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Circuit QED, i.e., a Cooper-pair box coupled to a transmission line, represents a solid-state version of an atom in a cavity. If the box possesses a rather small electric capacity, only the lowest two charge states play a role, such that it acts as a qubit. The coupling between the qubit and the cavity can induce Landau-Zener transitions of the qubit upon switching the magnetic flux that penetrates the superconducting loop. The adiabatic energies of this system are characterized by multiple exact and avoided level crossings, so that the usual two-level Landau-Zener formula is no longer applicable. We derive selection rules for the multi-level transitions and present an exact expression for the corresponding transition probabilities. Applications include quantum state preparations like single-photon generation and the controllable creation of qubit-oscillator entanglement. If the circuit is driven by an rf signal, the phase of the reflected signal depends on the state of the qubit. We discuss the possibility and the limitations of monitoring the qubit dynamics in that way. |