Coherent Control Of Atomic Tunneling In A Kind Of Chaotic System

At the beginning of 21st century, there appears the same trend of develop-ment that people hope to realize the quantum manipulation of a single atom in several important fields of science and technology, such as genetic engineering in biology, choosing reaction of chemical bond, and miniature computer and machine. The development of laser technology provides a effective tool for us to realize the coherent control of a single atom, and theoretically and experimentally leads to the rapid development of the research about the interaction between laser field and a single atom. Now, the research about atomic manipulation induced by laser field has been made great progress. The main content of the thesis is the coherent manipulation of tunneling for a single atom in a few-well system, we investigate systematically the coherent control of a single atom in a kind of classi-cally chaotic systems, such as the driven one-dimensional double-well, triple-well and two-dimensional four-well systems. The results obtained in our work provide a theoretical reference for the research of quantum devices, such as quantum switch and single-atom transistor.The thesis is divided into six chapters. In the first chapter, we give a brief introduction about the laser-cooling and-trapping of atom(s), Floquet theory and the research progress for coherent control of quantum tunneling in periodically driven few-well system.In the second chapter, we investigate the coherent control of quantum tunnel-ing for a single atom held in a one-dimensional driven double-well potential, where the barrier is controlled by a laser field. Three frequency regions are found based on Newton's classical equation. For given parameters, the space-time evolution of atomic wavepacket exhibits different dynamics of atomic tunneling in different frequency regions. When the driving frequency is in a moderate-frequency region, the classical dynamics is chaotic and the irregular quantum tunneling is demon-strated. In low- and high-frequency regions, the classical trajectories are located in initially occupied wells regularly, and the corresponding tunneling dynamics are il-lustrated. For a given driving amplitude, a lower parameter v is found below which the atom possesses nonzero probabilities in the two wells simultaneously, except for the discrete values of driving frequencies,ωn=v/n with n=1,2,... and v is a constant that depends on driving strength. Based on the space-time evolution of probability wavepacket, we find that, for such discrete driving frequencyωn with odd n, the wavepacket is completely located in one well alternately for a long time after n tunneling around the lowest barrier. For even n, the wavepacket always is located in the initially occupied well for a long time after n tunneling. Thus, time average of the probability reveals the Rabi oscillation for odd n and the approxi-mate coherent destruction of tunneling for even n. In high-frequency region, the long-playing localization of wavepacket is shown and the time located in one well can be modulated by adjusting the ratio of driving strength and frequency, where the smaller ratio leads to the longer time located in each well.In chapter three, we investigate the coherent control of a single atom held in a quartic double-well driven by two-frequency laser fields, which can be used to simulate symmetric or asymmetric sawtooth driving field by adjusting the driv-ing parameters. Based on perturbation methods, it is shown analytically and numerically that the coherent destruction of tunneling could occur only for the symmetric intense driving, and application of the asymmetric sawtooth driving field leads to the increase of tunneling rate. The results agree with the recent experimental results. We also exhibit the effect of multiple photon resonances on the tunneling withεO=nω, through a additional dc field. Finally, we demonstrate a connection between the classical chaos and high quantum tunneling rate induced by asymmetric driving field numerically.In chapter four, the coherent control of quantum tunneling is investigated for a single atom held in a driven triple-well potential without tight-binding ap-proximation. In the high-frequency regime within multiphoton resonance, we find the analytical solutions and their numerical correspondences, including the spe-cial Floquet states of invariant populations and the non-Floquet states of slowly varying populations. The Floquet quasienergy spectrum exhibits anticrossings and crossings for different values of the driving parameters, which are associated with different tunneling properties described by the non-Floquet states. In the non-resonance case, the effect of the dc field on quantum tunneling is displayed, where the proper dc strength can strongly prevent atomic tunneling between wells. Ap-plying the presented results, we suggest a scheme for transporting a single atom between nonadjacent wells or between adjacent wells.In chapter five, we investigate the tunneling dynamics of a single atom in a planar four-well potential driven by a high-frequency laser field. We consider the diagonal coupling and obtain analytically Floquet energy spectrum, Floquet state and non-Floquet state. The Floquet state describes the atomic CDT effect. The quasienergy spectrum exhibits anticrossing and crossing, for which the set of driving parameters leads to the effect known as selective coherent destruction of tunneling described by the non-Floquet states. By adjusting the strength and direction of driving field, the tunneling pathway of atom can be manipulated in the three selectable directions, where the switch-like effect can be applied in quantum switch device. Applying the present results, we suggest a scheme for designing a single-atom quantum motor with the driving field as a quantum starter.In chapter six, a summary of the work and a outlook of this topic are given.