| The synchronization theory has been developed and perfected by lots of scholars and its application values have been demonstrated in a variety of different fields,such as physic-s,biology,computer science and even sociology,since the synchronization phenomenon was noticed firstly by C.Huygens in the 17th century and its characteristics have been studied continually and systcematically.In recent years,researchers observed some similar phenomena in the microscale experiments and the synchronization behaviors in microsystems can not be described and analyzed accurately by adopting the existing classical synchronization theories because of unique properties of quantum mechanics.Therefore a new kind of syncchronization theory basing on quantum mechanics,that is,the so-called quantum synchronization theory,is established and becomes one of research hotspots.The quantum synchronization theory can be regarded as a new interdiscipline of quantum mechanics,information science and cyber-netics,and its fundamental investigation goals include proposing the definition and measure of quantum synchronization phenomena,designing the schemes to synchronize quantum sys-tems,exploring the appropriate application projects of quantum synchronization,and so on.Hence,the principal contents of this thesis will be aimed at the key questions listed above,that is,a kiund of nonlocal measure of quantum syuchronization based on relative error has been proposed;the scheme realizing quantum synchronization between the optomechanical systcems was designed using the coupling or control,at the same time,the scheme was further extended to multi-body systerns and the synchronization conditions wore obtained;and the applications of quantum synchronization upon the approximation acceleration scheme and parameter identification have been discussed in detail.The specific research contents are as follows.The definition and the corresponding synchronization criterion of the quantum general-ized synchronization have been given on the basis of the quantum complete synchronization and phase synchronization.And the criterion can significantly lower the difficulty of the pro-cess in determining whether the systems can achieve synchronization by analyzing the system dynamic parameters.Meanwhilce,the neccessity of introducing nonlocal terms in tie quan-tum synchronization measure was explained from the perspective of quantum measuremen,and four basic postulates needed to be satisfied in quantum synchronization measure were proposed.On this foundation.a quanhtum synchronization measure satisfying simultaueously the postulates mentiouned above is gained,and those postulates and measure distinguish whether a synchronization phenomenon is quantum synchronization or semiclassical synchro-nization.Taken two-body optomchanical systems as an example the schemes of achieving quan-tum synchronization between systems were proposed by using of coupling and control field,respectively,and the explicit analytic expression of the control filed was also got.It was found that the coupling synchronization is of the advantages of simple model and smaller quantum fluctuation.By contrast,the control synchronization method has the merits such as the flex-ible designing,easy realization of generalized synchronization,especially the systems can be driven to synchronization state rapidly.Subsequently,this task was extended to multi-body systems.The corresponding synchronization conditions of realizing quantum synchroniza-tion among systems are obtained when the coupled quantum systems are taken as nodes to construct the star network,the small world network and the scale-free network,respectively.In particular,these synchronization conditions are still applicable even though the coupling structure among systems is varying and their validities are further verified through simulating the evolutions of quantum networks composed of cavity QED systems and optomechanical systems.Finally,two schemes to optimize quantum information processing by utilizing quan-tum synchronization are proposed,that is,quantum approximation acceleration scheme and quantum parameter identification scheme.By considering the quantum Zeno approxima-tion acceleration as a.quantum generalized synchronization issue,the general formulae for the acceleration Hamiltonian and acceleration field were given.Compared with the rela-tive investigations of common approximate acceleration scheme,the quantum generalized synchronization relaxes the limitation of the control target so that the acceleration Hamilto-nian can be selected flexibly.Subsequently,a scheme to identify the unknown parameters in quantum systems was designed by constructing dynamic equations of a virtual system and making them synchronize with the target parameters.This scheme is still applicable when the evolution of the system presents the random chaotic behaviors. |
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