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The quadratic Zeeman shift coefficient of 3P0 clock state for strontium is determined in theory and experiment. In theory, we derived the expression of the quadratic Zeeman shift of 3P0 clock state for 88Sr and 87Sr in the weak-magnetic-field approximation. By using the multi-configuration Dirac-Hartree-Fock theory, the quadratic Zeeman shift coefficients were calculated. To determine the calculated results, the quadratic Zeeman shift coefficient of 3P0,F=9/2,MF=+/-9/2 clock state was measured in our 87Sr optical lattice clock. The calculated results C2=-23.38(5) MHz/T2 for 88Sr and the 3P0,F=9/2,MF=+/-9/2 clock state for 87Sr agree well with the other experimental and theoretical values, especially the most accurate measurement recently. As the 1S0,F=9/2,MF=+/-5/2-3P0,F=9/2,MF=+/-3/2 transitions have been used as another clock transition for less sensitive to the magnetic field noise, we also calculated the quadratic Zeeman shift coefficients for the other magnetic states., Comment: 14 pages,2 figures

Large scale ab initio calculations of the electric contribution (i.e. the electric field gradient) to the electric quadrupole hyperfine interaction constants $B$ for the $5p~^2P_{3/2}$ state in $^{109}$Cd$^+$ ion and the $5s5p~^3P_{1,2}$ states in neutral $^{109}$Cd atom were performed. To probe the sensitivity of $B$ to different electron correlation effects, six sets of variational multi-configuration Dirac-Hartree-Fock and relativistic configuration interaction calculations employing different strategies were carried out. The calculated electric field gradients, together with experimental values of $B$, allow us to extract a new value of the nuclear electric quadrupole moment $Q$($^{109}$Cd) = 0.634(22) b which is about 5\% larger than the recommended value [Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); Pyykk\"{o}, Mol. Phys. 116, 1328 (2018)]. Efforts were made to provide a realistic theoretical uncertainty for the final $Q$ value based on statistical principles and correlation with the magnetic dipole hyperfine interaction constant $A$., Comment: 15 pages,2 figures. arXiv admin note: text overlap with arXiv:1906.08465

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 Landé g-factors and quadratic Zeeman shift coefficients of the nsnp 3 P 0 o clock states for 111,113Cd and 25Mg 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 Landé g-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.

We conducted measurement and calculation to resolve the long-standing large discrepancy in the metastable state lifetime for the 88Sr atom between theoretical and experimental results. The present lifetime τ = 830 − 240 + 600 s, measured using the magneto-optical trap as a photon amplifier to detect the weak decay events, is approximately 60% larger than the previous experimental value τ = 520 − 140 + 310 s. By considering the electron correlation effects in the framework of the multiconfiguration Dirac–Hartree–Fock theory, we obtained a theoretical lifetime of 1079(54) s, which lies in the range of measurements with error bars. Furthermore, we considered the higher-order electron correlation and Breit interaction to control the uncertainty of the theoretical calculation. The significant improvement in the agreement between calculations and measurements is attributed to the updated blackbody radiation-induced decay rate.

In this paper, we demonstrate in situ synchronous frequency comparison between distinct regions in a one-dimensional optical lattice. The synchronous comparison instability is well below the Dick limit and agrees with the limit induced by atomic detection noise. The absolute atom number is extracted from the synchronous comparison instability with an uncertainty below 3%. Surpassing the performance of absorption imaging, this method provides a way to directly and precisely determine the absolute atom number from detection noise. Taking advantage of the inhomogeneous density distribution over the whole lattice, the density shift can also be conveniently measured by this synchronous frequency comparison method. Inconsistent with the expectation of the linear relationship between density shift and atom number difference, nonlinearity is observed, indicating that the assumption of an identical density shift coefficient over the whole lattice is not always safe.

The values of the nuclear electric quadrupole moment are different by about 7% for the $^{87}\mathrm{Sr}$ nucleus between the recommended value [Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); Pyykk\"o, Mol. Phys. 116, 1328 (2018)] and earlier results [e.g., M\aa{}rtensson-Pendrill, J. Phys. B 35, 917 (2002); Yu, Wu, Gou, and Shi, Phys. Rev. A 70, 012506 (2004)]. In this paper, we report the value $Q(^{87}\mathrm{Sr})=328(4)$ mb, making use of our calculated electric-field gradients produced by electrons at the nucleus in combination with experimental values for hyperfine structures of the $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{1,2}$ states of the neutral Sr atom. In the framework of the multiconfiguration Dirac-Hartree-Fock theory, the electron correlations were taken into account systematically so as to control the uncertainties of the electric-field gradient at about 1% level. The present result is different from the recommended value, but in excellent agreement with those by M\aa{}tensson-Pendrill and Yu et al.. We would recommend the present $Q$ value as a reference for $^{87}\mathrm{Sr}$.

In the weak-magnetic-field approximation, we calculated the hyperfine-induced Lande g -factors of the 3 P 0 o clock states in 27 Al + and 87 Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, δ g hfs ( 1 ) ( 3 P 0 o ) = − 1.183 ( 6 ) × 10 − 3 for 27 Al + and δ g hfs ( 1 ) ( 3 P 0 o ) = 7.78 ( 30 ) × 10 − 5 for 87 Sr, agree with experimental values very well. The influence of relativistic effects and electron correlations on the involving hyperfine interaction and Zeeman matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the g -factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. Based on these, the computational uncertainties were systematically analyzed for the hyperfine-induced Lande g -factors of the 3 P 0 o clock states in these two atomic systems.

