PhD Dissertation Defense
Department of Physics, University of Connecticut
We theoretically and numerically study the Bose-Hubbard model for two bosons in a one-dimensional optical lattice. We begin with a single-channel model describing two interacting atoms, known as a lattice dimer, and then examine the more nuanced two-channel model. The two-channel model accounts for the presence of an association resonance that facilitates the conversion of an atom pair into a molecule and adds a separate molecular degree of freedom. Lattice dimers in the single-channel case have been extensively investigated, but we resolve the conundrum between these dimers and molecules by employing a two-channel model. The stationary states for the time-independent Schrodinger equation are determined and these states reveal some unusual features, including the existence of the celebrated repulsively bound state. We examine the similarities and differences between the single and two-channel models and find a peculiar qualitative difference between the two. Whereas the usual atoms-only theory yields one bound state for a molecular dimer for either an attractive or repulsive atom-atom interaction, a two-channel atom-molecule theory may give two bound states that represent attractively and repulsively bound dimers occurring simultaneously. Possible methods for experimentally detecting both the dimers and the simultaneous bound states are discussed and we identify several systems for observing this novel aspect of molecular physics. In addition to our theoretical work, we also present the results and verification of our quantum Monte Carlo simulations of the two-channel model.