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.

A proposal for detecting weak electromagnetic waves around 2.6μm wavelength with Sr optical clock

Infrared signal detection is widely used in many fields.Due to the detection principle,however,the accuracy and range of detection are limited.Thanks to the ultra stability of the^(87)Sr optical lattice clock,external infrared electromagnetic wave disturbances can be responded to.Utilizing the ac Stark shift of the clock transition,we propose a new method to detect infrared signals.According to our calculations,the theoretical detection accuracy in the vicinity of its resonance band of 2.6μm can reach the order of 10-14W,while the minimum detectable signal of common detectors is on the order of 10^(-10)W.

Laboratory demonstration of geopotential measurement using transportable optical clocks

We report an experimental demonstration of geopotential difference measurement using a pair of transportable ^(40)Ca^(+) optical clocks(TOC-729-1 and TOC-729-3)in the laboratory,each of them has an uncertainty of 1.3×10^(−17) and an instability of 4.8×10^(−15)/√τ.Referenced to a stationary clock of TOC-729-1,the geopotential difference measurements are realized by moving TOC-729-3 to three different locations and the relevant altitude differences are measured with uncertainties at the level of 20 cm.After correcting the systematic shifts(including gravitational red shift),the two-clock frequency difference is measured to be–0.7(2.2)×10^(−17),considering both the statistic(1.0×10^(−17))and the systematic(1.9×10^(−17))uncertainties.The frequency difference between these two clocks is within their respective uncertainties,verifying the reliability of transportable ^(40)Ca^(+) optical clocks at the low level of 10^(−17).

A cryogenic radio-frequency ion trap for a 40Ca^(+) optical clock

A liquid-nitrogen cryogenic40Ca^(+)optical clock is presented that is designed to greatly reduce the blackbody radiation(BBR) shift. The ion trap, the electrodes and the in-vacuum BBR shield are installed under the liquid-nitrogen container,keeping the ions in a cryogenic environment at liquid-nitrogen temperature. Compared with the first design in our previous work, many improvements have been made to increase the performance. The liquid-nitrogen maintenance time has been increased by about three times by increasing the volume of the liquid-nitrogen container;the trap position recovery time after refilling the liquid-nitrogen container has been decreased more than three times by using a better fixation scheme in the liquid-nitrogen container;and the magnetic field noise felt by the ions has been decreased more than three times by a better design of the magnetic shielding system. These optimizations make the scheme for reducing the BBR shift uncertainty of liquid-nitrogen-cooled optical clocks more mature and stable, and develop a stable lock with a narrower linewidth spectrum,which would be very beneficial for further reducing the overall systematic uncertainty of optical clocks.

A combined magnetic field stabilization system for improving the stability of 40Ca^(+) optical clock

Future applications of portable40Ca^(+)optical clocks require reliable magnetic field stabilization to improve frequency stability, which can be achieved by implementing an active and passive magnetic field noise suppression system. On the one hand, we have optimized the magnetic shielding performance of the portable optical clock by reducing its apertures and optimizing its geometry;on the other hand, we have introduced an active magnetic field noise suppression system to further suppress the magnetic field noise experienced by the ions. These efforts reduced the ambient magnetic field noise by about 10000 times, significantly reduced the linewidth of the clock transition spectrum, improved the stability of the portable40Ca+optical clock, and created the conditions for using portable optical clocks in non-laboratory magnetic field environments. This active magnetic field suppression scheme has the advantages of simple installation and wide applicability.

Study of optical clocks based on ultracold ^171Yb atoms

The optical atomic clocks have the potential to transform global timekeeping,relying on the state-of-the-art accuracy and stability,and greatly improve the measurement precision for a wide range of scientific and technological applications.Herein we report on the development of the optical clock based on 171Yb atoms confined in an optical lattice.A minimum width of 1.92-Hz Rabi spectra has been obtained with a new 578-nm clock interrogation laser.The in-loop fractional instability of the 171Yb clock reaches 9.1×10-18 after an averaging over a time of 2.0×104 s.By synchronous comparison between two clocks,we demonstrate that our 171Yb optical lattice clock achieves a fractional instability of 4.60×10-16/√τ.

Suppression of servo error uncertainty to 10^(-18)level using double integrator algorithm in ion optical clock

A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator.Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments.The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters.According to the experimental results,the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107.In a week-long comparison of optical clocks,the relative uncertainty of the servo error is determined to be 1.9×10^(-18),which is meaningful for the systematic uncertainty of the transportable single^(40)Ca^(+)ion optical clock entering the 10^(-18)level.

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 AI＋ 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 167nm laser. The expected clock laser stability can reach 9.0 × 10^-17/√τ. For the second trap, in addition to 167nm laser Doppler cooling, a second stage pulsed 234nm 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.

All polarization-maintaining Er:fiber-based optical frequency comb for frequency comparison of optical clocks

We demonstrate an optical frequency comb(OFC)based on a turnkey mode-locked laser with a figure-9-shape structure and polarization-maintaining fibers,for the comparison of frequency among optical clocks with wavelengths of 698 nm,729 nm,1068 nm,and 1156 nm.We adopt a multi-branch approach in order to produce high power OFC signals at these specific wavelengths,enabling the signal-to-noise ratio of the beatnotes between the OFC and the clock lasers to exceed30 d B at a resolution bandwidth of 300 k Hz.This approach makes the supercontinuum spectra much easier to be generated than a single branch OFC.However,more out-of-loop fibers degrade the long-term frequency instability due to thermal drift.To minimize the thermal drift effect,we set the fiber lengths of different branches to be similar,and we stabilize the temperature as well.The out-of-loop frequency instability of the OFC due to the incoherence of the multi-branch is about5.5×10^(19) for 4000 s,while the in-loop frequency instability of fceo and that of fbeat are 7.5×10^(18) for 1 s and 8.5×10^(18) for 1 s,respectively.The turnkey OFC meets the requirement for the comparison of frequency between the best optical clocks.

