  A non-perturbative treatment is developed for the dephasing produced by the
shot noise of a one- dimensional electron channel. It is applied to two
systems: a charge qubit and the electronic Mach-Zehnder interferometer, both of
them interacting with an adjacent partitioned electronic channel acting as a
detector. We find that the visibility (interference contrast) can display
oscillations as a function of detector voltage and interaction time. This is a
unique consequence of the non-Gaussian properties of the shot noise, and only
occurs in the strong coupling regime, when the phase contributed by a single
electron exceeds pi. The resulting formula reproduces the recent surprising
experimental observations reported in [I. Neder et al., cond-mat/0610634], and
indicates a general explanation for similar visibility oscillations observed
earlier in the Mach-Zehnder interferometer at large bias voltage. We explore in
detail the full pattern of oscillations as a function of coupling strength,
voltage and time, which might be observable in future experiments.
