Coherent Manipulation Of Few-Particle Tunneling Via Special Quantum States And Spin-Orbit Coupling

Coherent manipulation of quantum tunneling in a few-particle system has been the focus for scientific research workers. It is not only the heart part of quan-tum coherent control, but also one of major tasks in quantum engineering and quantum information processing. Further, the rapid development of laser technol-ogy provides an effective tool for us to realize the quantum control of quantum tunneling in a few-particle system. In 2011, Lin et al. firstly realized a synthetic spin-orbit (SO) coupling in the spinor Bose-Einstein condensate (BEC) in exper-iment. In recent years, many researchers have focused on studying the ultracold atomic system with spin-orbit coupling, because the effect of spin-orbit coupling can lead to a lot of novel physical phenomena. The thesis mainly studies the coher-ent control of quantum tunneling dynamics of three bosons held in a driven double well without considering spin-orbit coupling and a spin-orbit-coupled single atom trapped in an optical bipartite lattice via special quantum states and SO coupling. These results obtained in our work provide a theoretical reference for the research of a more complicated many-body system, the design of quantum switch, atomic transistor and quantum information processing, etc. The thesis is divided into five chapters. Our own main works are concentrated on the chapters two, three and four. The thesis is organized as follows.The first chapter, we give a brief introduction about the basic theory and experiment of ultracold atom physics, quantum tunneling dynamics phenomena and coherent control of quantum tunneling in an untracold atomic system, and a system of SO-coupled ultracold atoms.In the second chapter, we study transparent control of quantum tunneling via unusual analytical solutions for three bosons held in a driven double-well. Under high-frequency approximation, we analytically obtain the fine band structure and general non-Floquet state. At some collapse points of the quasienergy spectra, the latter becomes the unusual special quantum states. Based on the analytical results and their numerical correspondences, we clearly reveal the mechanism of coherent tunneling and suggest a scheme to transparently control the tunneling of three bosons from one well to another. The results can be observed with the current experimental capability [Chen et al., Phys. Rev. Lett.107,210405 (2011)].In chapter three, we use three bosons held in a depth-tilt combined-modulated double-well to study coherent control of quantum transitions between the dark stationary-like states (DSLSs) with the same quasienergy. Within the high-frequency approximation and multiple-resonance conditions, we analytically solve the time-dependent three-body Schrodinger equation and obtain all Floquet eigenstates and quasienergies. By appropriately adjusting the driving parameters and ini-tial conditions, we get different DSLSs and selective CDT (coherent destruction of tunneling) states, which enable us to transparently manipulate the transitions between DSLSs. The analytical results are confirmed numerically and the good agreement between the both results is shown. The transitions between DSLSs without quasienergy difference can be observed and controlled by adjusting the initial and the final atomic distributions in the currently proposed experimental setup, and possess potential applications in quantum device design and quantum information processing.In chapter four, we study coherent control of spin-dependent dynamical lo-calization (DL) and directed transport (DT) of a SO-coupled single atom held in a driven optical bipartite lattice. Under the high-frequency limit and nearest-neighbour tight binding approximation, we find a new decoupling mechanism be-tween states with the same (or different) spins, which leads to two sets of analytical solutions describing DL and DT with (or without) spin flipping. The analytical results are numerically confirmed and perfect agreements are found. Extending the research to SO-coupled single atoms (only a single atom occupying a different double-well in a set of double wells), the spin-current and quantum information transport with controllable propagation speed and distance are investigated. The results can be experimentally tested in the current setups and may be useful in quantum information processing.In chapter five, we give a summary of the work and a brief outlook about the coherent control of quantum tunneling of many-body system with spin-orbit coupling.