PhD Dissertation Defense
Department of Physics, University of Connecticut
Theory of Two Distinguishable Atoms in an Optical Lattice
We study the Bose-Hubbard model of two atoms in a one-dimensional optical lattice, with onsite atom-atom interaction and periodic boundary conditions. Though this model has been solved analytically, the majority of the analytical solutions do not seem to include stationary states. These are needed to analyze the spectroscopy of a dimer of two atoms in an optical lattice. We develop a unique analytical method and remedy this problem in the case of two identical bosons in a fixed one-dimensional optical lattice. Our results compare well with the existing experimental results. Then, we extend this method to two distinguishable atoms and find that, among other things, a dimer of two distinguishable atoms can be formed in an optical lattice. We highlight the differences in these results from those in the case of two identical bosons. These include stationary states that do not depend on the atom-atom interactions and the ability of the dimer to dissociate into a continuum of states with odd symmetry. Lastly, we investigate the two atoms in the lattice when the lattice is allowed to rotate. The main outcome of this is that the atoms in the lattice can be controlled through adjusting the rotation speed of the lattice.