绝热跃迁方法测量铯喷泉钟冷原子碰撞频移

冷原子碰撞频移是限制铯原子喷泉钟频率不确定度性能的主要因素之一.在使用外推法测量冷原子碰撞频移时,制备密度均匀成比例的原子团是减小系统误差的关键.绝热跃迁方法可以用来实现均匀跃迁比例,均匀度可达10–3.通过理论分析Bloch矢量的演化,导出了误差满足的方程,实验测量了不同参数对跃迁几率的影响,印证了理论分析.在此基础上可以优化实验参数并评估原子有效密度比的不确定度,实现了冷原子碰撞频移的高精度测量.

Investigation of cold atom collision frequency shift measured by rapid adiabatic passage in cesium fountain clock

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 W 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 W.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 W and pulse length T,i.e.WT:The increase of WT 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^–3 uncertainty,which leads to a systematic relative uncertainty of cold collision shift up to 1.6×10^–16.