A quantum system interacting with its environment is subject to dephasing which ultimately destroys the information it holds. Using a superconducting qubit, we experimentally show thatthis 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.
An individual excited two level system decays to its ground state by emitting a single photon in a process known as spontaneous emission. In accordance with quantum theory the probabilityof detecting the emitted photon decreases exponentially with the time passed since the excitation of the two level system. 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 microwave cavity with a fast decay rate. 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.