  In a Rabi oscillation experiment with a superconducting qubit we show that a
visibility in the qubit excited state population of more than 90 % can be
attained. We perform a dispersive measurement of the qubit state by coupling
the qubit non-resonantly to a transmission line resonator and probing the
resonator transmission spectrum. The measurement process is well characterized
and quantitatively understood. The qubit coherence time is determined to be
larger than 500 ns in a measurement of Ramsey fringes.
