Spin-1/2 geometric phase driven by decohering quantum fields

We calculate the geometric phase of a spin-1/2 system driven by one and two mode quantum fields subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when considering adiabatic and nonadiabatic evolutions. We discuss the implications of our results from both fundamental as well as quantum computational perspectives.