Electron interferometry in integer quantum Hall edge channels

TL;DR

This paper explores electron interferometry in quantum Hall edge channels, analyzing how interactions affect electron collision and coherence, with implications for quantum information processing.

Contribution

It introduces a detailed analysis of electron collision in quantum Hall edge channels, highlighting the effects of interactions on decoherence and indistinguishability.

Findings

In the integer quantum Hall regime, current correlations show a dip at zero delay.

Interactions at filling factor ν=2 cause charge fractionalization and decoherence.

Decoherence reduces the contrast of the Hong-Ou-Mandel interference signal.

Abstract

We consider the electronic analog of the Hong-Ou-Mandel interferometer from quantum optics. In this realistic condensed matter device, single electrons are injected and travel along opposite chiral edge states of the integer quantum Hall effect, colliding at a quantum point contact (QPC). We monitor the fate of the colliding excitations by calculating zero-frequency current correlations at the output of the QPC. In the simpler case of filling factor $\nu=1$, we recover the standard result of a dip in the current noise as a function of the time delay between electron injections. For simultaneous injection, the current correlations exactly vanish, as dictated by the Pauli principle. This picture is however dramatically modified when interactions are present, as we show in the case of a filling factor $\nu=2$. There, each edge state is made out of two co-propagating channels, leading to charge fractionalization, and ultimately to decoherence. The latter phenomenon reduces the degree of indistinguishability between the two electron wavepackets, yielding a reduced contrast in the HOM signal. This naturally brings about the question of stronger interaction, offering a natural extension of the present work to the case of fractional quantum Hall effect where many open and fascinating questions remain.