Coherent Control Of Ultracold Atomic Regular And Chaotic Transport

Transport phenomena are the heart of many problems in physics. In recent years, the coherent control of interacting ultracold atomic transport by employing external field has attracted great interest. We investigate the tunneling dynamics of two interacting bosons and Bose-Einstein condensate in this thesis via utilizing a periodic driving field, based on the Bose-Hubbard model and GP equation, respectively. The thesis is divided into five chapters. Our own main works are concentrated on the chapters two, three and four. This thesis is organized as follows.In the first chapter, we give a brief introduction about the development of ultracold atom physics and the experimental realization of quantum well, and the dynamics of few-atom held in tight-binding model and transport phenomena of Bose-Einstein condensate.In chapter two, we investigate quantum tunneling of two repulsive bosons in a triple-well potential subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-off-resonant strongly-interacting regime in which the dominant tunneling of paired states is a second order process, and the selected coherent destruction of tunneling occurs either be-tween doublons, or between unpaired states. Two Floquet quasienergy bands of the both kinds of states are given analytically, where a fine structure up to the second order corrections is displayed. The analytical results are confirmed numerically based on the exact model, and may be particularly relevant to controlling corre-lated tunneling in experiments. The second order results of long time scale could be conveniently applied to adiabatic manipulation of the paired particle correlated tunneling, and may serve as a useful stepping stone to understand the transport behavior of particles in a driven lattice system. The results from the triple-well system can also be extended to the three-level system and triple-quantum-dot system, exhibiting richer new physics.In chapter three, we investigate the coherent control of two bosons held in a one-dimensional optical lattices with an impurity via time-periodic driving field. In the high-frequency driving regime, we deduce analytically the time-independent effective Hamiltonian by using a unitary transformation. We study the effects of the impurity and the interaction strength between the atoms on the dynamics of the two atoms in the dynamic localization condition. The tunneling of two atoms can take place between the impurity and its two nearest-neighbor sites when the ratio of the impurity potential strength and the ac driving frequency is an integer. For weakly interacting strength of atoms, the atoms can move independently around the three sites, but for more strongly interacting strength, the atoms can form a stable bound pair, and they cannot move independently. Two atoms will occur CDT in the whole optical lattice when the interaction strength between the atoms is equal to the impurity strength. When the ratio of the interaction strength and the impurity strength becomes other integers, the atoms tend to separate due to they can absorb energy from the driving field.In chapter four, under the effective particle approximation, we study temporal ratchet effect for chaotically transporting a matter-wave soliton consisting of an attractive Bose-Einstein condensate held in a quasi-one-dimensional symmetric optical supperlattice with biperiodic driving. It has been known that chaos can substitute for disorder in Anderson’s scenario and only a higher level of disorder can induce Anderson localization for some special systems, and a matter-wave soliton could transit to chaos with high or low probability in the high-or low-chaoticity region. We demonstrate that varying the driving phase to break time reversal symmetry of the system can enlarge a size of the high-chaoticity region for the low-and moderate-frequency regions. Consequently, the parameter region of exponential spatial localization is enlarged the same size and the delocalization region which includes the subregions of ratchet effect and its reversal related to the low chaoticity is correspondingly shorten. The positive dependence of the localization on the driving frequency has also been revealed. The results mean that the high-chaoticity could replace the higher disorder and assists Anderson localization. From the results we suggest a method for controlling directed motion of the matter-wave soliton by adjusting the driving frequency and amplitudes to strengthen or suppress even reverse the temporal ratchet effect.In chapter five, we give a conclusion of the work and an outlook about the transport of ultracold atom in the spatiotemporal potential.