We study the guiding of $^{87}$Rb 59D$_{5/2}$ Rydberg atoms in a linear, high-gradient, two-wire magnetic guide. Time delayed microwave ionization and ion detection are used to probe the Rydberg atom motion. We observe guiding of Rydberg atoms over a
period of 5 ms following excitation. The decay time of the guided atom signal is about five times that of the initial state. We attribute the lifetime increase to an initial phase of $l$-changing collisions and thermally induced Rydberg-Rydberg transitions. Detailed simulations of Rydberg atom guiding reproduce most experimental observations and offer insight into the internal-state evolution.
Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in
the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses the dispersion of the condensate in momentum space. When the mean field becomes large, soliton and vortex structures appear in the condensate wavefunction.
The superfluid to one-dimensional Mott-insulator transition of a 87Rb Bose-Einstein condensate is demonstrated. In the experiment, we apply a one-dimensional optical lattice, formed by two laser beams with a wavelength of 852 nm, to a three dimension
al BEC in a shallow trap. We use Kapitza-Dirac scattering to determine the depth of the optical lattice without knowledge of its exact geometry. We further study the dynamics of the transition as well as steady-state phase behavior specific to the one-dimensional case.
