Geometric Phase and Non-Adiabatic Effects in an Electronic Harmonic   Oscillator
  Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting qubit as a non-linear probe of the phase, otherwise unobservable due to the linearity of the oscillator. Our results demonstrate that the geometric phase is, for a variety of cyclic trajectories, proportional to the area enclosed in the quadrature plane. At the transition to the non-adiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. The demonstrated controllability makes our system a versatile tool to study adiabatic and non-adiabatic geometric phases in open quantum systems and to investigate the potential of geometric gates for quantum information processing. 
M. Pechal, S. Berger, A. A. Abdumalikov Jr., J. M. Fink, J. A. Mlynek,   L. Steffen, A. Wallraff and S. Filipp
quant-ph