Measuring the transmission phase of a quantum dot in a closed interferometer

TL;DR

This paper provides an exact calculation of electron transmission through a closed Aharonov-Bohm interferometer with a quantum dot, exploring how conductance measurements relate to the intrinsic transmission phase and amplitude.

Contribution

It introduces a model for exact transmission calculation and proposes a method to extract the quantum dot's phase from conductance data, including a new direct relation for phase measurement.

Findings

Conductance is an even function of magnetic flux due to Onsager's relations.

Measured conductance can be used to infer the intrinsic transmission amplitude and phase.

A proposed direct relation links the phase to the normalized transmission amplitude.

Abstract

The electron transmission through a {\it closed} Aharonov-Bohm mesoscopic solid-state interferometer, with a quantum dot (QD) on one of the paths, is calculated exactly for a simple model. Although the conductance is an even function of the magnetic flux (due to Onsager's relations), in many cases one can use the measured conductance to extract both the amplitude and the phase of the "intrinsic" transmission amplitude $t_D=-i|t_D|e^{i\alpha_D}$ through the "bare" QD. We also propose to compare this indirect measurement with the (hitherto untested) direct relation $\sin^2(\alpha_D) \equiv |t_D|^2/\max(|t_D|^2)$.