Interplay between dissipation and driving in nonlinear quantum systems [Elektronische Ressource] / Carmen Vierheilig

In this thesis we investigate the interplay between dis-sipation and driving in nonlinear quantum systems for a special setup: a flux qubit read out by a DC-SQUID - a nonlinear quantum oscillator. The latter is embedded in a harmonic bath, thereby mediating dissipation to the qubit. Two different approaches are elaborated: First we con-sider a composite qubit-SQUID system and add the bath afterwards. We derive analytical expressions for its ei-genstates beyond rotating wave approximation (RWA), by applying Van Vleck perturbation theory (VVPT) in the qubit-oscillator coupling. The second approach is an ef-fective bath approach based on a mapping procedure, where SQUID and bath form an effective bath seen by the qubit. Here the qubit dynamics is obtained by ap-plying standard procedures established for the spin-boson problem. This approach requires the knowledge of the steady-state response of the dissipative Duffing oscillator, which is studied within a resonant and an off- Carmen Vierheiligresonant approach: The first is applicable near and at an N-photon resonance using VVPT beyond a RWA. The Interplay between second is based on the exact Floquet states of the non-linear driven oscillator. dissipation and The dissipative qubit dynamics is described analytically for weak system-bath coupling and agrees well for both driving in nonlinear approaches.