We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (“wobbling”) of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctuating external electrical fields for a quantum gate operation (controlled-NOT) is determined and the fidelity for that operation derived.

• Received 15 October 1998

DOI:https://doi.org/10.1103/PhysRevA.59.3766