Strontium optical lattice clock at the National Time Service Center

We report the ~(87)Sr optical lattice clock developed at the National Time Service Center. We achieved a closed-loop operation of the optical lattice clock based on ~(87)Sr 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~(-15)τ~(-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.     

浅光晶格中量子隧穿现象的实验观测

基于一维水平光晶格的锶原子光晶格钟实验平台,当系统的稳定度和不确定度达到10-18量级以上时,由量子隧穿效应引起的钟频移变得不容忽视.在浅光晶格中,量子隧穿效应会使钟跃迁谱线发生明显的展宽现象,因此,本文通过研究浅光晶格中的量子隧穿现象,为⁸⁷Sr原子光晶格钟系统不确定度的评估奠定基础.本实验在一维⁸⁷Sr原子光晶格钟平台上,利用超稳超窄线宽的698 nm激光激发⁸⁷Sr冷原子~lS₀(|g>)→~3P₀(|e>)跃迁(即钟跃迁),实现了对锶原子分布在特定量子态的制备.在深光晶格中,将原子制备到|e,n_z=1>态后,再绝热地降低光晶格阱深,然后在浅光晶格中,探测激发态的载波-边带可分辨的钟跃迁谱线.从钟跃迁谱线中观测到载波谱线发生了明显的劈裂,表明原子在光晶格相邻格点间产生了明显的量子隧穿现象.通过对光晶格中量子隧穿机制的理解,不仅有利于提高光晶格钟的不确定度,也可为观测光晶格中费米子的自旋轨道耦合效应提供基础数据.     

Hg~+离子5d~(10)6s ~2S_(1/2)→5d~96s~2 ~2D_(5/2)钟跃迁同位素位移和超精细结构的理论研究

本文首先在Dirac-Hartree-Fock近似下理论评估了Hg~+离子5d~(10)6s ~2S_(1/2)→5d~96s~2 ~2D_(5/2)钟跃迁的质量位移(mass shift, MS)和场位移(field shift, FS)在其同位素位移(isotope shift, IS)中的相对贡献,发现MS远小于FS而可以被忽略.在此基础上,通过系统地考虑该原子体系中主要的电子关联效应,计算了这条钟跃迁FS的精确值以及涉及到的上下两个能级的超精细结构常数,并得到了几种稳定汞同位素离子该跃迁的IS和超精细结构分裂.其中,计算的~(199)Hg~+和~(198)Hg~+离子之间的钟跃迁频率偏移与已有实验测量值相比误差为2%左右.最终,本文给出了汞离子7种常见同位素该谱线的绝对频率值,为实验上的谱线测量提供了有效的理论依据.     

锶光钟Zeeman减速器中截止速度对蓝磁光阱原子数的影响

基于分布函数理论,分析了Zeeman减速器中截止速度对蓝磁光阱装载的影响,研究了Zeeman减速器中截止速度与蓝磁光阱俘获原子数目之间的关系,对比了分布函数理论和通用理论两种模型的拟合结果,结果表明,分布函数理论模型能更好地描述两者之间的关系。利用多匝Zeeman减速器对进入蓝磁光阱的热原子束进行减速,制备了锶光钟的冷原子样品。在光钟系统研制中,利用分布函数理论对Zeeman减速器进行了优化设计,提高了Zeeman减速器的工作效率,为实现更高效更紧凑的Zeeman减速器及光钟小型化提供了参考。     

Experimental Determination of the Landé g-Factors for 5s~2 ~1S and 5s5p ~3P States of the ~(87)Sr Atom

We present an experimental determination on the Lande g-factors for the 5 s~2 ~1 S_0 and 5 s5 p ~3 P_0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the ~(87)Sr optical lattice clock. The Zeeman shift of the 5 s5 p ~3 P_0-5 s~2 ~1 S_0 forbidden transition is measured with the π-polarized andσ~±-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 5 s~2 ~1 S_0 g-factor for the ~(87)Sr 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-factorδg between the 5 s5 p~3 P_0 state and the 5 s~2 ~1 S_0 state of the ~(87)Sr atoms is measured in the experiment as well,which are-7.67(36) ×10~(-5) with π-transition spectra and-7.72(43) X 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.     

