Resonant Processes in a Frozen Gas

In this thesis are presented analytical results and numerical simulations concerning resonant processes in a frozen gas. This work was begun with the intent of modeling experiments involving energy transfer due to dipole-dipole interactions between ultracold Rydberg atoms, and the subsequent propagation of dipolar excitons. However, the results and the techniques developed to obtain them are more generally applicable to a wide variety of problems. We start by studying a simplified model that considers only the energy transfer process in an infinite medium of randomly distributed atoms. This model is very instructive, because it gives a simplified arena in which to develop the techniques that are used again and again throughout the thesis. Exact analytical results are obtained for the time evolution of energy transfer, its dependence on the detuning from resonance, and the localization distance over which the transfer process is effective. The result for the initial rate of energy transfer turns out to have general validity. This soluble model also provides an excellent means for testing the numerical simulations that are carried out for a finite sample. When we allow for the propagation of dipolar excitons, it is no longer possible to obtain exact analytical solutions, but an approximation has been found that agrees quite well with the numerical simulations for the amplitude of the overall process. Simulations are necessary to find the sample-averaged probability...