The self-comparison method is a powerful tool in the uncertainty evaluation of optical lattice clocks, but any drifts will cause a frequency offset between the two compared clock loops and thus lead to incorrect measurement result. We propose a drift-insensitive self-comparison method to remove this frequency offset by adjusting the clock detection sequence. We also experimentally demonstrate the validity of this method in a one-dimensional 87Sr optical lattice clock. As the clock laser frequency drift exists, the measured frequency difference between two identical clock loops is (240 ± 34) mHz using the traditional self-comparison method, while it is (−15 ± 16) mHz using the drift-insensitive self-comparison method, indicating that this frequency offset is cancelled within current measurement precision. We further use the drift-insensitive self-comparison technique to measure the collisional shift and the second-order Zeeman shift of our clock and the results show that the fractional collisional shift and the second-order Zeeman shift are 4.54(28) × 10−16 and 5.06(3) × 10−17, respectively.

We review recent experimental progress concerning the 87Sr optical lattice clock at the National Time Service Center in China. Hertz-level spectroscopy of the 87Sr clock transition for the optical lattice clock was performed, and closed-loop operation of the optical lattice clock was realized. A fractional frequency instability of 2.8 &times, 10&minus, 17 was attained for an averaging time of 2000 s. The Allan deviation is found to be 1.6 &times, 15/&tau, 1/2 and is limited mainly by white-frequency-noise. The Land&eacute, g-factors of the (5s2)1S0 and (5s5p)3P0 states in 87Sr were measured experimentally, they are important for evaluating the clock&rsquo, s Zeeman shifts. We also present recent work on the miniaturization of the strontium optical lattice clock for space applications.

The work presented in this paper is based on an optical frequency comb injection-locking, active filtering and amplification method to build a narrow linewidth laser for second cooling of the strontium atoms in an optical lattice clock. An optical femtosecond laser comb with mode spacing of 250 MHz as master laser is applied to directly inject into an external cavity semiconductor laser at 689 nm called slave laser, a single mode is selected and amplified from the optical femtosecond laser comb.

In the ultra-cold 87Sr atomic system, the Zeeman shift of the clock transition was measured with the σ±-polarized interrogation to accurately determine the g-factors of the 5s2 1S0 and 5s5p 3P0 states.

We report experiments on the observation of the 1S0-3P0 transition spectrum of 88Sr in the Lamb-Dicke regime. After going through a two-stage magneto-optical trap (MOT), 88Sr cold atoms with number of about 1 \times 105 and a longitudinal temperature of 8.4 μK are loaded into a one-dimensional (1D) optical lattice, which is realized with a semiconductor laser at 813.4 nm. Using the magnetic field-inducing 3P1 state mixing into 3P0 state, the spectroscopy of the 1S0-3P0 transition with a linewidth of 180 Hz is detected.

We presented experimental and theoretical studies of the effect of an external magnetic field on the forbidden transition in the bosonic Sr atom. In our ultra-cold atomic system, the excitation fraction of $5s5p$~$^3P_0$~-~$5s^2$~$^1S_0$ forbidden transition was measured under the circumstance of the different magnetic field strengths by using the normalized detection method. Based on perturbation theory, we calculated the magnetic-field-induced $5s5p$~$^3P_0$~-~$5s^2$~$^1S_0$ transition rate. The excitation fraction as a function of the magnetic field strength was deduced according to the calculated results. A good agreement was found between the experimental measurements and the calculations. This study should be helpful in evaluating the magnetic field effects on the forbidden transition rate with higher accuracy. Moreover, it can help to understand the ultra-cold atomic interaction in the external magnetic field., 17 pages, 4 figures, 055017

We present an experimental determination on the Lande g-factors for the 5s2 1S0 and 5s5p 3 P0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the 87Sr optical lattice clock. The Zeeman shift of the 5s5p 3P0–5s2 1S0 forbidden transition is measured with the π-polarized and σ±-polarized interrogations at different magnetic field strengths. Moreover, in the g-factor measurement with the σ±-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5s2 1S0 g-factor for the 87Sr atom is −1.306(52)×10−4, which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential g-factor δg between the 5s5p 3P0 state and the 5s2 1S0 state of the 87Sr atoms is measured in the experiment as well, which are −7.67(36) × 10−5 with π-transition spectra and −7.72(43) × 10−5 with σ±-transition spectra, in good agreement with the previous report [Phys. Rev. A 76 (2007) 022510]. This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.

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 , affected primarily by the white noise. The fractional frequency difference averages down to for an averaging time of 3000 s.

At present the optical clock with accuracy and stability achieves to 10-18 level, which could be the next generation of time and frequency standard. This paper gives an introduction of the progress of researching on the optical lattice clock of Strontium atom in NTSC (National Time Service Center). We realize the (5s5s)1S0—(5s5p)1P1 cooling (blue MOT) and (5s5s)1S0—(5s5p)3P1 cooling (red MOT) in succession for the optical lattice clock, and loading these cold atoms in a lattice composed by a magic wave-length is studied. By using our narrow line-width diode laser and the fiber femtosecond optical frequency comb, we precisely measure the absolute frequencies of the inter-combination transitions (5s5s)1S0—(5s5p)3P1 of four isotopes of Strontium referenced to an H maser.

We report on frequency measurement of the intercombination (5s2)1S0–(5s5p)3P1 transition of the four natural isotopes of strontium, including 88Sr (82.58%), 87Sr (7.0%), 86Sr (9.86%), and 84Sr (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.