Two-electron coherence and its measurement in electron quantum optics

TL;DR

This paper introduces the concept of intrinsic two-electron coherence in quantum Hall edge channels, relating it to wavefunctions and noise, and proposes a measurement protocol inspired by photon optics to detect entanglement.

Contribution

It defines a new measure of two-electron coherence and proposes a measurement method using a Franson interferometer to identify entanglement in electron pairs.

Findings

Defines intrinsic two-electron coherence in quantum Hall systems.

Proposes a measurement protocol using low-frequency current correlations.

Demonstrates the protocol's ability to distinguish entangled states from mixed states.

Abstract

Engineering and studying few-electron states in ballistic conductors is a key step towards understanding entanglement in quantum electronic systems. In this Letter, we introduce the intrinsic two-electron coherence of an electronic source in quantum Hall edge channels and relate it to two-electron wavefunctions and to current noise in an Hanbury Brown--Twiss interferometer. Inspired by the analogy with photon quantum optics, we propose to measure the intrinsic two-electron coherence of a source using low-frequency current correlation measurements at the output of a Franson interferometer. To illustrate this protocol, we discuss how it can distinguish between a time-bin entangled pure state and a statistical mixture of time shifted electron pairs.