  Coherent Rabi oscillations between quantum states of superconducting
micro-circuits have been observed in a number of experiments, albeit with a
visibility which is typically much smaller than unity. Here, we show that the
coherent coupling to background charge fluctuators [R.W. Simmonds et al., Phys.
Rev. Lett. 93, 077003 (2004)] leads to a significantly reduced visibility if
the Rabi frequency is comparable to the coupling energy of micro-circuit and
fluctuator. For larger Rabi frequencies, transitions to the second excited
state of the superconducting micro-circuit become dominant in suppressing the
Rabi oscillation visibility. We also calculate the probability for Bogoliubov
quasi-particle excitations in typical Rabi oscillation experiments.