锶玻色子的“魔术”波长光晶格装载实验研究

光晶格中性原子光钟的不确定度已达到10^-18量级. 本文介绍了碱土金属锶原子玻色子⁸⁸Sr在“魔术”波长处的一维光晶格装载, 实现冷锶原子的囚禁并使锶原子的钟跃迁能级(5s²) ¹S₀-(5s5p) ³P₀在此波长处的交流斯塔克光频移一致. 实验中半导体激光器产生“魔术”光波长(813 nm), 通过实验搭建光学驻波场并获得晶格激光聚焦光束, 束腰半径为38 μm. 经过一级冷却和二级冷却后温度约为2 μK的冷锶原子被此“魔术”波长光晶格囚禁. 通过实验测量得到锶原子玻色子⁸⁸Sr光晶格寿命为270 ms, 数目约为1.2×10⁵, 温度在3.5 μK左右, 此外研究了晶格光功率对晶格囚禁原子数目及温度的影响作用. 原子的光晶格装载为后续的钟跃迁提供了长的探测时间, 为进一步的光钟闭环提供了实验基础.     

锶原子二级Doppler冷却及温度的测量

为了减小锶原子跃迁谱线的多普勒增宽及频移,需要对锶原子进行激光冷却以降低它的速度,而一级冷却只能将原子温度降低至mK量级,这样的原子其速度过大而无法有效地装载至光晶格中,因此必须进行二级冷却.锶原子存在单重态与三重态(5s2)1S0-(5s5p)3P1间互组跃迁,利用与其跃迁波长在689 nm的窄线宽激光对锶原子进一步冷却,可将锶原子团温度降低至μK量级.利用时序有效、准确地控制磁场和光场与原子相互作用时间,通过飞行时间法对锶冷原子温度进行了测算.实验中应用计算机精确控制磁光阱区域中冷原子团下落时间,EMCCD记录冷原子团初始时刻和下落20 ms后的状态.经过分析计算二级冷却温度为4.39 μK,不确定度仅为0.19 μK,二级冷原子团数目约为1.2×10 7.低温二级冷却锶原子温度及原子数目的获得为锶光钟跃迁信号的信噪比估计提供实验参考,也是实现高精度时间频率标准的前提.     

Precision frequency measurement of ~1S_0–~3P_1 intercombination lines of Sr isotopes

We report on frequency measurement of the intercombination(5s2)1S0–(5s5p)3P1transition of the four natural isotopes of strontium,including88Sr(82.58%),87Sr(7.0%),86Sr(9.86%),and84Sr(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 2.8×10-13at 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.     

Theoretical calculation of the quadratic Zeeman shift coefficient of the 3P0o clock state for strontium optical lattice clock

In the weak-magnetic-field approximation, we derived an expression of quadratic Zeeman shift coefficient of $^3P^{\rm o}_0$ clock state for $^{88}$Sr and $^{87}$Sr atoms. By using this formula and the multi-configuration Dirac-Hartree-Fock theory, the quadratic Zeeman shift coefficients were calculated. The calculated values $C_2$ = $-23.38(5)$ MHz/T$^2$ for $^{88}$Sr and the $^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm9/2$ clock states for $^{87}$Sr agree well with the other available theoretical and experimental values, especially the most accurate measurement recently. In addition, the calculated values of the $^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm9/2$ clock states were also determined in our $^{87}$Sr optical lattice clock. The consistency with measurements verifies the validation of our calculation model. Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition, for example, the new proposed $^1S_0$, $F = 9/2$, $M_F = \pm5/2$-${}^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm3/2$ transitions.     

Reconciliation of Theoretical Lifetimes of the 5s5p3P2o Metastable State for 88Sr with Measurement: The Role of the Blackbody-Radiation-Induced Decay

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⁺⁶⁰⁰s,measured using the magneto-optical trap as a photon amplifier to detect the weak decay events, is approximately60% larger than the previous experimental value τ = 520_-140⁺³¹⁰s. By considering the electron correlation effec...