Relativistic Effects on Entangled Single-Electron Traps

TL;DR

This paper investigates how relativistic corrections, specifically Darwin terms, influence quantum entanglement in a system of two harmonically trapped electrons, revealing conditions where relativistic effects are significant for entanglement generation.

Contribution

It introduces a model analyzing relativistic Darwin corrections in trapped electron systems and identifies parameter regimes where these effects impact entanglement.

Findings

Relativistic effects become relevant at specific frequencies and distances.

Darwin corrections influence entanglement dynamics.

Conditions for significant relativistic contributions are identified.

Abstract

The manipulation of individual charged particles has been deeply explored in physics's theoretical and experimental domains during the past decades. It is the pillar of several existing devices used for metrology and sensing and is a promising platform for realizing future technologies, such as quantum computers. It is also known that in the relativistic regime, interactions between charged particles become affected by post-Coulombian corrections, with the dominant couplings encoded in the Darwin Hamiltonian. The Darwin term has been extensively studied in atomic physics, where the interaction range is confined to the sub-angstrom scale. Still, there is a lack of understanding about whether (and when) Darwin's contributions are relevant at larger scales. In this paper, we explore the effects of these corrections in a system of two harmonically trapped electrons, where we look into the behaviour of quantum entanglement present in the static and dynamical regimes. We explore the parameter space of the developed model and seek frequencies, distances, and squeezing parameters for which relativistic effects become relevant for the generation of entanglement.