Geometric phase and nonadiabatic 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 its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.

Measurement of geometric dephasing using a superconducting qubit.

A quantum system interacting with its environment is subject to dephasing, which ultimately destroys the information it holds. Here we use a superconducting qubit to experimentally show that this dephasing has both dynamic and geometric origins. It is found that geometric dephasing, which is present even in the adiabatic limit and when no geometric phase is acquired, can either reduce or restore coherence depending on the orientation of the path the qubit traces out in its projective Hilbert space. It accompanies the evolution of any system in Hilbert space subjected to noise.

Observation of Dicke superradiance for two artificial atoms in a cavity with high decay rate.

An individual excited two-level system decays to its ground state in a process known as spontaneous emission. The probability of detecting the emitted photon decreases exponentially with the time passed since its excitation. In 1954, Dicke first considered the more subtle situation in which two emitters decay in close proximity to each other. He argued that the emission dynamics of a single two-level system is altered by the presence of a second one, even if it is in its ground state. Here, we present a close to ideal realization of Dicke's original two-spin Gedankenexperiment, using a system of two individually controllable superconducting qubits weakly coupled to a fast decaying microwave cavity. The two-emitter case of superradiance is explicitly demonstrated both in time-resolved measurements of the emitted power and by fully reconstructing the density matrix of the emitted field in the photon number basis.