# Macroscopic electron quantum coherence in a solid-state circuit

## TL;DR

This paper demonstrates macroscopic quantum coherence of electrons over 0.1 mm in a solid-state circuit, surpassing previous limits and enabling advanced quantum interference devices in the quantum Hall regime.

## Contribution

It introduces a method to achieve and observe long-range electronic quantum interference in solid-state circuits, overcoming Coulomb interaction limitations.

## Key findings

- Electronic quantum interference observed over 0.1 mm pathways.
- Interference visibility up to 80%, indicating strong coherence.
- Phase coherence length of approximately 0.25 mm achieved.

## Abstract

The quantum coherence of electronic quasiparticles underpins many of the emerging transport properties of conductors at small scales. Novel electronic implementations of quantum optics devices are now available with perspectives such as 'flying' qubit manipulations. However, electronic quantum interferences in conductors remained up to now limited to propagation paths shorter than $30\,\mu$m, independently of the material. Here we demonstrate strong electronic quantum interferences after a propagation along two $0.1\,$mm long pathways in a circuit. Interferences of visibility as high as $80\%$ and $40\%$ are observed on electronic analogues of the Mach-Zehnder interferometer of, respectively, $24\,\mu$m and $0.1\,$mm arm length, consistently corresponding to a $0.25\,$mm electronic phase coherence length. While such devices perform best in the integer quantum Hall regime at filling factor 2, the electronic interferences are restricted by the Coulomb interaction between copropagating edge channels. We overcome this limitation by closing the inner channel in micron-scale loops of frozen internal degrees of freedom, combined with a loop-closing strategy providing an essential isolation from the environment.