Mesoscopic solid state Aharonov-Bohm interferometers have been used to measure the “intrinsic” phase, ${\alpha }_{\mathrm{QD}},$ 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 $\beta$ only “jumps” between 0 and $\pi .$ Additional terminals open the interferometer but then $\beta$ depends on the details of the opening. Using a theoretical model, we present quantitative criteria (which can be tested experimentally) for $\beta$ to be equal to the desired ${\alpha }_{\mathrm{QD}}:$ the “lossy” channels near the QD should have both a small transmission and a small reflection.

• Received 13 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.115311