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

TL;DR

This paper demonstrates methods to determine the intrinsic transmission phase of a quantum dot using Aharonov-Bohm interferometers, resolving previous ambiguities in phase measurement in closed and open configurations.

Contribution

It shows that the transmission phase can be deduced from conductance measurements without interferometry and clarifies conditions for phase extraction in open interferometers.

Findings

The phase alpha can be obtained from |t_D| in single-channel leads.

The conductance dependence on cos(phi) allows extraction of both |t_D| and alpha.

Optimizing open interferometer conditions can accurately measure the intrinsic phase.

Abstract

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(phi), where Phi= (hbar c phi)/e is the magnetic flux through the ring. The absence of a phase shift in the phi-dependence led to the conclusion that closed interferometers do not yield the 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 for interferometry; (b) the explicit dependence of G(phi) on cos(phi) (in the closed case) allows a determination of both |t_D| and alpha; (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 alpha.