Manipulation of resonances in an open three-terminal interferometer with an embedded quantum dot

A three-terminal Aharonov-Bohm ring with a quantum dot embedded in one arm is investigated using the exactly solvable formalism of the tight-binding model. We show that by tuning the degree of coupling to the third terminal, the zero of the Fano resonance in the transmission moves off the real-energy axis and the phase jump of π at the resonance diminishes and softens. This behavior is illustrated with a simple model involving the zero and pole of the Fano resonance. The manifestation of the Fano resonance on the conductance, due to the unique interplay between the magnetic flux through the ring and coupling to the third terminal, is discussed.