Noise fluctuations and the Berry phase: Towards an experimental test

Abstract
Due to its geometric nature Berry's geometric phase exhibits stability to a great extent when exposed to parametric noise fluctuations. Considering an adiabatic evolution of a non-degenerate quantum system the variance of the geometric phase resulting from fluctuations vanishes as the evolution time tends to infinity. Here we present numerical data marking the domain of validity of the adiabatic approximation. We notice that due to second-order effects the variance does not vanish, but rather increases again for evolutions longer than a certain critical time. Furthermore, the occurence of a shift of the mean geometric phase is demonstrated and we give a simple geometrical description in terms of probability distributions of this effect. Finally, an experiment utilizing ultra-cold neutrons is proposed to verify the remarkable dephasing survival of the geometric phase.