Chaotic Dynamics For Single Particle In An Optical Lattice With Periodical Modulation

In recent years,attribute to the fast development of experimental techniques on preparing and operating ultra-cold atomic gases,one can implement precision quantum engineering via artificial quantum systems,which also provide a new platform for exploring atomic frequency standard,quantum manipulation,quantum precision measurement,quantum entanglement and quantum device.The periodic modulated optical lattice system is widely used to study the quantum tunneling and quantum transport in the classical chaotic systems.In this paper,we studied the chaotic dynamics and manipulation of single particle in one-dimensional tilted lattice with periodic modulation.Under the strong modulating case,the effect of chaos on quantum transport is studied.It is found that the quantum transport of the particle can be manipulated via adjusting periodical modulation.The text is divided into four chapters,which are as follows:In the first chapter we introduce the basic of cold atoms,the optical lattice and its experimental realization,theory of chaotic dynamics,as well as the periodic modulated optical lattices.In the second chapter,we studied the chaotic dynamics and manipulation of single particle in one-dimensional tilted lattice with periodic single-frequency-modulation.Based on the tight binding approximation,the full quantum Hamiltonian of the system is given.The chaotic and regular region are numerically given by employing Poincare section.It is found that the chaos assist quantum tunneling only when the modulation frequency matches with the gradient of lattice;otherwise,the chaos promotes localization by investigating the effect of chaos on quantum transport.Therefore,the quantum transport of the particle can be manipulated via adjusting periodical modulation.In the third chapter,we investigate the chaotic dynamics for a single particle held in an optical lattice with biharmonic modulation.By numerically calculating the Poincare section under different modulation parameters,we find that compared with the case of single frequency modulation,depending on parameter n and phase?,biharmonic modulation can induce regulation island in original high chaotic region,and also can promote high chaotic region.It is found that biharmonic modulation can induce fractional resonance tunneling by investigating the relationship between chaos and quantum transport.In the end,we summarized and discussed our results.