Quantum state preparation in circuit QED via Landau- Zener tunneling

– We study a qubit undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the qubit, being independent of the frequency of the QED mode. Possible applications are single-photon generation and the controllable creation of qubit-oscillator entanglement. Superconducting loops are promising candidates for solid state qubit implementations [1–4]. Since the direct observation of Rabi-oscillations in these systems [1], they form the basis of many experiments on coherent quantum dynamics. Particularly interesting are the experiments in circuit quantum electrodynamics (QED) [2–4], which is the solid-state analogue of a two-level atom in an optical cavity. Superconducting circuits possess the advantage that many of their parameters are tunable over a broad range. This can be exploited for controlling efficiently the qubits. One particular way of controlling a qubit works by switching the difference of its diabatic energies from a large negative to a large positive value, yielding an avoided crossing for the adiabatic energies. For sufficiently slow switching, the qubit will adiabatically follow its instantaneous eigenstates. In the opposite limit of fast switching, however, the qubit will abandon the adiabatic eigenstate and undergo a so-called Landau-Zener (LZ) transition. The LZ transition probability can be raised upon increasing the switching rate [5–7]. LZ transitions can be used to effectively control qubit gate operations [8,9] and to read out qubits [10]. Recently, LZ transitions have been observed in various experiments with superconducting qubits [11–14] and nanomagnets [15]. Landau-Zener transitions can also occur for a qubit that is coupled to a circuit oscillator. Then, the adiabatic following to the final ground state takes place even in the absence of a direct coupling between the two qubit levels, induced instead by the indirect coupling to the