Phase Estimation Of Multichannel Interferometers

Mach-Zehnder interferometer(MZI)and SU(1,1)(SUI)interferometer are the mainstream interferometers in the field of current research,but both of them have some defects.In a generic interferometric measurement using an MZI and classical light sources the precision of estimating the relative phase delay inside the interferometer is bounded by standard quantum limit(SQL):(?),where is the average photon number inside interferometer.SU(1,1)interferometer cannot tolerate large photon numbers,resulting in poor absolute phase accuracy.For this reason,a new type of multi-channel interferometer is proposed by combining MZI and SUI.In this paper,the phase estimation limit of multichannel interferometers and the phase sensitivity of intensity detection and homodyne detection under the condition of loss are studied.Firstly,we use quantum Fisher information and quantum Fisher information matrix to study the phase estimation limit of multichannel interferometer in the case of specific input.The results show that in the case of single MZI input,quantum Cram(?)r-Rao bound(QCRB)of the quantum Fisher information after phase averaging is the same as the QCRB obtained by the quantum Fisher information matrix.This bound is not limited by the quantum properties of the input states,but only depends on the input light intensity.Then we further investigate the case of the input double coherent states.It is found that we can eliminate the influence of the initial phase carried by coherent light on the QCRB by adjusting the transmission coefficient.Secondly,the phase sensitivity of intensity detection and homodyne detection in multichannel interferometer is studied by using error propagation theory.The results show that the two detection methods can beat the SQL approximation QCRB in lossless condition.When the photon number loss is considered,the accuracy of homodyne detection is better than that of intensity detection.Moreover,the antiloss ability of the multichannel interferometer can be further enhanced by adjusting the coupling parameters of the homodyne detector.