铯原子喷泉钟Rabi和Ramsey牵引频移的理论研究  

Theoretical study of Rabi and Ramsey frequency pulling shift in Cesium fountain clock

作　　者：施俊如 阮军[1,2] 管勇[1,2,3] 王心亮[1,2,3] 刘丹丹[1,2,3] 林睿[1,2,3] 张辉[1,2] 陈江[1,2,3] 余凤翔[1,2,3] 张首刚[1,2] SHI Jun-ru RUAN Jun GUAN Yong WANG Xin-liang LIU Dan-dan LIN Rui ZHANG Hui CHEN Jiang YU Feng-xiang ZHANG Shou-gang(National Time Service Center, Chinese Academy of Sciences, Xi＇an 710600, China Key Laboratory of Time and Frequency Primary Standards, Chinese Academy of Sciences, Xi＇an 710600, China University of Chinese Academy of Sciences, Beijing 100049, China)

机构地区：[1]中国科学院国家授时中心,西安710600 [2]中国科学院时间频率基准重点实验室,西安710600 [3]中国科学院大学,北京100049

出　　处：《时间频率学报》2016年第4期255-265,共11页Journal of Time and Frequency

基　　金：国家自然科学基金资助项目(61127901)

摘　　要：Rabi和Ramsey牵引效应是影响铯原子喷泉钟频率不确定度的重要因素之一。构建了铯原子喷泉钟中微波腔的辐射场与冷原子团相互作用的物理模型,获得了原子—辐射场哈密顿量和时间演化算符。通过数值求解时间演化算符的薛定谔方程,用蒙特卡洛方法模拟原子团速度和密度的二维分布,获得了钟跃迁概率和Rabi和Ramsey频移,并对频移量与初始原子|3,±1>态对称性、|3,0>与|3,±1>态相干和相干相位的关系进行了理论分析,应用于铯原子喷泉钟得到Ramsey腔微波脉冲面积是7π/2时非相干和相干初始原子态对应Rabi和Ramsey牵引频移量级分别为10-18和10-14,且频移量与相干相位呈三角函数关系,与PTB评定该项频移得到的理论及实验结果一致。Rabi and Ramsey frequency pulling effect is one of the important factors, which influence the uncertainties in the Cesium fountain clock. This paper builds a physical model that describes the interaction between radiation field and cold atom molasses in the Cesium fountain clock＇s microwave cavities, also gets the Hamiltonian and time evolution operator for the interaction between atom and radiation field. By solving the timeevolution operator＇s Schrodinger equation numerically and using Monte Carlo to simulate the two dimensional distribution of atoms＇ velocity and density, we got the transition probability and the Rabi and Ramsey frequency shift for the clock. We also theoretically analyzed the relation between the frequency shift and the initial atomic symmetry between ｜3, ＋1〉 states, the coherence between ｜3, 0〉 and ｜3, ＋1〉 states, the coherent phase, obtaining the related functional relations. Applying to the Cesium fountain clock, we obtained that the magnitudes of Rabi and Ramsey frequency pulling shift for initial atomic coherence or incoherence are 10^-18 or 10^-14 respectively when the microwave pulse area in the Ramsey cavity is 7π/2, and also obtained that the frequency shift varies with the coherent phase as a trigonometric function, which coincide with PTB＇s theoretical and experimental result in evaluating this frequency shift.

关 键 词：Rabi和Ramsey牵引频移 初始原子相干态 铯原子喷泉钟 频率不确定度 

分 类 号：TM935.115[电气工程—电力电子与电力传动]