| Humans have always sought the capacity to precisely and effectively manipulate quantum systems as part of their pursuit of understanding matter.The standard experimental technique for setting up and controlling the system is usually realized in the form of a static external field,which severely restricts the range and adjustability of the regulatory parameters.With the development of driving technology such as laser and microwave,periodic drive can provide new methods for this purpose.In the continuous exploration of cycle driving,a set of research methods based on Floquet theory has been proposed.As a preliminary step for further Floquet engineering to govern and control the state of matter,Floquet theory is utilized to build the drive’s Hamiltonian and study the evolution outcomes of various periodically driven systems.With the help of Floquet engineering,quantum systems can be tuned to a wider range of nonequilibrium states,and their properties can be tuned "on demand".At present,the practical application of this technology is still in the preliminary stage,and many methods still require detailed theoretical analysis,while quantum simulation technology can be used to verification and optimization for this purpose.Among various quantum simulation platforms,the Nitrogen-Vacancy color center(NV center)in diamond lattice stands out because of its long coherence time at room temperature and ease of manipulation by microwave and optical readout.In this thesis,the basic concepts of Floquet theory,including effective Hamiltonian,quasi-energy and micro-motion,and the application of Floquet engineering in band adjustment are introduced first.After the introduction of basic background knowledge,our work and achievements in the research of periodically driven system are shown in the following chapters,which mainly include the following contents:1.Construction of the NV center system’s experimental platform is realized.In this thesis,the main features and technical principles of NV center are reviewed,including the basic optical initialization and readout processes,as well as microwave manipulation methods.In addition,dynamical decoupling techniques and its applications in protecting coherence and detecting nuclear spin are also introduced,which provides the technical basis for NV’s larger scale quantum control experiments.The technical details of platform construction are shown in the following section and another set of scanning imaging system based on NV center that we have built is introduced later.This scanning imaging system can be directly used for local detection of many-body systems,and will become a powerful tool for future Floquet system research.2.The dynamical quantum phase transition of the periodically driven system is studied through experiments using NV electron spin.Dynamically quantum phase transition is a theoretical concept rising in recent years.Different from the traditional phase transition governed by temperature drive,this type of phase transition is governed by time parameter and usually triggered by quantum quench.The target of our simulation is a kind of dynamical quantum phase transition induced by periodic drive without quenching,called Floquet dynamical quantum phase transition.This phase transition is caused by the Floquet micro-motion characteristics,and has rich topological properties.This work simulate the occurrence of phase transition,and detect the return amplitude,rate function,topological number and other physical quantities characterizing the phase transition.3.The topological properties of the Floquet version of the Haldane model are studied through experiments using NV electron spin.In the original Haldane model,the topological number is extremely limited.With the help of periodic drive,the parameters of the model and the band gap of the system can be effectively adjusted,and the topological number of the band can be further improved.In this work,the static spin texture structure under the Floquet quasi-energy band is experimentally detected,and the topological number of the system is calculated based on it.In addition,the experiment of dynamical spin texture in this work can also give the same topological number results,which provides more options for further experiments.At the end of this thesis,the content of the thesis is summarized briefly.And we will look forward to more application possibilities of the combination of periodic drive technology and NV center system. |
