# Coulomb and exchange interaction effects on the exact two-electron dynamics in the Hong-Ou-Mandel interferometer based on Hall edge states

## TL;DR

This paper investigates how Coulomb and exchange interactions influence two-electron dynamics in a quantum Hall interferometer, revealing Coulomb dominance and quantifying entanglement generation.

## Contribution

It provides a detailed numerical analysis of two-electron interactions in a quantum Hall setup, comparing exact simulations with simplified models, and analytically characterizing entanglement.

## Key findings

- Coulomb repulsion dominates over exchange energy in realistic geometries.
- Energy broadening significantly affects interaction dominance.
- Quantitative measure of entanglement generation capabilities.

## Abstract

The electronic Hong-Ou-Mandel interferometer in the integer quantum Hall regime is an ideal system to probe the building up of quantum correlations between charge carriers and it has been proposed as a viable platform for quantum computing gates. Using a parallel implementation of the split-step Fourier method, we simulated the antibunching of two interacting fermionic wave packets impinging on a quantum point contact. Numerical results of the exact approach are compared with a simplified theoretical model based on one-dimensional scattering formalism. We show that, for a realistic geometry, the Coulomb repulsion dominates over the exchange energy, this effect being strongly dependent on the energy broadening of the particles. We define analytically the spatial entanglement between the two regions of the quantum point contact, and obtain quantitatively its entanglement-generation capabilities.