Interference and transport of Bose-Einstein condensates - Xiong, Bo (2009)
This dissertation studies the dynamics of atomic Bose-Einstein condensates (nEes) and Bose gases in a suddenly modified potential. Firstly, we investigate the correlation between vortex formation and interference in merging Bose-Einstein condensates. This inherent correlation can explain some experiments in which vortices are formed in interfering condensates. Furthermore, we show the interference properties of merging condensates, particularly the relation of interference among colliding, expanding, and merging condensates, which can explain some complex interference phenomena in recent experiments. Secondly, using the truncated Wigner approximation, we investigate the role of quantum fluctuations in different forms on the transport properties of bosonic atoms in a ID optical lattice. The dynamics of transport with respect to quantum fluctuations in the plane-wave modes is distinct from that in the single-harmonic-oscillator modes. The discrepancies are demonstrated in detail. Quantum fluctuations in Bogoliubov modes lead to stronger damping behaviour of the centre-of-mass motion than quantum fluctuations in the plane-wave and single-harmonic-oscillator modes, which is in agreement with the experiment. Thirdly, the role of the relative phase variation and velocity of two low-density condensates, and quantum noise on interference properties are discussed. In particular, the incoherent atoms have significant effect on the interference visibility and microscopic dynamics. Although the interference pattern is not broken by quantum fluctuations, indicating the robust character of this interference, the process of inner correlations and dynamics is very complex and cannot he understood purely with mean-field theory. Finally, we investigate the elementary excitation spectrum and mode functions of a trapped Bose gas by numerically solving the Bogoliubov-De Gennes equation. The characteristic form of the Bogoliubov matrix, determined by the interatomic interactions, and the interaction between atoms and confining potential, specifies excitation spectra and mode functions. The role of these interactions on the properties of spectra and mode functions are shown.