Abstract: The frequency shift caused by blackbody radiation is one of the dominant corrections to the evaluation of the optical lattice clock. The frequency shift of blackbody radiation is closely related to the dynamic and static correction factor, ambient temperature and atomic polarizability. The blackbody radiation shift is mainly affected by ambient temperature. During the normal operation of the strontium atom optical lattice clock, the experimental environment and other heat sources around the vacuum cavity have complicated the environment around the vacuum cavity, resulting in the fact that the external surface temperature of the vacuum cavity does not truly reflect the temperature change of the vacuum cavity. For the strontium atomic optical clock experimental apparatus of the National Time Service Center, the uncertainty and correctionof the blackbody radiation frequency shift are evaluated by the theoretical analysis, measurement of the temperature of the vacuum cavity outer surface, and software simulation. Among them, the frequency shift of black body radiation caused by strontium atom furnace, sapphire heating window, room temperature radiation entering into the vacuum cavity through the window plate, and the thermal radiation at the atomic group caused by Zeeman reducer are analyzed. Five temperature measuring points are set on the external surface of the vacuum chamber, and the temperature changes on the external surface of the vacuum chamber are monitored in real time by using the calibrated platinum resistance temperature sensor while the system is running normally. We obtain the average temperature of the five temperature measuring points. The model of vacuum cavity is established by using the SolidWorks. The method of finite element analysis is used to simulate the variation of the temperature around atom samples. We also obtain the temperature distribution around the atomic groups in the vacuum cavity. The result shows that the temperature around atoms varies with the temperature of the vacuum cavity. When the temperature of the ambient temperature changes 0.72 K, the fluctuation of the temperature around the atoms is 0.34 K. Finally, the total correction of blackbody radiation of the system is evaluated to be –2.13(1) Hz, and the correction uncertainty is about 2.4 × 10〈sup〉–17〈/sup〉.

Abstract: We demonstrate a spin-polarized clock transition spectrum of the 87Sr optical lattice clock. The clock transition 5s2 1S05s5p 3P0 of isotope 87Sr has a hyperfine structure due to non-zero nuclear spin, inducing ten -polarized transitions from each individual mF state under the condition of a bias magnetic field along the probing polarization axis. In this experiment, atoms are driven to a certain mF state by a circular-polarization pump light to maximize the atomic population, which is beneficial to the stability and uncertainty evaluation of the optical lattice clock. After two stages cooling and trapping, about 3.5106 atoms are trapped in the red magneto-optical trap with a temperature of 3.9 K. A grating-feedback external cavity diode laser with a tapered amplifier is used to build the optical lattice with a magic-wavelength of 813.426 nm. Both waists of the counter-propagating lattice beam along the horizontal direction are overlapped to form a one-dimensional (1D) optical lattice. The lifetime of the atoms trapped in the 1D optical lattice is 1600 ms. The clock laser at 698 nm is a grating-feedback diode laser, which is locked to an ultra-low expansion cavity by the Pound-Drever-Hall technique to stabilize the frequency and phase. As a result, the linewidth of clock laser is narrowed to Hz level. By the normalized shelving method, we obtain a resolved sideband spectrum of 87Sr 5s2 1S05s5p 3P0 transition. According to the spectrum, the lattice temperature along the longitudinal direction is approximately 4.2 K. After that a linewidth of 6.7 Hz of the degenerate clock transition is obtained at a probing time of 150 ms by utilizing a three-dimensional (3D) bias magnetic field, which is used to eliminate the stray magnetic fields. Then a small bias magnetic field of 300 mGs is applied along the polarization axis of the lattice light to achieve the spectrum of Zeeman magnetic sublevels of the clock transition. Furthermore, the mF=+9/2 and mF=-9/2 magnetic sublevels are picked to be respectively pumped by the +-polarized and --polarized light at 689 nm, a variable liquid crystal wave plate is employed to switch on both polarizations. Finally, the spin polarized clock transition spectrum is obtained at the interrogating pulse of 150 ms, and the linewidths of the mF=+9/2, mF=-9/2 magnetic sublevel transitions are 6.8 Hz and 6.2 Hz respectively.

