Dynamics of a flux qubit coupled to a nonlinear structured environment

We investigate the dynamical decoherence and dephasing of a quantum two-state system (qubit) where the environment is formed by a broadened localized nonlinear mode. This situation mimics recent experimental set-ups where the flux qubit is coupled to a DC-SQUID, the latter used as a flux-sensitive Josephson inductor for qubit readout. Depending on the amplitude of the readout resonant driving, the SQUID behaves as a linear or a nonlinear oscillator. We consider the case of a flux qubit coupled to a SQUID considered as a nonlinear environment, which is itself coupled to an Ohmic bath. For small nonlinearities, we can find an effective bath description for the environment seen by the qubit. The problem can in fact be mapped onto a spin-boson model with a structured spectral density containing two or more peaks. For vanishing nonlinearity, the spectral density shows a single broadened peak centered at the SQUID plasma frequency. By calculating the qubit's dynamics within the non-interacting-blip approximation, effects of the non-linearity show up in multiple Rabi peaks, a feature which could also be experimentally detected. (orig.)