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Abstract

In this paper, our prime objective is to connect the curvature of our
observable De Sitter Universe with the spectroscopic study of entanglement of
two atoms in an open quantum system (OQS). The OQS considered in our work is
made up of two atoms which are represented by Pauli spin tensor operators
projected along any arbitrary direction. They mimic the role of a pair of
freely falling Unruh De-Witt detectors, which are allowed to non-adiabatically
interact with a conformally coupled massless probe scalar field in the De
Sitter background. The effective dynamics of the atomic detectors are actually
an outcome of their non-adiabatic interaction, which is commonly known as the
Resonant Casimir Polder Interaction (RCPI) with the thermal bath. We find from
our analysis that the RCPI of two stable entangled atoms in the quantum vacuum
states in OQS depends on the De Sitter space-time curvature relevant to the
temperature of the thermal bath felt by the static observer. We also find that,
in OQS, RCPI produces a new significant contribution appearing in the effective
Hamiltonian of the total system and thermal bath under consideration. This will
finally give rise to Lamb Spectroscopic Shift, as appearing in the context of
atomic and molecular physics. This analysis actually plays a pivotal role to
make the bridge between the geometry of our observed Universe to the
entanglement in OQS through Lamb Shift atomic spectroscopy. Thus, we are
strongly aiming to connect the curvature of the background space-time of our
Universe to open quantum Lamb Shift spectroscopy by measuring the quantum
properties of a two entangled OQS in the atomic experiment.