Novel Dynamical Resonances in Finite-Temperature Bose-Einstein Condensates

We describe a variety of intriguing mode-coupling effects which can occur in a confined Bose-Einstein condensed system at finite temperature. These arise from strong interactions between a condensate fluctuation and resonances of the thermal cloud yielding strongly non-linear behaviour. We show how these processes can be affected by altering the aspect ratio of the trap, thereby changing the relevant mode-matching conditions. We illustrate how direct driving of the thermal cloud can lead to significant shifts in the excitation spectrum for a number of modes and provide further experimental scenarios in which the dramatic behaviour observed for the $m=0$ mode at JILA (Jin {\it et al.} 1997) can be repeated. Our theoretical description is based on a successful second-order finite-temperature quantum field theory which includes the full coupled dynamics of the condensate and thermal cloud and all relevant finite-size effects.