马赫-曾德尔干涉仪中位相测量系统的误差分析

山西大学理论物理研究所,太原 030006

凝聚态物理; 马赫-曾德尔干涉仪; 蒙特卡罗方法; 矩估计; 位相; 粒子数差; 高斯分布

Systematic error analysis for phase measurement with the Mach-Zehnder interferometer
Niu Qing, Li Yan, and Li Weidong

Niu Qing, Li Yan, and Li WeidongInstitute of Theoretical Physics, Shanxi University, Taiyuan 030006, P.R.China

condensed matter physics; Mach-Zehnder interferometer; Monte-Carlo algorithm; the method of moments; phase; particle number difference; Gaussian distribution

DOI: 10.3724/SP.J.1249.2015.03306

备注

利用蒙特卡罗(Monte-Carlo)方法对一端输入相干态,另一端输入真空态的马赫-曾德尔(Mach-Zehnder)干涉仪的位相测量误差进行了研究.通过分析粒子数差的测量结果,验证该测量方法所测得的位相值的误差依赖于待测位相θ: 当θ靠近0或π时,测量误差较大,当θ靠近0.5π时,可达到测量误差的最小极限(散粒噪声极限).理论分析发现,待测位相与测量结果之间的函数关系f-1的非线性导致位相的估计出现偏差.

Using the Monte-Carlo algorithm, we investigate the phase measurement error of the Mach-Zehnder interferometer with a coherent state in one input port and a vacuum state in the other input port. By analyzing the phase measurements based on the difference of particle numbers, we find that the phase accuracy of the Mach-Zehnder interferometer is dependent on the measured phase θ. The minimum limit on measurement accuracy(the shot noise limit)is obtained when θ is around 0.5π, while the measurement error is larger for θ close to 0 or π. Through theoretical analysis, we find that the result is caused by the non-linearity of the function f-1, which is a function between the phase to be measured and the measurement to be estimated.

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