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.

• Received 25 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.020402