  We demonstrate enhancement of the dispersive frequency shift in a coplanar
waveguide resonator induced by a capacitively-coupled superconducting flux
qubit in the straddling regime. The magnitude of the observed shift, 80 MHz for
the qubit-resonator detuning of 5 GHz, is quantitatively explained by the
generalized Jaynes-Cummings model which takes into account the contribution of
the qubit higher energy levels. By applying the enhanced dispersive shift to
the qubit readout, we achieved 90% contrast of the Rabi oscillations which is
mainly limited by the energy relaxation of the qubit.
