Towards single shot read-out in circuit quantum electrodynamics (QED)

In recent experiments we have demonstrated the resonant coherent coupling of individual photons to a single qubit implemented as a Cooper pair box in a high quality superconducting cavity [1]. In the non-resonant case, the dispersive coupling between the qubit and the cavity field is used to perform quantum non-demolition (QND) measurements of the qubit state [2]. Using this read-out technique we have performed high visibility measurements of Rabi oscillations and Ramsey fringes [3]. Here we present a detailed experimental and theoretical analysis of the cavity response for continuous and pulsed measurements in a wide range of cavity drive amplitudes. We also discuss an optimal read-out strategy for qubits in a continuous QND measurement and aim at demonstrating single shot read-out in the circuit QED architecture [4].\\ \\ $[1]$ A. Wallraff et al. Nature (London) 431, 162 (2004)\\ $[2]$ D. I. Schuster et al. Phys. Rev. Lett. 94, 123602 (2005)\\ $[3]$ A. Wallraff et al. Phys. Rev. Lett. 95, 060501 (2005)\\ $[4]$ A. Blais et al. Phys. Rev. A 69, 062320 (2004)\\