Measuring the Transmission of a Quantum Dot Using Aharonov–Bohm Interferometers

The conductance G through a closed Aharonov-Bohm mesoscopic solid-stateinterferometer (which conserves the electron current), with a quantum dot (QD)on one of the paths, depends only on cos(phi), where Phi= (hbar c phi)/e is themagnetic flux through the ring. The absence of a phase shift in thephi-dependence led to the conclusion that closed interferometers do not yieldthe phase of the "intrinsic" transmission amplitude t_D=|t_D|e^{i alpha}through the QD, and led to studies of open interferometers. Here we show that(a) for single channel leads, alpha can be deduced from |t_D|, with no need forinterferometry; (b) the explicit dependence of G(phi) on cos(phi) (in theclosed case) allows a determination of both |t_D| and alpha; (c) in the opencase, results depend on the details of the opening, but optimization of thesedetails can yield the two-slit conditions which relate the measured phase shiftto alpha.Comment: Invited talk, Localization, Tokyo, August 200