationship between different pulsar data exists.Different from the classical weighted average algorithm,the co-integration method provides the chance for a pulsar with significant red noises to be included in the establishment of an ensemble pulsar timescale.Based on data from the North American Nanohertz Observatory for Gravitational Waves(NANOGrav),we found that the co-integration algorithm can successfully reduce several timing noises and improve the long-term stability of the ensemble pulsar timescale.

A long-term frequency-stabilized erbium-fiber-laser-based optical frequency comb with an intra-cavity electro-optic modulator

We demonstrate an optical frequency comb based on an erbium-doped-fiber femtosecond laser with the nonlinear polarization evolution scheme. The repetition rate of the laser is about 209 MHz. By controlling an intra-cavity electro- optic modulator and a piezo-transducer, the repetition rate can be stabilized with a high-bandwidth servo in a frequency range of 3 kHz, enabling long-term repetition rate phase-locking. The in-loop frequency stability of repetition rate is about 1.6× 10-13 in an integration time of 1 s, limited by the measurement system; and it is inversely proportional to integration time in the short term. Furthermore, using a common path f-2f interferometer, the carrier envelope offset frequency of the comb is obtained with a signal-to-noise ratio of 40 dB in a 3-MHz resolution bandwidth. Stabilized cartier envelope offset frequency exhibits a deviation of 0.6 mHz in an integration time of 1 s.

Strontium optical lattice clock at the National Time Service Center

We report the 87Sr optical lattice clock developed at the National Time Service Center. We achieved a closed-loop operation of the optical lattice clock based on 87Sr atoms. The linewidth of the spin-polarized clock peak is 3.9 Hz with a clock laser pulse length of 300 ms, which corresponds to a Fourier-limited linewidth of 3 Hz. The fitting of the in-loop error signal data shows that the instability is approximately 5 × 10 15τ-1/2, affected primarily by the white noise. The fractional frequency difference averages down to 5.7 × 10 ^-17 for an averaging time of 3000 s.

A transportable optical lattice clock at the National Time Service Center

We report a transportable one-dimensional optical lattice clock based on 87Sr at the National Time Service Center.The transportable apparatus consists of a compact vacuum system and compact optical subsystems.The vacuum system with a size of 90 cm×20 cm×42 cm and the beam distributors are assembled on a double-layer optical breadboard.The modularized optical subsystems are integrated on independent optical breadboards.By using a 230 ms clock laser pulse,spin-polarized spectroscopy with a linewidth of 4.8 Hz is obtained which is close to the 3.9 Hz Fourier-limit linewidth.The time interleaved self-comparison frequency instability is determined to be 6.3 × 10^-17 at an averaging time of 2000 s.

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^-14τ^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.

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.

An All-Polarization-Maintaining Multi-Branch Optical Frequency Comb for Highly Sensitive Cavity Ring-Down Spectroscopy

We demonstrate a multi-branch all polarization-maintaining Er:fiber frequency comb with five application ports for precise measurement of atomic/molecular transition frequencies in the near-infrared region.A fully stabilized Er:fiber frequency comb with a nonlinear amplifying loop mirror is achieved.The in-loop relative instability of stabilized carrier-envelope-offset frequency is 5.6×10-18 at 1 s integration time,while that of the repetition rate is well below 1.8×10-12 limited by the measurement noise floor of the commercial frequency counter.Five application ports are individually optimized for applications with different wavelengths(1064 nm,1083 nm,1380 nm,1637 nm and 1750 nm).The beat note between the optical frequency comb and continuous laser exhibits the signal-to-noise ratio of at least 30 dB at a resolution bandwidth of 100 kHz.The in-loop frequency instability of the comb is evaluated to be good enough for measurement of rotation-resolved transitions of molecules below 1 kHz resolution.