Cavity quantum electrodynamics with separate photon storage and qubit readout modes.

We present the realization of a cavity quantum electrodynamics setup in which photons of strongly different lifetimes are engineered in different harmonic modes of the same cavity. We achieve this in a superconducting transmission line resonator with superconducting qubits coupled to the different modes. One cavity mode is strongly coupled to a detection line for qubit state readout, while a second long lifetime mode is used for photon storage and coherent quantum operations. We demonstrate sideband-based measurement of photon coherence, generation of n photon Fock states and the scaling of the sideband Rabi frequency with square root of n using a scheme that may be extended to realize sideband-based two-qubit logic gates.