Abstract: The optical lattice clock with neutral atoms occupies an outstanding position in the research field of atomic clocks, demonstrating the great potential of its performance (like the uncertainty and the stability). At present, the optical lattice clock has realized a 10-18 level of its uncertainty. In this paper, we present the realization of loading bosonic atoms 88Sr (strontium, alkaline-earth metals) into a one-dimensional (1D) optical lattice in our laboratory. The optical lattice where the atoms are trapped can make the energy level shift, called Stark shift. But there is the special optical lattice operating at the “magic” wavelength for clock transitions (5s2) 1S0-(5s5p) 3P0, which can make the same Stark light-shift for both of them, indicating a zero light-shift relative to the clock. In our experiment, Sr atoms are cooled in a two-stage cooling and its temperature can be as low as 2 μK. Then these cold atoms are confined in the Lamb-Dicke region by the lattice laser output from an amplified diode laser operating at the “magic” wavelength, 813 nm. Experimentally, it is straightforward to provide 850 mW of lattice power focused to a 38 μm beam radius. After the cold atoms have trapped in the optical lattice, the lifetime of atoms in 1D optical lattice is measured to be 270 ms. The temperature and the number are about 3.5 μK and 1.2×105 respectively. Besides, effects of the power of the lattice laser on both the number and temperature are analyzed. The number changes linearly with the laser power, while there is no obvious influence on the temperature by the power. This original and special approach for atoms trapped in the optical lattice can provide a long interrogation time for probing the clock transition. Furthermore, it may be the foundation for developing our optical lattice clock of strontium atoms.

Abstract: We have conducted experimental investigations on the effect of repumping laser on the cooling and trapping of strontium atoms. More than 3.1×10888Sr atoms have been trapped with 679 nm and 707 nm repumping laser added. The two repumping lasers enhance the trappopulation by a factor of 17. We also made experimental investigations on the effect of 707 nm repumping laser detuning on the cooling and trapping of strontium atoms. The fluctuation of atom trapping population is less than 3 ‰ when the detuning from 707 nm is 5 MHz.

Abstract: Cold collision frequency shift is one of the major systematic effects which limit the frequency uncertainty of the cesium fountain atomic clock. It is proportional to the effective atomic density, which is defined as the average density over the initial spacial and velocity distribution. The measurement of the frequency shift is based on a differential method, in which the fountain clock is operated with two different atomic densities, i.e. high density and low density, in turn. The clock frequency without collision shift can be achieved by linear extrapolation with the frequencies and density ratios of two states. For the density ratio is estimated with the atom number, it plays a crucial role in generating atoms with same density distribution for reducing systematic uncertainty in cold collision frequency shift estimation. The rapid adiabatic passage method is used in Cesium fountain clock to realize homogeneous transition probability, which modulates the amplitude and frequency of microwave continuously to prepare atom sample. To investigate the precision of this method, theoretical analysis and experimental measurement are both used here. An equation of deviation is derived from the time evolution of Bloch vector. The vector rotates at angular speed 〈i〉Ω〈/i〉 with the rotation axis processing at lower angular speed. The deviations in the two directions on the surface of Bloch sphere are determined by the equations which are similar to wave equations, and can be simplified into wave equations when the deviations are sufficiently small. It is shown in the equations that the deviations are stimulated by angular velocity and angular acceleration of the precession, and is inversely proportional to the square of 〈i〉Ω〈/i〉. Further calculation shows that the deviation becomes smaller when the amplitude of microwave frequency and Rabi frequency are close to each other. It is then confirmed experimentally. The effects of some other parameters, such as the pulse length and time delay, on transition probability are also measured, showing that the RAP method is insensitive to these parameters up to a large scope. The precision of RAP method is dominated by three factors. The first factor is the product of rotating angular speed 〈i〉Ω〈/i〉 and pulse length 〈i〉T〈/i〉, i.e. 〈i〉ΩT〈/i〉: The increase of 〈i〉ΩT〈/i〉 can reduce the uncertainty to a satisfactory degree. The second factor is the uncertainty of resonant frequency, so the measurement is required to be precise. The third factor is the unexpected atoms which are not selected by the microwave, and may be attributed to pulling light. After optimizing the parameters, the ratio of low density to high density can approach to 0.5 with 3 × 10〈sup〉–3〈/sup〉 uncertainty, which leads to a systematic relative uncertainty of cold collision shift up to 1.6 × 10〈sup〉–16〈/sup〉.

Abstract: 〈sec〉 The Gaussian radius and temperature of cold atomic cloud are important parameters in describing the state of cold atoms. The precise measuring of these two parameters is of great significance for studying the cold atoms. In this paper, we propose a new method named knife-edge to measure the Gaussian radius and temperature of the cold atomic cloud. 〈/sec〉〈sec〉 A near-resonant and supersaturated laser beam, whose size is controlled by a knife-edge aperture, is used to push away the cold atoms in the free falling process of cold atomic cloud. By detecting the intensity of fluorescence signal, the numbers of residual atoms under different-sized near-resonant beams can be obtained. According to the characteristic of cold atoms′ distribution, we construct a theoretical model to derive the Gaussian radius of cold atomic cloud from the recorded residual atom number and near-resonant beam size. Since the Gaussian radius and temperature of cold atomic cloud are associated with each other, we can finally obtain the temperature of cold atomic cloud through the recorded residual atom number and beam size. 〈/sec〉〈sec〉 By using this method, we successfully measure the Gaussian radii of cold atomic cloud at the heights of 10 mm and 160 mm below the center of 3D-MOT (three dimensional magneto-optical trap) to be (1.54 ± 0.05) mm and (3.29 ± 0.08) mm, respectively. The corresponding temperature of cold atomic cloud is calculated to be (7.50 ± 0.49) μK, which is well consistent with the experimental result obtained by using the time-of-flight method under the same condition. This experiment is conducted on the platform of Cesium atomic fountain clock of National Time Service Center, China. 〈/sec〉

