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

The geometric phase of a spin-1/2 system driven by one and two mode quantum fields subject to decoherence was discussed. It was found that the corrections to the phase in the no-jump trajectory were different when considering adiabatic and nonadiabatic evolutions. The state trajectory on the projective Hilbert space tend to be unaffected by the decoherence. The implications of the results were also analyzed from both fundamental as well as quantum computational perspective