Orbital entanglement production in Andreev billiards with time-reversal symmetry

TL;DR

This paper investigates how orbital entanglement is generated in a chaotic quantum cavity with a superconducting lead under time-reversal symmetry, revealing enhanced entanglement compared to normal cavities.

Contribution

It introduces a numerical analysis of orbital entanglement production in Andreev billiards with superconducting leads, highlighting the impact of the proximity effect under TRS.

Findings

Entanglement increases with the strength of the superconductor's influence.

The proximity effect enhances the average entanglement in the system.

Orbital entanglement is significantly larger than in normal cavities.

Abstract

We study orbital entanglement production in a chaotic cavity connected to four single-channel normal-metal leads and one superconducting lead, assuming the presence of time-reversal symmetry (TRS). The scattered state of two incident electrons is written as the superposition of several two-outgoing quasi-particle states, four of which are orbitally entangled in a left-right bipartition. We calculate numerically the mean value of the squared norm of each scattered state's component, as functions of the number of channels in the superconducting lead. Its behavior is explained as resulting from the proximity effect. We also study statistically the amount of entanglement carried by each pair of outgoing quasi-particles. When the influence of the superconductor is more intense, the average entanglement is found to be considerably larger than that obtained using normal cavities.