Theoretical Study Of Quantum Phase Measurement Based On Squeezed-state Interferometer

Quantum metrology is a comprehensive discipline in estimating the parameters of a quantum system with high-resolution and high-sensitivity measurements.Theoretically,quantum metrology,developed from the combination of quantum mechanics and statistical mechanics,becomes an important topic in the basic research.Quantum metrology is also important for multiple areas of scientific research,such as gravitational wave detection,quantum imaging,quantum location and high-precision atomic cdocks.Essentially,quantum metrology belongs to the quantum phase estimation,which depends on the quantum state,the way of phase accumulation and the measurement scheme.In addition,the phase estimator can be obtained by performing a data processing on the measured outcomes.For the unbiased estimator,the fluctuation between the phase estimator and the phase true value is given by the Cramer-Rao bound,which is determined by the classical Fisher information.The core of quantum phase estimation is find the optimal quantum state and the measurement scheme,to make the classical Fisher information equal to the quantum Fisher information,and be proportional to the square of the number of detected states(i.e.,the so-called Heisenberg limit).In this thesis,we analyze the photon counting measurement and the binary-outcome homodyne detection based on the squeezed state interferometer,and then employ the two measurements to calculate the output signal and the phase sensitivity.The main results are as follows.1.For the photon counting measurement of the squeezed state interferometer,we consider the generated N photon state under postselection.The result shows that under the phase-matching condition,the classical Fisher information always saturates the quantum Fisher information.In addition,considering the generation probabilities of N photon state,the phase estimation precision cannot improve the precision beyond the classical limit.2.Take into account all the photon-counting events,the estimation precision of squeezed state interferometer can surpass the classical limit,however,which subjects to the upper threshold of photon-number-resolving detectors.Our analytical and numerical results show when the number resolution threshold is approximately equal to the input photon number,the estimation precision is better than the classical limit.When the resolution threshold is larger than 5 times the photon number,the classical Fisher information returns to the ideal result of the Fisher information.Correspondingly,the phase estimation precision can reach the Heisenberg limit.3.Based on the squeezed state interferometer,we consider the output signal and the phase sensitivity of the binary-outcome homodyne measurement.Both of them can surpass the classical limit,respectively,which is in agreement with the experiment results.Optimizing the parameter,we find the estimation precision can reach the Heisenberg limit.In order to obtain the above results,we first introduce the fundamental goals of the quantum phase estimation,the recent research progresses,and our research basis.Next,we review the definition of light quantum states,their representation in the phase space,i.e.,Wigner’s quasi-probability distribution.Beginning with the chapter 3,according to the recent experiments,we calculate the Fisher information of N photon state,the Fisher information with the number resolution threshold.Moreover,we consider the signal and the sensitivity by using the homodyne detection in the squeezed state interferometer.Finally,we derive the conclusion.