Phase measurement in the mesoscopic Aharonov-Bohm interferometer

Mesoscopic solid state Aharonov-Bohm interferometers have been used to measure the ``intrinsic'' phase, α<sub>QD</sub>, of the resonant quantum transmission amplitude through a quantum dot (QD). For a two-terminal ``closed'' interferometer, which conserves the electron current, Onsager's relations require that the measured phase shift β only ``jumps'' between 0 and π. Additional terminals open the interferometer but then β depends on the details of the opening. Using a theoretical model, we present quantitative criteria (which can be tested experimentally) for β to be equal to the desired α<sub>QD</sub>: the ``lossy'' channels near the QD should have both a small transmission and a small reflection.