Landau-Zener dynamics in qubits-oscillator settings

In a Cooper-pair box realization of a qubit, the energy splitting of the logical states can be tuned upon variation of the penetrating magnetic flux. Then the coupling of the qubit to a circuit QED oscillator can induce Landau-Zener transitions between the qubit levels. By summing a perturbation series to all orders, we obtained an exact expression for the corresponding LZ transition probability. Moreover, we determined the parameters for which a non-adiabatic transition is accompannied by single-photon generation and showed that LZ transitions can create qubit-oscillator entanglement in a controlled manner [1]. Replacing the oscillator by a quantum heat bath, we encounter a nontrivial problem of dissipative quantum mechanics which can be solved in a similar way. As a main application, we discuss the determination of both the reorganization energy and the integrated spectral density of the bath [2]. Moreover, this provides a convenient test bench for numerical schemes for real- time dissipative quantum dynamics. \\{} [1] K. Saito \textit{et al.}, Europhys.\ Lett.\ \textbf{76}, 22 (2006). \\{} [2] M.\ Wubs \textit{et al.}, Phys.\ Rev.\ Lett.\ \textbf{97}, 200404 (2006).