Exploring the Effect of Noise on the Berry Phase using circuit QED*

The Berry phase is independent of both energy and time: it solely depends on the trajectory of the quantum system in state space, and is equipped with a certain degree of robustness against slow fluctuations [1,2]. By introducing artificial distortions in the path in state space, we measure the geometric contributions to the dephasing of an effective two-level system. Our experiments, realized with a microwave-driven superconducting qubit, demonstrate that only those fluctuations which deform the path cause geometric dephasing. A direct comparison with the path-independent dynamic phase reveals that the Berry phase is less affected by noise-induced dephasing in the adiabatic limit of long evolution times. \newline [1] G.~De Chiara and G.~M.~Palma, \emph{Phys.~Rev.~Lett.~}\textbf{91}, 090404 (2003) \newline [2] S.~Filipp \emph{et al.}, \emph{Phys.~Rev.~Lett.~}\textbf{102}, 030404 (2009)