Researches Of Quantum Metrology And Quantum Battery In Periodic Driven System

As an important branch of modern physics,quantum mechanics describes the basic dynamic laws of the world.Through quantum mechanics,we have further explored the world,especially the microscopic fields where the quantum effects are more obvious.With further development,we gradually turn our attention from quantum theory to application.In the field of science and technology,more and more technical schemes about quantum devices have been proposed.Especially,quantum precision measurement and quantum energy storage devices,such as quantum batteries,have aroused attention in recent years.In this paper,we will focus on the periodic quantum driven systems to study the quantum precision measurement theory and the quantum batteries.In Chapter 1,we introduce the quantum precision measurement theory and the quantum batteries briefly as the research background.And the periodic quantum driven system is also briefly introduced.In Chapter 2,we first introduce the Floquet theory,and with it,we get the solution of the general periodic quantum driven model.Then we introduce a quantum system driven by the harmonic fields.To solve the system,we introduce the traditional rotating wave approximation(RWA)and the counter-rotating hybridized rotating wave approximation(CHRWA).With these two methods,we get the approximate solution of the model.Then we introduce the fidelity of the time evolution operator to compare the effective ranges of these two approximations.In Chapter 3,we first introduce the theory of the parameter estimation,and give the Cramer-Rao inequality with the Fisher information.Then we further derive the quantum Cramer-Rao inequality and the quantum Fisher information.The maximal quantum Fisher information in the general unitary parameterization process has also been solved in this chapter.With the results,we get the maximal quantum Fisher information in the su(2)type unitary parameterization process.As an example,we apply the theory on semi-classical Rabi model and get the maximal quantum Fisher information of the parameters in the model.With the results,we find the optimal measurement scheme for the parameters in the semi-classical Rabi model.In Chapter 4,we give the charging model of quantum batteries based on the quan-tum driven system.In order to study how to improve the charging efficiency,we introduce a general harmonic driving in which the driving strengths,driving frequencies and initial phases of the three orthogonal directions are all adjustable.We introduce timedependent charge saturation to describe the charging efficiency of quantum batteries,and propose the unsaturated charging mode.With CHRWA method,we get the analytical solution of the time-dependent charging saturation of the charging system.The relationships between the time-dependent charge saturation and the parameters of general driving field are discussed both analytically and numerically.And according to the Floquet theorem,we give the expressions of time-dependent charge saturation with the quasienergy and the Floquet states of the system.With both the analytical and numerical results,we find the optimal parameters to reach the best charging efficiency.In Chapter 5,we summarize the results of this article and give some further prospects.