  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 the square root of n using a scheme that may be extended to
realize sideband based two-qubit logic gates.
