Theoretical Study Of Novel Optical Lattices And Quantum-controlled Spectrum Of Cold Atoms

Over the past two decades, optical lattices have witnessed fast development and been widely used in various fields, such as laser cooling and trapping of neutral atoms, dynamics of quantum degenerate gases, quantum computing and information processing, and fundamental phenomena in condensed matter. This thesis is mainly dedicated to the generation of novel optical lattices. Corresponding spectrum properties with optical lattices under quantum coherent manipulation is theoretically investigated as well.We first propose a new scheme to form various optical multi-well traps in radial direction by using a simple optical system composed of a line-type cosine grating and a single lens. Evolution of the light field configuration from multi-well trap to single-well trap can be easily controlled by changing the modulation frequency of the fringe patterns of the cosine grating. We also discuss ways to produce two-dimensional optical lattices of various configurations by using an orthogonally or non-orthogonally modulated cosine grating illuminated by incoherent multiple laser beams.Secondly, we propose a novel scheme to produce an optical trap consisting of three wells in axial direction by using a circular cosine grating. Upon illumination by a YAG laser beam with power of～1mW the three optical wells are separated by an average distance of～37μm. Each of them has an average depth of～0.5μK and a volume of～74μm3, suitable for trapping and manipulating an atomic Bose-Einstein condensate (BEC). Due to a controllable grating implemented by a spatial light modulator, evolution of the light filed configuration from a triple-well trap to a single-well one can be easily realized. Within the framework of mean-field treatment, we numerically simulate the dynamic process of loading and splitting BEC as well as the interference among three condensate components after splitting. By fitting the interference fringes with three cosine functions with Gaussian envelope, the information on relative phases of three condensate components is extracted. Afterwards, we further propose a new scheme to generate a three-dimensional (3D) array of 2x2x3 micro wells by using the combination of a circular cosine grating and a line-type one. We numerically simulate the process of loading cold atoms into the optical wells. Our study shows that the atom loading efficiency can be greatly improved by using the method of "dynamic loading". Furthermore, both the loading efficiency and the ratio of atoms trapped in each well have strong dependence on the initial temperature To of cold atoms as well as the grating parameter to. This scheme has potential applications in preparation of 3D addressable optical lattices and quantum information processing.Finally, we propose a controllable photonic band gap structure and study the spectrum properties of cold atoms in one-dimensional CO2 optical lattices under quantum coherent manipulation. Our study indicates that there is a significant photonic forbidden gap near the resonant frequency of Rb atom. By analyzing the reflection and transmission spectrums of cold atoms in the quantum controlled lattices, we obtain the dependences of the spectrum parameters on the cold atom temperature, the mean number of trapped cold atoms, and the size of the lattices. By using a focused resonant laser beam, defect sites can be created in optical lattices. We theoretically study the influence on spectrum caused by a single or two symmetric defect sites in optical lattices. We also explore a method to address each individual site of the optical lattices and detect cold atoms trapped inside.