Theoretical Study Of Quantized Vortices And Quantum Reflection In Bose-Einstein Condensation

Bose-Einstein condensates (BECs) is a relatively newly discovered form of matter that was observed in dilute atomic gases for the first time in 1995, and is now a subject of intensive theoretical and experimental study. Because of its unique properties, the investigation of BECs has unanticipated impact for people to understand and exploit the important and fundamental issue in quantum mechanics. The past decade has seen a dramatic progress in the research of BECs both theoretically and experimentally. In this dissertation, we focus our investigation on the quantized vortex and the quantum reflection in BECs. The main contents are as follows:1. We have proposed the concept of vortex-antivortex coherently superposed state (VAVCSS) in BECs and verified that the VAVCSS can be stable in a harmonic potential. And we also have investigated the fundamental properties of VAVCSS. The density distribution of the VAVCSS has a petal structure which is determined by the quantum circulations and proportion of the vortex and antivortex. Furthermore, we have proposed a feasible scheme to generate a single quantized coherently superposed vortex and antivortex state with arbitrary proportion by compressing and rehabilitating the harmonic trap with specific time order, which is proven by numerical simulations.2. We have investigated the two-dimensional quantum reflection with vortices in Bose-Einstein condensates incident on a solid surface of silicon. This is a unique quantum reflection process considering the fundamental properties of quantized vortex. Our investigation has shown that:â…°) there was an interference effect between the incident and reflected matter waves as all the atoms in BECs were coherent;â…±) considering the rotation of a vortex, the nonuniform velocity distribution along the surface would play an important role in the quantum reflection process. For example, they would change the characteristics of the interference fringes between the incident and reflected matter waves;â…²) the reflected vortex became unstable for sufficiently low incident velocity or strong interaction. This sort of instability physically originated from dynamics excitations induced by the atomic interaction in the quantum reflection process. The stability diagram was given and we have found that a simple expansion ratio described the boundary between the stable and unstable regions.3. We have investigated the interaction between BECs and the potential barrier formed by the far-off resonant blue-detuned laser. According to the interaction between BECs and the potential, we have proposed:â…°) an experimental scheme to observe the collision between two wave packets in in an infinitely deep well formed by two far-off resonance laser beams (which are used to avoid exciting of the atom) of sufficiently high intensity.â…±) an experimental scheme to achieve a controllable coherent beam-splitter (especially the beam-splitter with 50/50 splitting ratio) by tuning the intensity of the laser beams and then trapping the wave packets after being split with far-off resonance laser beams of sufficiently high intensity.