Applications Of Quantum Metrology In Phase Estimation And Quantum Phase Transitions

As one of the pillars of modern physics,quantum mechanics has completely changed people’s understanding of the microscopic world since its birth.Moreover,the quantum technology developed based on quantum mechanics is also widely appied to the fields of laser technology,computing,measurement and communication.Quantum metrology is a discipline that studies how to improve the precision of measuring physical quantities through quantum properties.Compared with the measurement system in the classical framework,quantum effects such as entanglement and squeezing used in quantum metrology will further improve the measurement precision.In this paper,we mainly exploit quantum parameter estimation and quantum Fisher information to investigate the phase estimation and the quantum phase transitions.In chapter 1,we focus on the development and recent progress of quantum physics and quantum metrology.In chapter 2,we mainly introduce the basic theory of quantum parameter estimation.We begin with classical estimation theory and give the definition of classical Cramer-Rao bound and classical Fisher information.Then we give the definition of quantum Cramer-Rao bound and quantum Fisher information in combination with quantum measurement theory.Moreover,we also give the quantum Fisher information matrix and the corresponding inequality in the case of multiple parameters,and we also discuss the Cramer-Rao bound for biased estimators.After that,we focus on the calculation of the quantum Fisher information via the spectral decomposition method and we also give the quantum Fisher information under the Bloch representation.In chapter 3,we mainly investigate the application of quantum metrology in the phase estimation.We first introduce the basic architecture and working principle of Mach-Zehnder interferometer,and use SU(2)algebra to give the corresponding unitary transformation of this interferometer.Then we introduce the working principle of the atomic gyroscope based on the Bose-Hubbard model,and make use of the unitary parameterization method to give the expression of quantum Fisher information for any initial state.On this basis,we also discuss the optimal initial state in phase estimation,and take the atomic gyroscope as an example to discuss the optimal initial state on both lossless and lossy conditions.We mainly compare the precision of the NOON state,entangled coherent state,squeezed entangled state and our proposed entangled even squeezed state,and find that entangled even squeezed state has the highest precision when the loss rate is less than 50%.In chapter 4,we focus on the central spin model.Firstly,we analytically solve the dynamic evolution of the central spin model in a spin-spin interaction system without external magnetic field.We take spin 1/2 particle and thermal states as an example to calculate the dynamic evolution and discuss the influence of different environmental conditions on the central spin polarizability.Then we discuss the mapping relationship between the central spin model and Jaynes-Cummings model.We can prove that the operators of two different systems can map to each other when the number of bath spins tends to infinity.The existence of such similarity also leads to collapse and revival in the dynamics of central spin systems.In chapter 5,we mainly study the quantum phase transitions and the applications of quantum metrology in quantum phase transitions.Different from the superradiant phase transition occuring in the Dicke model,the ratio of atomic frequency to the frequency of cavity field in the quantum Rabi model tends to infinity,which has the same effect as the thermodynamic limit.We first present the process of solving the ground state and energy spectrum analytically for the quantum Rabi model and the finite Jaynes-Cummings lattice system under the condition of the frequency ratio tends to infinity,and then we apply this method to the XXZ central spin model.We also investigate the effects of the longitudinal interactions on critical points,the excitation number and the coherence of the ground state in the XXZ central spin model.Finally,we verify the correctness of the longitudinal interaction range and critical point by using the quantum Fisher information,and give a specific measurement scheme for parameter estimation exploiting the XXZ central spin model.In chapter 6,we summarize the full text and give an outlook.