Measurement of the Transmission Phase of an Electron in a Quantum Two-Path Interferometer

TL;DR

This study demonstrates that the anti-phase relation of output currents in a quantum interferometer reliably measures the true electron transmission phase, unlike the smooth phase shift in Aharonov-Bohm oscillations which can be misleading.

Contribution

The paper clarifies the criteria for accurate phase measurement in quantum interferometers, confirming the anti-phase relation as a reliable indicator of the true transmission phase.

Findings

Anti-phase relation ensures correct phase measurement.

Smooth phase shift can be misleading due to multiple paths.

Anti-phase criterion is validated against theoretical predictions.

Abstract

A quantum two-path interferometer allows for direct measurement of the transmission phase shift of an electron, providing useful information on coherent scattering problems. In mesoscopic systems, however, the two-path interference is easily smeared by contributions from other paths, and this makes it difficult to observe the \textit{true} transmission phase shift. To eliminate this problem, multi-terminal Aharonov-Bohm (AB) interferometers have been used to derive the phase shift by assuming that the relative phase shift of the electrons between the two paths is simply obtained when a smooth shift of the AB oscillations is observed. Nevertheless the phase shifts using such a criterion have sometimes been inconsistent with theory. On the other hand, we have used an AB ring contacted to tunnel-coupled wires and acquired the phase shift consistent with theory when the two output currents through the coupled wires oscillate with well-defined anti-phase. Here, we investigate thoroughly these two criteria used to ensure a reliable phase measurement, the anti-phase relation of the two output currents and the smooth phase shift in the AB oscillation. We confirm that the well-defined anti-phase relation ensures a correct phase measurement with a quantum two-path interference. In contrast we find that even in a situation where the anti-phase relation is less well-defined, the smooth phase shift in the AB oscillation can still occur but does not give the correct transmission phase due to contributions from multiple paths. This indicates that the phase relation of the two output currents in our interferometer gives a good criterion for the measurement of the \textit{true} transmission phase while the smooth phase shift in the AB oscillation itself does not.