Quantum State Manipulating Using Weak Measurement

Quantum measurement is not only the basic problem of quantum mechanics,but also plays an important role in the field of quantum manipulation and quantum precision measurement.The quantum measurement model we usually use is the strong measurement.The measurement of quantum states in the strong measurement model leads to wave packet collapse,so it is difficult to apply to scientific problems with practical application value.In the late 1980 s,the quantum weak measurement proposed by Aharonov and other physicists not only promoted the original measurement theory but also provided a new feasible scheme for the development of quantum control field.Over the past 30 years,a large number of theoretical and experimental work have proved the potential advantages of quantum weak measurement theory in weak signal amplification,precision measurement and quantum theory in the field of basic problems,and strongly promote scientists to propose and improve the new theory and experimental methods of microscopic particle motion.Although a lot of innovative work has been done on the preparation and manipulation of states based on quantum strength measurement and has been widely applied in related fields,the preparation,optimization and manipulation of quantum states based on quantum weak measurement has not been explored in detail.We recognize the importance of the problem and based on the preliminary work of the project,we have carried out some work in the preparation and manipulation of quantum states based on quantum weak measurement in the last two years.This dissertation mainly introduces our recent research achievements.Firstly,several important optical devices or instruments are briefly introduced in this paper.Based on the theoretical optical model designed in this paper,the working principle and application of optical beam splitter,Mach-Zehnder interferometer and balanced zero-difference detector are explained.Then the basic theoretical knowledge and different operation methods of quantum state control are introduced emphatically.The coherent state and the compressed state are taken as the ground states to output new quantum states under different operating conditions.The characteristics and applications of these states different from Fock states are summarized.The quantum measurement theory is simply described,and several classifications of quantum measurement are summarized,leading to the theory of quantum weak measurement.The background of weak measurement is described from the proposed,development and application of weak measurement,and the theoretical knowledge of weak measurement is introduced,as well as the importance and application of its unique weak value.On this basis,the state preparation process in the three-wave mixing process is studied by post-selective weak measurement method.It is assumed that the signal input modes are vacuum state,coherent state or compressed vacuum state respectively,and the inert input modes are weakly coherent state respectively,and pass through a medium with second-order nonlinear magnetic susceptibility characteristics.The characteristics of output state compression,signal amplification,second-order correlation and Wigner function based on weak measurement are studied.In the second part,firstly,the work of Yiming Pan et al is briefly introduced.Based on their work,the coherent state is discussed as a pointer state,and the measurement conversion factor is changed by controlling the coupling strength and other related parameters between the measuring instrument and the measuring system,and finally the measurement strength is transformed.The position and momentum of the prepared state and the offset between the initial state are calculated.The transition process from weak measurement to strong measurement is obtained by comparing the curves drawn by the expected value of weak coupling and strong coupling with the calculated results,and observing the three-dimensional function diagram of the expected value of density function in the coherent state,and the controllable parameters of the process are analyzed.