Abstract
The major focus of this thesis is the dynamic effects of Feshbach resonances on Bragg scattering from Bose–Einstein condensates. This work is motivated by the JILA experiment of Papp et al. [Phys. Rev. Lett. 101 (2008)], in which Bragg spectroscopy was used to probe the behaviour of a strongly interacting Bose–Einstein condensate of 85Rb, near a Feshbach resonance. This experiment was deliberately designed to explore a region of parameter space in which perturbation theory is not expected to be valid. Close to the resonance, the results from this experiment showed significant deviations from the Bragg scattering behaviour predicted by the simplest perturbative and mean-field theories.
We develop a c-field formalism to study Bose–Einstein condensates with interactions altered by a Feshbach resonance. Recognising that the change in scattering length close to the resonance is caused by the existence of a bound state, we formulate a method for treating ultracold Bose gases in terms of coupled atom and molecule fields. We show how to incorporate this atom-molecule model with a truncated Wigner formalism, and derive expressions for the scattering length and binding energy within this formalism. We also demonstrate how to accurately determine the phenomenological parameters in our c-field formalism by relating these to the corresponding experimental parameters.
Using the model of coupled atoms and molecules, we investigate the properties of a strongly interacting Bose–Einstein condensate, and discuss how the results differ from those obtained using a model of structureless atoms. We derive expressions for the condensate profiles in the Thomas–Fermi limit close to a Feshbach resonance, formulate the Bogoliubov theory for excitations in a coupled atom-molecule system, and investigate the case of Bragg scattering from a uniform condensate using Bogoliubov excitations. We show that even when there is very little difference in the condensate appearance between the atom-molecule model and the structureless atom model — as can be seen in the Thomas–Fermi profile — there can be significant changes in the line shifts of the Bragg spectra.
Finally, we perform numerical simulations, modelling the experiment of Papp et al.. We describe the numerical techniques used for this purpose, and also outline some of the difficulties encountered in simulating the experiment. The results from these simulations are directly comparable to the results from the experiment, and we show that although the experiment was not designed to test this kind of theory, we obtain quantitative agreement with the experimental results.