Multi-outcome Homodyne Detection And Quantum Measurement In A Coherent-state Light Interferometer

Quantum metrology,which combines statistics and quantum mechanics,is a comprehensive discipline that uses quantum means to improve the accuracy of parameter estimation.It has broad application prospects in such fields as gravitational wave detection,quantum imaging,quantum lithography and high-precision atomic clocks.How to prepare a suitable detection state,choose the optimal measurement scheme,and construct the optimal phase estimator to make the phase measurement accuracy break through the classical limit is the core problem of quantum metric.In order to break through the classical limit,some scholars have proposed to use the N-photon entangled state,the squeezed vacuum state and other quantum states as the detection state,but these quantum states are difficult to prepare and easy to wear,so we consider breaking the classical limit through simple coherent states and suitable measurement schemes.Based on the coherent-state light interferometer,this paper adopts the measurement method of multi-outcome homodyne detection to further study the output signal and phase sensitivity of the measurement results.The specific research contents are as follows:1.The direct product of coherent light and vacuum light is input as input light to both ends of the Mach-Zehnder interferometer.The inverse function estimator is constructed by the measurement method of homodyne detection.The Wigner function of the output state and the measured probability is analytically derived.The output signals of the binary-outcome and multi-outcome homodyne detection are obtained by data classification of the measurement results,and we obtain that the phase sensitivity is close to the limit of shot noise,and the output signal achieves super resolution,which is consistent with the experimental results.2.By using Monte Carlo method,the multi-outcome homodyne detection experiment is numerically simulated,its output signal and phase sensitivity under different eigenvalues are analyzed,and the classic Fisher information and the Cramer-Rao lower limit of its phase measurement accuracy of multi-outcome homodyne detection scheme are deeply studied.3.For a specific eigenvalue(that is,the adjacent observable eigenvalues are opposite to each other),the optimal mechanical quantity and average output signal are obtained.The numerical calculation is based on the inverse function estimator of the output signal.It is found that the estimator is asymptotically unbiased,and its phase fluctuations can saturate the lower Cramer-Rao limit,allowing us to obtain more complete phase information.This may also apply to parameter estimation in other multi-output measurementsIn the first chapter,this paper introduces the background,experimental model,research method,relevant research progress and selection basis of quantum metrology In the second chapter,we describe quantum states of light field such as photon number state,coherent state of single mode light field and path entangled state,derivation process of Wigner quasi-probability distribution of coherent state,quantum Fisher information and quantum Cramer-Rao theorem.At the the third and the fourth chapters,based on the experimental progress in recent years,we theoretically calculate the Fisher information of the coherent state and the Cramer-Rao bound(CRB).Finally,we study the output signal and phase sensitivity by binary-outcome homodyne detection and multi-outcome homodyne detection.Finally,we summarize the fill paper.