| In this thesis I detail the background, implementation and results of two experiments from relatively different fields of study, both of which involve ultra-cold Rubidium atoms trapped in an optical lattice. The first is an analysis of the superpositions of vibrational states of the lattice. This includes a characterization and modelling of the dephasing of the states, an effect inherent to the lattice. It is found that the lattice geometry is a primary factor in the observed dephasing. This geometry results in position-dependent energy eigenstates in the lattice. Modelling this distribution of energies allows the accurate prediction of several experimental observables and provides useful information for future experiments. Several methods of applying pulse echoes to recover the state in the face of this dephasing are demonstrated, characterized and successfully modelled.;The effects of reversing the sinusoidal potential every q kick periods with q = 0, l, 2,3 are examined numerically with the q = 0, 1, 2 cases being verified experimentally. I have found that when considering the energy absorption of the system the q = 1 case is qualitatively and quantitatively the same as the standard kicked rotor, while the q = 2 case is qualitatively the same as the standard kicked rotor with an effective increase in the scaled dimensionless kick strength parameter, k, of k→ k+ p2 .;The second set of experiments centre around using the optical lattice and Rubidium atoms as a delta-kicked rotor system. First I examine quantum resonances in the delta-kicked rotor. These are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances exist when the effective Planck's constant, a parameter that determines how quantum-mechanically the system behaves, has a value of &plank;&d5;=rs ˙4p , for integers r and s. However only for &plank;&d5;=r˙2p are resonances easily observable. Here I report on the first observation of high-order quantum resonances in a non-condensed atomic sample at values of &plank;&d5;=r16 ˙4p for integers r = 2--6. Quantum numerical simulations suggest that this observation of high-order resonances indicates a much longer spatial coherence than expected from an initially thermal atomic sample. |
