Phase measurement in the mesoscopic Aharonov-Bohm interferometer

Mesoscopic solid state Aharonov-Bohm interferometers have been used to measure the “intrinsic” phase, α_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 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_QD: the “lossy” channels near the QD should have both a small transmission and a small reflection.