Measuring the transmission of a quantum dot using Aharonov-Bohm Interferometers

The conductance G through a closed Aharonov-Bohm mesoscopic solid-state interferometer (which conserves the electron current), with a quantum dot (QD) on one of the paths, depends only on cos, where π = h cross signcφ/e is the magnetic flux through the ring. The absence of a phase shift in the φ-dependence led to the conclusion that closed interferometers do not yield the phase of the "intrinsic" transmission amplitude t_DD = |t_D|e^ia through the QD, and led to studies of open interferometers. Here we show that (a) for single channel leads, a can be deduced from |t_D|, with no need for interferometry; (b) the explicit dependence of G(φ) on cos φ(in the closed case) allows a determination of both |t_DD | and a; (c) in the open case, results depend on the details of the opening, but optimization of these details can yield the two-slit conditions which relate the measured phase shift to a.