Light-Induced Hofstadter＇s Butterfly Spectrum in Optical Lattices

We propose a scheme to create an effective magnetic field, which can be perceived by cold neutral atoms in a two-dimensional optical lattice, with a laser field with a space-dependent phase and a conventional laser field acting on A-type three-level atoms. When the dimensionless parameter a, being the ratio of flux through a lattice cell to one flux quantum, is rational, the energy spectrum shows a fractal band structure, which is so-called Hofstadter＇s butterfly.     

Light-Induced Hofstadter＇s Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagomé Lattice

We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper＇s equations from the Schr？dinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper＇s equations. We analyze the properties of the Hofstadter＇s butterfly spectrum and discuss its observability.     

Current Density and Local Magnetic Field of Spontaneous Magnetization States in One-Dimensional Superconducting Corner Junction Arrays

Current density and local magnetic field of spontaneous magnetization states in one-dimensional superconducting connected corner-junction arrays have been analysed by solving the phase equation of the arrays. The solutions can be expressed by the Jacobian elliptic functions, which have been calculated numerically. Our results show that the corner fluxons with a fraction of half flux quantum are arranged in an antiferromagnetic fashion, which is In agreement with the recent experiments observed by Hilgenkamp et al. (Nature 422(2003)50). In addition,we present the magnetization flux of each corner junction in the array as a function of facet length.     

Effect of the Initial Laser Phase on the Interaction Between Relativistic Electron and Ultra－Intense Laser Field in a Strong Uniform Magnetic Field

We investigate the influence of the initial laser phase on the interaction between relativistic electron and ultraintense linear polarized laser field in a strong uniform magnetic field. It is found that the dynamic behaviour of the relativistic electron and the emission spectrum varies dramatically with different initial laser field phases.The effect of changing initial phase is contrary in the two parameter regions divided by the resonance condition.The phase dependence of the electron energy and velocity components are also studied. Some beat structure is found when the initial laser phase is zero and this structure is absent when the initial laser phase is a quarter of a period.