Atomic And Oscillator Synchronization And Its Nonlinear Effects In Coupled-cavity Optical Systems

Since the beginning of this century,there has been a great increase in research interest in synchronization because of its wide application prospects in biology,chemistry,electrical engineering,quantum key distribution,and other fields.The phenomenon of synchronization was first discovered by Huygens in the 17th century.In the subsequent development of classical physics,people have been exploring the mystery of synchronization.The development of synchronous chaos theory among them is a typical one.Since Mari et al.proposed quantum synchronization and clarified the difference between quantum and classical synchronization in 2013,various systems have been used to explore quantum synchronization,including the cavity photo-mechanical system.Cavity optomechanical system has attracted much attention due to its classical and quantum correspondence.And its photoacoustic coupling technology has developed from theoretical exploration to experimental implementation,so it has become a superior platform for studying quantum synchronization.By introducing periodic driving,nonlinearity to the the systems of mechanical oscillators coupled with optical cavities.Many theoretical works has been devoted to improve the degree of synchronization.A natural question is how the addition of atoms in the optical cavity will affect synchronization.In previous studies,synchronization problems in mechanical oscillator,cavity coupling systems have been studied,and it is found that the introduction of additional Kerr nonlinearity improves the synchronization.A natural question is that How do the adding atoms coupling to the cavity affect the synchronization?In this work,we study the synchronization of mechanical oscillator,cavity,atom(MCA)coupling system.Firstly,we construct the Hamiltonian of MCA coupling model,which includes two oscillators and the coupling between them,two optical cavities and the coupling between them,the coupling between oscillators and optical cavities,the coupling between optical cavities and atoms.Then,we phenomenologically calculate the Heisenberg Langevin equation of this model in linear environment.The equation of operator mean value and operator fluctuation are obtained by linearizing operator scheme.Next,the quantum synchronization of the two mechanical oscillators is investigated in the optical coupling channel and the acoustic coupling channel.In order to explore the synchronization between two atoms,using the mean value and fluctuation of atomic operators,we define the atomic synchronization and numerically calculate the atomic synchronization.Generally speaking,the nonlinear term can improve the synchronization effect.However,in this system,the quantum synchronization is suppressed because the nonlinear term induces the increase of system fluctuation.