  We investigate experimentally the quantum coherence of an electronic
two-level system in a double quantum dot under continuous charge detection. The
charge-state of the two-level system is monitored by a capacitively coupled
single quantum dot detector that imposes a back-action effect to the system.
The measured back-action is well described by an additional decoherence rate,
approximately linearly proportional to the detector electron tunneling rate. We
provide a model for the decoherence rate arising due to level detuning
fluctuations induced by detector charge fluctuations. The theory predicts a
factor of two lower decoherence rate than observed in the experiment,
suggesting the need for a more elaborate theory accounting for additional
sources of decoherence.
