Abelian and Non-Abelian Geometric Phases in Circuit Quantum Electrodynamics Abstract: Geometric phases depend neither on time nor on energy, but only on the trajectory of a quantum system in state space. We have observed geometric phases in a circuit quantum electrodynamics architecture in which a superconducting qubit is strongly coupled to microwave photons in an on-chip cavity. We first study the geometric phase of a harmonic oscillator realized as the electromagnetic field in the cavity. In this case the qubit serves as an interferometer to measure the geometric phase, which is otherwise unobservable due to the linearity of the harmonic oscillator. We demonstrate the proportionality of the geometric phase to the enclosed area for a variety of path shapes and analyze non-adiabatic corrections to the geometric phase as well as the dephasing due to residual entanglement between the two-level system and the harmonic oscillator. Second, we investigate the contribution of higher excited states to the qubit geometric phase. Going beyond the two-level approximation of the transmon-type qubit, we find very good agreement with theory treating higher levels perturbatively. We also analyze the effect of artificially added noise on the geometric phase and demonstrate the dependence of the geometric dephasing on the path. Finally, we realize non-abelian non-adiabatic geometric phase gates employing the transmon as a three-level system. Our implementation of non-commuting Hadamard-gates and NOT-gates arising from non-abelian quantum holonomies are a first demonstration of one-qubit gates for holonomic quantum computation.
Biography: Dr. Stefan Filipp has joined the quantum device lab in January 2008. In May 2009 he has won an Erwin Schroedinger Fellowship of the FWF Austrian Science Fund. Stefan completed his PhD at the Atominstitut, Vienna, Austria in 2006 and continued as a postdoctoral fellow until his move to ETH Zurich. |