Chaos-assisted Quantum Transport Of Cold Atom

Chaotic behaviour is ubiquitous and plays an important role in the most fields of modern science and technology. The chaos science develops rapidly with other fields of science, and has been widely applied to physics 、 maths、chemistry、 biology and so on. With the development of laser technology, the coherent ma-nipulation of single particle realized by using laser has attracted more and more attention, and has obtained great progress in theoretically and experimentally. The investigation of the relation between chaos and quantum behaviour in clas-sic chaos system also has get theoretical progress and experimental breakthrough, and gradually develops a hot topic. However, quantum-classical correspondence in chaotic system is still a extremely challenged difficult problem. In this thesis, we study systematically the dynamic of the particle held in a amplitude-modulated and tilted optical lattice based on the chaos theory and quantum mechanics theory, and get some significant results and provide a feasible experiment project for the considered system. The thesis is divided into five chapters, and the first chapter is the introduction of the related theory, we present our own main works in the chapters two、three and four. The main content is:In the first chapter, we introduce briefly the laser-cooling and -trapping of atoms, the optical lattice system, the dynamic of particle in the tight binding approximation and chaos-assisted quantum transport.In the second chapter, we investigate quantum transport of a single particle held in a one-dimensional amplitude-modulated and tilted optical lattice,we define the chaos-assisted localization and delocalization appeared in the classically chaotic regions. We analytically and numerically illustrated the near-resonant regions crossing chaotic and regular regions, whose width are determined by the system parameters. The area of chaotic regions are shrunk with increasing the tilt. In the classical Poincare section, the central regions of the potential wells consist of some small-amplitude " islands " of stability which are separated by the " chaotic sea ". In classical mechanics, the particle localized in a regular island will move in the stable island and can not tunnel to other islands. The particle will spread to the both ends of lattice under the parameters in the resonance region, resulting in delocalization. Chaos-assisted delocalization can occur in the chaos-resonance overlapping regions, while chaos-assisted localization may appear in the other chaotic regions. The degree of localization is controlled by tuning the lattice tilt and the distance between parameter points and the near-resonant regions. The results clarify the long-standing contradiction " does chaos assist localization or delocalization? " and could be useful for experimentally manipulating chaos-assisted quantum transport of single particles in the shaken and tilted optical or solid-state lattices.In chapter three, we investigate the effect of classical chaos on quantum trans-port for a single particle held in an amplitude-modulated and tilted optical lattice. In the nearest-neighbour tight binding approximation, we provide a new exact so-lution of the time-dependent Schrodinger equation for the Hamiltonian and derive the expressions of possibility and mean displacement of the particle. The initial conditions corresponding to the classically chaotic sea and the different phases of initial states are defined. Under such initial conditions and the parameters of quantum resonance, the mean probability distribution of the particle is generally asymmetric, resulting in a nonzero double-mean displacement which describes the chaos-assisted directed transport. For any fixed phase the transport speed is pos-itively related to the driving amplitude, and the transport direction depends on the signs of the tilt. While for any given set of parameters, both the transport speed and direction can be controlled by adjusting the phase of the initial state theoretically. By using a deterministic source of single atoms to detect the double-mean displacement one by one in the related experimental setup, we can confirm the above analytical results, and the numerical value obtained in the experiment can ensure the phase of the particle. The results can be extended directly to dif-ferent physical systems with the governing Hamiltonian similar to our considered system, such as the solid-state lattice, periodic optical waveguide and quantum dot arrays. Applying the obtained results, we can prepare an "accelerators" which can help ones to get particles with different transport speeds, and can design a quantum switch to control transport direction of single particles carrying quantum information.In chapter four, we use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from a unentangled initial state associated with the regular " island " of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in increase of the generation speed and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical " chaotic sea ", which don’t affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.In chapter five, we give a summary of the thesis and a brief outlook of the effects of chaos on the quantum transport of the particle in a amplitude-modulated and tilted optical lattice.