  Sideband transitions are spectroscopically probed in a system consisting of a
Cooper pair box strongly but non-resonantly coupled to a superconducting
transmission line resonator. When the Cooper pair box is operated at the
optimal charge bias point the symmetry of the hamiltonian requires a two photon
process to access sidebands. The observed large dispersive ac-Stark shifts in
the sideband transitions induced by the strong non-resonant drives agree well
with our theoretical predictions. Sideband transitions are important in
realizing qubit-photon and qubit-qubit entanglement in the circuit quantum
electrodynamics architecture for quantum information processing.
