Mode coupling and superfluidity of a Bose-Einstein condensed gas

This thesis describes experiments carried out with magnetically trapped Bose-Einstein condensates of 87Rb and the theoretical calculations carried out to explain these results. The first set of experiments explored the connection between superfluidity as manifested in its response to rotation. Superfluids are constrained to have irrotational flow and we saw direct evidence for this in the time-of-flight expansion of a condensate released from a novel purely-magnetic rotating trap. The conservation of angular momentum combined with irrotationality caused the condensate to expand in a distinctively different way to one released from a static trap. A thermal gas may have both rotational and irrotational flow and we showed from analytic calculations and Monte Carlo simulations that it rotates as a rigid-body and this rotational flow was verified by experiment. When the trapping potential was rotated faster than a certain threshold value we observed the nucleation of vortices. In our experiment one or several vortices were reliably nucleated over a range of rotation rates for a given eccentricity. The size of this range increased as the eccentricity of the trap increased. We derived an expression for the upper boundary of the nucleation region for the hydrodynamic equations of superfluids, but the dependence of the lower boundary, corresponding to the threshold rotation rate, on the eccentricity has not yet been explained theoretically. The second set of experiments investigated the nonlinear coupling between collective excitations of the condensate and their strong dependence on the trap geometry. We observed harmonic generation and strong dispersion of the quadrupole mode frequency when tuning our trap geometry across a nonlinear resonance. The matrix element for coupling between two quadrupole modes was calculated and the observations fully explained. In a similar experiment we investigated degenerate down-conversion from a high- to a low-lying scissors mode and observed energy transfer back and forth between the two modes. The coupling rate was found to be proportional to the temperature. (author)