Abstract: Kalman filter time scale algorithm is a method of real-time estimating atomic clock state. It is of great practical value in the time-keeping work. Reliable Kalman filter time scale algorithm requires a reliable atomic clock state model, a random model and a reasonable estimation method. However, it is difficult to construct accurate state model when the noises of atomic clock change. The random model is generally based on the prior statistical information about atomic clock noises, and the prior statistical information may be distorted. In the process of time scale calculation, the noises of atomic clocks need estimating in the Kalman filter time scale algorithm, which is quantified according to the intensity of the noise. With the change of the external environment or aging of atomic clock, the noise intensity may change, resulting in the disturbance of atomic clock state estimation in the Kalman filter time scale algorithm, which further affects the accuracy and stability of the time scale. On the other hand, the error of the noise intensity estimation of atomic clocks will also affect the performance of time scale. Therefore, it is necessary to control the disturbance caused by the variation of noise intensity or the estimation error of noise intensity. In this regard, an adaptive factor is introduced to improve the Kalman filter time scale algorithm, and another adaptive factor is introduced into the state prediction covariance matrix in Kalman filter time scale algorithm. And the values of the two adaptive factors are calculated in real time by using statistics to control the growth of the state prediction covariance. The disturbance of state estimation of atomic clock is reduced, and the accuracy and stability of time scale are improved. In this paper, the sampling interval of simulated data and the measured data are 300 s and 3600 s respectively. The simulated data and measured data are used to calculate the overlapping Allan deviations of the time scale. The results show that the improved Kalman filter time scale algorithm can improve the stability of the sampling time more than 14400 s compared with classical Kalman filter time scale algorithm, and affect the stability of the sampling time less than 14400 s. The degree of influence is related to the weight algorithm of atomic clock. The measured data in this paper are treated by the “predictability” weighting algorithm, which guarantees the long-term stability of time scale. So the simulated data and measured data show that compared with classical Kalman filter time scale algorithm, the improved Kalman filter clock time scale algorithm can improve the accuracy and the long-term stability of time scale.

Abstract: Precision measurement of the density shift caused by the interaction among neutral atoms trapped in an optical lattice has important applications in the study of multi-body interaction and the realization of high-performance optical lattice clocks. The common methods of measuring the density are the self-comparison technique and frequency comparison between two optical lattice clocks. Both methods are based on the identical density shift coefficient and should interrelatedly operate the clock at high- and low-density state, respectively. The precision of self-comparison method is limited by the Dick effect. The synchronous frequency comparison between two optical lattice clocks can realize the precision beyond the Dick limit. However, both methods can only obtain the average density shift and ignore the fact that the magnitude of the density shift is different over the lattice sites as inhomogeneous density distribution in the lattice. In this paper, the synchronous frequency comparison technique based on in situ imaging is used to accurately measure the density shift coefficient of optical lattice clock. Atoms in the optical lattice are simultaneously and independently excited by the same clock laser beam, and the clock transition probability of 11 uncorrelated regions of the optical lattice is simultaneously detected by in situ imaging. Thus, the clock laser noise, which is the root cause of the Dick effect, is common-mode rejected as the frequency difference between uncorrelated regions is measured by the clock transition spectrum. Beyond the Dick-noise-limited stability, the stability of synchronous frequency comparison between uncorrelated regions is consistent with the limit resulting from the atom detection noise. Between the center and margin of the lattice, the differential shifts of the black-body radiation shift, lattice AC Stark shift, probe Stark shift, DC Stark shift, and quadratic Zeeman shift are all below 5 × 10〈sup〉–6〈/sup〉 Hz, which is three orders of magnitude smaller than the density shift and can be ignored in this experiment. Benefitting from the inhomogeneous distribution of atom number and negligible external field gradient in the optical lattice, the compared frequency shift between uncorrelated regions indicates the density shift. By measuring the relationship between the density shift and atom difference, the density shift coefficient is determined as –0.101(3) Hz/atom/site (with a measurement time of 10〈sup〉3〈/sup〉 s), and the fractional measurement uncertainty of the mean density shift of our system is 1.5 × 10〈sup〉–17〈/sup〉.

