The electronic structures and optical properties of N-doped ZnO bulks and nanotubes are investigated using the first-principles density functional method. The calculated results show that the main optical parameters of ZnO bulks are isotropic (especially in the high frequency region), while ZnO nanotubes exhibit anisotropic optical properties. N doping results show that ZnO bulks and nanotubes present more obvious anisotropies in the low-frequency region. Thereinto, the optical parameters of N-doped ZnO bulks along the [100] direction are greater than those along the [001] direction, while for N-doped nanotubes, the variable quantities of optical parameters along the [100] direction are less than those along the [001] direction. In addition, refractive indexes, electrical conductivities, dielectric constants, and absorption coefficients of ZnO bulks and nanotubes each contain an obvious spectral band in the deep ultraviolet (UV) (100 nm ∼ 300 nm). For each of N-doped ZnO bulks and nanotubes, a spectral peak appears in the UV and visible light region, showing that N doping can broaden the application scope of the optical properties of ZnO.

We analytically and numerically discuss the stability and dynamics of neutral atoms in a two-dimensional optical lattice subjected to an additional harmonic trap potential and artificial magnetic field. The harmonic trap potential plays a key role in modifying the equilibrium state properties of the system and stabilizing the cyclotron orbits of the condensate. Meanwhile, the presence of the harmonic trap potential and lattice potential results in rich cyclotron dynamics of the condensate. The coupling effects of lattice potential, artificial magnetic field, and harmonic trap potential lead to single periodic, multi-periodic or quasi-periodic cyclotron orbits of the condensate. So we can control the cyclotron dynamics of neutral atoms in optical lattice by manipulating the strength of harmonic confinement, artificial magnetic field, and initial conditions. Our results provide a direct theoretical evidence for the cyclotron dynamics of neutral atoms in optical lattices exposed to the artificial gauge magnetic field and harmonic trap potential.

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We investigate the localization of a Bose-Einstein condensate trapped in a two-leg ladder in the presence of an artificial magnetic field via Bose-Hubbard model and discuss its abundant localized phenomena using variational approximation and direct numerical simulation. A two-leg bosonic ladder provides an ideal platform to study the complex dynamics of Bose-Einstein condensates in an optical lattice subject to an artificial magnetic field. As a main result, the system displays rich interesting localized states including self-trapping, soliton and breather. The coupling of the repulsive atomic interaction, artificial magnetic field, the rung-to-leg coupling ratio of the ladder, and the initial population difference of atoms between the two legs of the ladder results in the transitions between the localized states. The critical conditions for the transitions between the localized states are given analytically and are intuitively demonstrated in the phase diagram. Particularly, when the rung-to-leg coupling radio of the ladder satisfies a critical condition, we have the localized states with no local atomic currents between the two legs, otherwise, we observe the localized states with local atomic currents between the two legs. Finally, the results obtained via variational method are confirmed by the numerical simulations of the full discrete nonlinear Schrödinger equation describing the system.

Synopsis The nonlinear dynamics in two-leg ladder system subject to an artificial magnetic field are discussed in detail. The critical conditions for the formation of soliton and for the transition from diffusion to self-trapping are presented, and confirmed by the numerical simulations of the full discrete nonlinear Schrödinger equation.