Investigation Of Ultracold Atom And Molecule Collisions By Using Quantum Defect Theory

This dissertation develops theoretical models for ultracold atomic and molecular collisions in external fields based on quantum defect theory. The main works are summarized as follows.(1)We present a theoretical model for describing ultracold atomic collision based on the multichannel quantum defect theory. An analytical expression for the quantum-defect ma-trix Y is derived for the truncated1/R6model potential, and the threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known, or fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the6Li-40K scattering. The theoretical results agree quite well with the experimental values.(2)We investigate the scattering dynamics governed by the long-range van der Waals plus dipole-dipole interaction potential,-C6/R6-C3/R3, which describes the long-range interaction between two polar molecules in an electric field. In the spirit of quantum defect theory, a set of parameters which are nearly constants in the threshold regime is defined to characterize the scattering process. Using appropriate boundary conditions for the scattering wave functions and relevant parameters, we explore the quantum reflection by and quantum tunneling through the long-range potential. As a sample application, the reactive collision rates of40K87Rb+40K87Rb are calculated.(3)We investigate the quantum reflection by the Casimir-Polder potential which scales as-1/r3at short separation and as-1/r4at long separation. Using the available analytical solutions for the-1/r4potential and quantum defect theory, we develop a three-parameter model for quantum reflection. The three parameters characterizing the potential are es-sentially constant near the threshold. The application scope of the model is examined. For potential dominated by the-1/r4behaviour, which is the case in many realistic atom-surface systems, our model gives accurate results over the energy range in which the quantum re-flection is significant. Moreover, this parameterized model allows one to fit the experimental data efficiently.