Abstract: 〈sec〉 The Hong-Ou-Mandel (HOM) interferometer using entangled photon source possesses important applications in quantum precision measurement and relevant areas. In this paper, a simultaneous measurement scheme of multiple independent delay parameters based on a cascaded HOM interferometer is proposed. The cascaded HOM interferometer is composed of 〈inline-formula〉〈tex-math id="M3"〉\begin{document}$ n $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M3.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M3.png"/〉〈/alternatives〉〈/inline-formula〉 concatenated 50∶50 beam splitters and independent delay parameters 〈inline-formula〉〈tex-math id="M4"〉\begin{document}$ {\tau }_{1} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M4.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M4.png"/〉〈/alternatives〉〈/inline-formula〉, 〈inline-formula〉〈tex-math id="M5"〉\begin{document}$ {\tau }_{2} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M5.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M5.png"/〉〈/alternatives〉〈/inline-formula〉, ···, 〈inline-formula〉〈tex-math id="M6"〉\begin{document}$ {\tau }_{n} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M6.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M6.png"/〉〈/alternatives〉〈/inline-formula〉. The numbers 〈inline-formula〉〈tex-math id="M7"〉\begin{document}$ n=1, 2\;\mathrm{a}\mathrm{n}\mathrm{d}\;3 $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M7.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M7.png"/〉〈/alternatives〉〈/inline-formula〉 refer to the standard HOM interferometer, the second-cascaded HOM interferometer, and the third-cascaded HOM interferometer, respectively. Through the theoretical study of the cascaded HOM interference effect based on frequency entangled photon pairs, it can be concluded that there is a corresponding relationship between the dip position and the independent delay parameter in the second-order quantum interferogram. In the standard HOM interferometer, there is a dip in the second-order quantum interferogram, which can realize the measurement of delay parameter 〈inline-formula〉〈tex-math id="M8"〉\begin{document}$ {\tau }_{1} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M8.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M8.png"/〉〈/alternatives〉〈/inline-formula〉. In the second-cascaded HOM interferometer, there are two symmetrical dips in the second-order quantum interferogram, which can realize the simultaneous measurement of two independent delay parameters 〈inline-formula〉〈tex-math id="M9"〉\begin{document}$ {\tau }_{1} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M9.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M9.png"/〉〈/alternatives〉〈/inline-formula〉 and 〈inline-formula〉〈tex-math id="M10"〉\begin{document}$ {\tau }_{2} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M10.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M10.png"/〉〈/alternatives〉〈/inline-formula〉. By analogy, in the third-cascaded HOM interferometer, there are six symmetrical dips in the second-order quantum interferogram, which can realize the simultaneous measurement of three independent delay parameters 〈inline-formula〉〈tex-math id="M11"〉\begin{document}$ {\tau }_{1} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M11.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M11.png"/〉〈/alternatives〉〈/inline-formula〉, 〈inline-formula〉〈tex-math id="M12"〉\begin{document}$ {\tau }_{2} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M12.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M12.png"/〉〈/alternatives〉〈/inline-formula〉 and 〈inline-formula〉〈tex-math id="M13"〉\begin{document}$ {\tau }_{3} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M13.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M13.png"/〉〈/alternatives〉〈/inline-formula〉. Therefore, multiple independent delay parameters can be measured simultaneously based on a cascaded HOM interferometer. 〈/sec〉〈sec〉 In the experiment, the second-cascaded HOM interferometer based on frequency entangled photon source is built. The second-order quantum interferogram of the second-cascaded HOM interferometer is obtained by the coincidence measurement device. Two independent delay parameters 〈inline-formula〉〈tex-math id="M14"〉\begin{document}$ {\tau }_{1} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M14.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M14.png"/〉〈/alternatives〉〈/inline-formula〉 and 〈inline-formula〉〈tex-math id="M15"〉\begin{document}$ {\tau }_{2} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M15.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M15.png"/〉〈/alternatives〉〈/inline-formula〉 are measured simultaneously by recording the positions of two symmetrical dips, which are in good agreement with the theoretical results. At an averaging time of 3000 s, the measurement accuracy of two delay parameters 〈inline-formula〉〈tex-math id="M16"〉\begin{document}$ {\tau }_{1} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M16.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M16.png"/〉〈/alternatives〉〈/inline-formula〉 and 〈inline-formula〉〈tex-math id="M17"〉\begin{document}$ {\tau }_{2} $\end{document}〈/tex-math〉〈alternatives〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M17.jpg"/〉〈graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210071_M17.png"/〉〈/alternatives〉〈/inline-formula〉 can reach 109 and 98 fs, respectively. These results lay a foundation for extending the applications of HOM interferometer in multi-parameter quantum systems. 〈/sec〉