Noise cancellation effect in quantum systems

We consider the time evolution of simple quantum systems under the influence of random fluctuations of the control parameters. We show that when the parameters fluctuate sufficiently fast, there is a cancellation effect of the noise. We propose that such an effect could be experimentally observed by performing a simple experiment with trapped ions. As a byproduct of our analysis, we provide an explanation of the robustness against random perturbations of adiabatic population transfer techniques in atom optics.