Theoretical Investigation On The Sensitivity Of The Mach-Zehnder Interferometer

Improving the sensitivity on estimated phase is an endless goal. As one typical interferometer, Mach-Zehnder interferometer plays an important role in improvement the accuracy of estimated phase, which relates not only to the fundamental concepts, but also in real applications. Therefore how to improve sensitivity of estimating phase, is one of the hot points for current researches. Based on Mach-Zehnder interferometer and Fisher information, we are going to explore one kind of method with an high sensitivity, independent on the estimated phase.Searching a phase measurement which is independent of estimated phase is a hot point today. Because of the dependence of the estimating phase in the usual measurement method, to estimate a small phase shift with the highest resolution in the process of practical application, requires the addition of a feedback loop generally. In this paper, we focus on the study of the relationship between the phase and its sensitivity got from the commonly measurement method, especially on the cause of the low sensitivity on special estimated phase.In the first part, we briefly introduced the basic concepts on the MZ interferometer and relative theories, specially on the study of Fisher information. In the second part, we presented our theoretical analysis on the phase sensitivities dependent on the estimated phase to look for the measurement with high accuracy and independent on the estimated phase. We haves used the Monte-Carlo algorithm to investigate the phase sensitivity of the Mach-Zehnder interferometer, which is illuminated by a coherent state in one input part and a vacuum state in the other part. As usual, the phase information is extracted from the photon number difference. A phase dependent relation with estimating phase is explored. And further analysis shows that the phase sensitivity is due to the biased measurement in this region, where the nonlinearity of the function f-1 between the estimated phase and the measurement quantity lead the phase estimation is biased. In the end, we suggest one possible method to develop a independent sensitivity method.