Correlation between the magic wavelengths and the polarization direction of the linearly polarized laser in the Ca^+ optical clock

The magic wavelengths for different Zeeman components are measured based on the ^40Ca^＋ optical clock. The dynamic dipole polarizability of a non-zero angular moment level has correlation with the polarization direction of the linearly polarized laser beam, and we show that the four hyperfine structure levels of 4S1/2,m=±1/2 and 3d5/2,m=±1/2 for ^40Ca^＋ have the same dynamic dipole polarizability at the magic wavelength and a certain polarization direction. In addition, the existence of a specific direction of polarization may provide a new idea for improving the precision of magic wavelength measurement in experiment.

Progress on the^40Ca^+ion optical clock

Progress of the ^40Ca^+ion optical clock based on the 4^2S1/2-3d ^2D5/2 electric quadrupole transition is reported.By setting the drive frequency to the“magic”frequencyΩ0,the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10^-19 level.By precisely measuring the differential static scalar polarizability∆α0,the uncertainty due to the blackbody radiation(BBR)shift(coefficient)is reduced to the 10^-19 level.With the help of a second-order integrating servo algorithm,the uncertainty due to the servo error is reduced to the 10^-18 level.The total fractional uncertainty of the ^40Ca^+ion optical clock is then improved to 2.2×10^-17,whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations.The state preparation is introduced together with improvements in the pulse sequence,and furthermore,a better signal to noise ratio(SNR)and less dead time are achieved.The clock stability of a single clock is improved to 4.8×10^-15√τ(in seconds).

Magic Wavelengths of the Optical Clock Transition at 1107 nm of Barium

Magic wavelengths for laser trapping of barium atoms in the optical clock transition at l107nm between the 6s2 1So state optical lattices are calculated with considering the and 6s5d 3D1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated, Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser.

Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp ^(3)P_(0)^(o) clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) clock states for ^(111,113)Cd and ^(25)Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory.To obtain accurate values of these parameters,the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements,and energy separations were investigated in detail.We also estimated the contributions from perturbing states to the Landég-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy.Our calculations provide important data for estimating the first-and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.

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.

Realization of population inversion between 7S_(1/2) and 6P_(3/2) levels of cesium for four-level active optical clock

We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser.We calculate the relative population probabilities at each level theoretically with the density matrix method.In a steady state,5.8% atoms are at 7S1/2 level and 2.9% at 6P3/2 level,which builds up the population inversion between the two levels.We obtain the fluorescence spectra produced in thermal cesium cell in our experiment.The measured relative intensity of each available fluorescence spectral line in the experiment agrees very well with the theoretical result.The demonstrated population inversion between 7S1/2 and 6P3/2 levels can be used to construct an active optical clock of four-level system with a wavelength of 1469.9 nm.

Observation of the ^1S0-^3P0 optical clock transition in cold ^199Hg atoms

We report on the observation of the highly forbidden ^1S0–^3P0 optical clock transition in laser-cooled ^199Hg atoms.More than 95% depletion of cold ^199Hg atoms is detected in the magneto-optical trap. Using the free-of-field detection method, the AC Stark shift from the cooling laser is removed from the in-field spectroscopy. At low-power clock laser pumping, the linewidth of the clock spectroscopy is approximately 450 k Hz（full width at half-maximum）, which corresponds to a Doppler broadening at the atom temperature of 60 μK. We determine the -1S0–^13P0transition frequency to be 1,128,575,290.819（14） MHz by referencing with a hydrogen maser and measuring with a fiber optical frequency comb. Moreover, a weak Doppler-free signal is observed.

Synchronization of Fourier-Synthesized Optical Pulses to a Mode-Locked Optical Clock

A Fourier-synthesized 40-GHz optical pulse train was successfully synchronized to an 8-GHz optical clock generated from a mode-locked fiber ring laser. The measured timing jitter of the synchronization was 0.43 ps.

Sympathetic electromagnetically induced transparency ground state cooling of a~(40)Ca^(+)–~(27)Al^(+)pair in an~(27)Al^(+)clock

We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We observe simultaneous ground state cooling across all radial modes and axial modes of a ^(40)Ca^(+)–^(27)Al^(+)ion pair,occupying a broader cooling range in frequency space over 3 MHz.The cooling time is observed to be less than 1 ms.The mean phonon number and heating rates of all motional modes are measured.This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ^(27)Al^(+)optical clock,but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.

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.

First Evaluation and Frequency Measurement of the Strontium Optical Lattice Clock at NIM

An optical lattice clock based on 87Sr is built at National Institute of Metrology （NIM） of China. The systematic frequency shifts of the clock are evaluated with a total uncertainty of 2.3×10-16. To measure its absolute frequency with respect to NIM＇s cesium fountain clock NIM5, the frequency of a flywheel H-maser of NIM5 is transferred to the Sr laboratory through a 50-kin-long fiber. reference frequency of this H-maser, is used for the optical this Sr clock is measured to be 429228004229873.7（1.4）Hz. A fiber optical frequency comb, phase-locked to the frequency measurement. The absolute frequency of