Analyzing the measured phase in the multichannel Aharonov-Bohm interferometer

TL;DR

This paper investigates how the measured phase in a multichannel Aharonov-Bohm interferometer relates to the intrinsic quantum dot phases, revealing that the measured phase is a combination of multiple intrinsic phases rather than a single one.

Contribution

It provides a formula linking the measured phase to the intrinsic phases in multichannel quantum dot transport, clarifying the interpretation of experimental phase measurements.

Findings

Measured phase is a combination of intrinsic phases, not a single phase.

Variations of the measured phase can be less than π due to multichannel effects.

The case of a spin-1/2 quantum dot is specifically analyzed.

Abstract

We address the quantum dot phase measurement problem in an open Aharonov-Bohm interferometer, assuming multiple transport channels. In such a case, the quantum dot is characterized by more than one intrinsic phase for the electrons transmission. It is shown that the phase which would be extracted by the usual experimental method (i.e. by monitoring the shift of the Aharonov-Bohm oscillations, as in Schuster {\it et al.}, Nature {\bf 385}, 417 (1997)) does not coincide with any of the dot intrinsic phases, but is a combination of them. The formula of the measured phase is given. The particular case of a quantum dot containing a $S=1/2$ spin is discussed and variations of the measured phase with less than $\pi$ are found, as a consequence of the multichannel transport.