Traditional optical phase imprinting of matter waves is of a dynamical nature. In this paper we show that both Abelian and non-Abelian geometric phases can be optically imprinted onto matter waves, yielding a number of interesting phenomena such as w
avepacket re-directing and wavepacket splitting. In addition to their fundamental interest, our results open up new opportunities for robust optical control of matter waves.
Effects of a periodic driving field on Landau-Zener processes are studied using a nonlinear two-mode model that describes the mean-field dynamics of a many-body system. A variety of different dynamical phenomena in different parameter regimes of the
driving field are discussed and analyzed. These include shifted, weakened, or enhanced phase dependence of nonlinear Landau-Zener processes, nonlinearity-enhanced population transfer in the adiabatic limit, and Hamiltonian chaos on the mean field level. The emphasis of this work is placed on how the impact of a periodic driving field on Landau-Zener processes with self-interaction differs from those without self-interaction. Aside from gaining understandings of driven nonlinear Landau-Zener processes, our findings can be used to gauge the strength of nonlinearity and for efficient manipulation of the mean-field dynamics of many-body systems.
A two-mode Bose-Einstein condensate coupled by a high-frequency modulation field is found to display rich features. An effective stationary Hamiltonian approach reveals the emergence of additional degenerate eigenstates as well as new topological str
uctures of the spectrum. Possible applications, such as the suppression of nonlinear Landau-Zener tunneling, are discussed. An interesting phenomenon, which we call deterministic symmetry-breaking trapping associated with separatrix crossing, is also found in an adiabatic process.
Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection between two p
aradigms of nonlinear mapping systems, i.e., the kicked rotor model and the kicked Harper model, is established. In particular, it is shown that Hofstadters butterfly quasi-energy spectrum in periodically driven quantum systems may soon be realized experimentally, with the effective Planck constant tunable by varying the time delay between two sequences of control fields. Extensions of this study are also discussed. The results are intended to open up a new generation of cold-atom experiments of quantum nonlinear dynamics
