We generalize the dispersive theory of the Jaynes-Cummings model beyond the
frequently employed rotating-wave approximation (RWA) in the coupling between
the two-level system and the resonator. For a detuning sufficiently larger than
the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and
discuss the differences to the known RWA results. Our results extend the regime
in which dispersive qubit readout is possible. If several qubits are coupled to
one resonator, an effective qubit-qubit interaction of Ising type emerges,
whereas RWA leads to isotropic interaction. This impacts on the entanglement
characteristics of the qubits.Comment: 6 pages, 1 figur