We study the Fano effect and the visibility of the Aharonov-Bohm oscillations
for a mesoscopic interferometer with an embedded quantum dot in the presence of
a nearby second dot. When the electron-electron interaction between the two
dots is considered the nearby dot acts as a charge detector. We compute the
currents through the interferometer and detector within the Keldysh formalism
and the self-energy of the non-equilibrium Green functions is found up to the
second order in the interaction strength. The current formula contains a
correction to the Landauer-B\"{uttiker} formula. Its contribution to transport
and dephasing is discussed. As the bias applied on the detector is increased,
the amplitude of both the Fano resonance and Aharonov-Bohm oscillations are
considerably reduced due to controlled dephasing. This result is explained by
analyzing the behavior of the imaginary part of the self-energy as a function
of energy and bias. We investigate as well the role of the ring-dot coupling.
Our theoretical results are consistent to the experimental observation of Buks
{\it et al.} [Nature {\bf 391}, 871 (1998)].Comment: 24 pages, 8 figure
