Properties Of The Quantum Systems Under Periodic Driving Fields

Periodically driven quantum systems have more widely controllable special physical properties.They are applied in topological quantum systems firstly.Periodic drives can adjust and control the topological properties of the systems.Inspired by this,we study the physical properties of several quantum systems under the action of periodic driving field,including the quantum optical system and the change of one-dimensional quantum spin chain system under the action of periodic driving field.In this thesis,we first introduce the background of the research,and introduce the usual method of periodic driving in quantum systems,the Floquet theory.Then we introduce several common quantum system efficiencies.The acquisition and simple application of Hamiltonian.We first investigate the physical properties of a special periodic driving field,the Rabi model of quantum optical system under the action of periodic field.It is found that by adjusting the periodicity of the control field and the intensity of the control field,We can adjust the size of the rotational wave term and the non-rotating wave term in the Rabi model and obtain the conditions of the approximation of the rotating and non-rotating waves.Then we study the change and regulation of the quantum phase transition properties of the XY spin model under the action of periodic field,and obtain the exact analytical solution,the corresponding energy spectrum and the properties of the quantum phase transition.According to the analytical solution,we can determine how to adjust the properties of phase transition points and quantum transitions of XY spin chain system by changing the intensity and frequency of periodic field.Our study provides a meaningful reference for the application of periodic control fields in the regulation of quantum systems.