Collision of two interacting electrons on a mesoscopic beam splitter

Exact solution in the classical limit

authored by: Elina Pavlovska, Peter G. Silvestrov, Patrik Recher, Girts Barinovs, Vyacheslavs Kashcheyevs
Abstract: Experiments on collisions of isolated electrons guided along the edges in quantum Hall setups can mimic mixing of photons with the important distinction that electrons are charged fermions. In the so-called electronic Hong-Ou-Mandel (HOM) setup uncorrelated pairs of electrons are injected toward a beam splitter. If the two electron wave packets were identical, then Fermi statistics would force the electrons to scatter to different detectors, yet this quantum antibunching may be confounded by Coulomb repulsion. Here we model an electronic HOM experiment using a quadratic two-dimensional saddle point potential for the beam splitter and unscreened Coulomb interaction between the two injected electrons subjected to a strong out-of-plane magnetic field. We show that classical equations of motion for the drift dynamics of electrons' guiding centers take on the form of Hamilton equations for canonically conjugated variables subject to the saddle point potential and the Coulomb potential where the dynamics of the center-of-mass coordinate and the relative coordinate separate. We use these equations to determine collision outcomes in terms of a few experimentally tuneable parameters: the initial energies of the uncorrelated electrons, relative time delay of injection, and the shape of the saddle point potential. A universal phase diagram of deterministic bunching and antibunching scattering outcomes is presented with a single energy scale characterizing the increase of the effective barrier height due to interaction of coincident electrons. We suggest clear-cut experimental strategies to detect the predicted effects and give analytical estimates of conditions when the classical dynamics is expected to dominate over quantum effects.
External Organisation(s): University of Latvia
Technische Universität Braunschweig
Laboratory for Emerging Nanometrology Braunschweig (LENA)
Type: Article
Journal: Physical Review B
Volume: 107
ISSN: 2469-9950
Publication date: 07.04.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Electronic, Optical and Magnetic Materials, Condensed Matter Physics
Electronic version(s): https://doi.org/10.1103/PhysRevB.107.165304 (Access: Unknown)

BibTeX

@article{8a128aca8d6741f49ffa750152fb688d,
title = "Collision of two interacting electrons on a mesoscopic beam splitter: Exact solution in the classical limit",
abstract = "Experiments on collisions of isolated electrons guided along the edges in quantum Hall setups can mimic mixing of photons with the important distinction that electrons are charged fermions. In the so-called electronic Hong-Ou-Mandel (HOM) setup uncorrelated pairs of electrons are injected toward a beam splitter. If the two electron wave packets were identical, then Fermi statistics would force the electrons to scatter to different detectors, yet this quantum antibunching may be confounded by Coulomb repulsion. Here we model an electronic HOM experiment using a quadratic two-dimensional saddle point potential for the beam splitter and unscreened Coulomb interaction between the two injected electrons subjected to a strong out-of-plane magnetic field. We show that classical equations of motion for the drift dynamics of electrons' guiding centers take on the form of Hamilton equations for canonically conjugated variables subject to the saddle point potential and the Coulomb potential where the dynamics of the center-of-mass coordinate and the relative coordinate separate. We use these equations to determine collision outcomes in terms of a few experimentally tuneable parameters: the initial energies of the uncorrelated electrons, relative time delay of injection, and the shape of the saddle point potential. A universal phase diagram of deterministic bunching and antibunching scattering outcomes is presented with a single energy scale characterizing the increase of the effective barrier height due to interaction of coincident electrons. We suggest clear-cut experimental strategies to detect the predicted effects and give analytical estimates of conditions when the classical dynamics is expected to dominate over quantum effects.",
author = "Elina Pavlovska and Silvestrov, {Peter G.} and Patrik Recher and Girts Barinovs and Vyacheslavs Kashcheyevs",
note = "Publisher Copyright: {\textcopyright} 2023 American Physical Society. ",
year = "2023",
month = apr,
day = "7",
doi = "10.1103/PhysRevB.107.165304",
language = "English",
volume = "107",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Institute of Physics",
number = "16",
}