  In their comment, Aharony, Entin-Wohlman, Oreg and von Delft claimed that the
expression we obtained for the phase of the S-matrix does not give back the
correct result notably in the U=0 limit of the single level Anderson model
(SLAM). Their comment, however, misses the point of our argument, namely, that
the SLAM is insufficient to describe the interferometry experiment. Instead,
the quantum dot needs to be viewed as a multi-level artificial atom, and the
interferometry experiment as a scattering experiment off the atom. The
description is subject, in particular, to such scattering theorems as the
generalized Levinson theorem. As a result, we show how there exists a factor of
2 difference between the phase of the S-matrix responsible for the shift in the
Aharonov-Bohm (AB) oscillations, and the one controlling the conductance. We
point out how the results obtained this way are in remarkably good quantitative
agreement with measurements performed by AB interferometry for the conductance
as well as for the phase shift.
