Trap-induced resonances in controlled atomic collisions for quantum information processing

Controlled collisions of ultracold atoms in optical lattices provide new avenues for quantum control and quantum information processing. The ability to precisely vary lattice parameters and the rich internal structure of trapped atoms allow for novel state manipulation. In this research, we investigate and develop new methods for analyzing and designing coherent controlled collisions of ultracold atoms in separated traps.; In order to describe controlled atomic collisions, we develop a detailed scattering model, based on a fully generalized multichannel Fermi pseudopotential, which captures the complete scattering properties and bound states of the true atomic interaction. We derive a proper generalized version of Fermi's pseudopotential for all higher partial waves based on a delta-shell potential in the limit as the shell radius approaches zero, thereby taking into account the higher multipoles not captured by a delta-function at the origin. This pseudopotential corrects long-standing problems in previous generalizations and opens up new possibilities for studying interacting cold atomic gases with high accuracy. We show that this energy-dependent delta-shell potential not only captures the scattering behavior of realistic potentials correctly, but also reproduces the bound-state spectrum when the scattering length is extended to negative energies.; Our generalized pseudopotential can be applied to study interacting trapped atoms in harmonic traps. Using the delta-shell approach, we derive analytical equations for the energy eigenvalues and the eigensolutions. The resulting higher partial wave solutions are investigated and discussed in detail. By analyzing a spherical stepwell test potential, we evaluate and discuss the breakdown of the pseudopotential approximation in the regime of strong confinement by the trapping potential.; Of particular interest is the investigation of controlled collisions of atoms in separated but close traps. We show that for certain trap separations, resonances between molecular bound states and trap eigenstates appear. As the separation between the traps is increased, the energy of the molecular bound state closest to dissociation increases. Avoided crossings occur in the eigenspectrum when the energy of this molecular bound state becomes resonant with eigenstates of the trapping potential. These newly predicted "trap-induced resonances" represent the main result of this work. They are not accounted for in a perturbation theory approach and can be easily observed in very tight traps, which are typical, for example, in optical lattices. The properties of these trap-induced resonances are analyzed and discussed in detail for isotropic and anisotropic separated traps.; These newly predicted trap-induced resonances could feasibly be experimentally observed under realistic circumstances. A particularly promising candidate species is 133Cs. A detailed multichannel scattering calculation, based on realistic interaction potentials of 133Cs including higher partial waves and second order spin-orbit coupling, shows an extremely weakly bound state near dissociation. We apply a multichannel formulation of our generalized pseudopotential to calculate the energy spectrum for interacting 133Cs atoms as a function of trap separation. The energy gap in the spectrum provides a signature by which the trap-induced resonance could be experimentally observed, and we discuss how this could be done in detail. Furthermore, we evaluate the possible implementation of two-qubit logic gates under realistic conditions in 133Cs using this resonant interaction, and address some of the limitations to the fidelity of such gates.