  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.
