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In this paper, we explore the connection between the curvature of thebackground De Sitter space-time with the spectroscopic study of entanglement oftwo atoms. Our set up is in the context of an Open Quantum System (OQS), wherethe two atoms, each having two energy levels and represented by Pauli spintensor operators projected along any arbitrary direction. The system mimics therole of a pair of freely falling Unruh De-Witt detectors, which are allowed tonon-adiabatically interact with a conformally coupled massless probe scalarfield which has the role of background thermal bath. The effective dynamics ofthis combined system takes into account of the non-adiabatic interaction, whichis commonly known as the Resonant Casimir Polder Interaction (RCPI) with thethermal bath. Our analysis reveals that the RCPI of two stable entangled atomsin the quantum vacuum states in OQS depends on the de Sitter space-timecurvature relevant to the temperature of the thermal bath felt by the staticobserver. We also find that, in OQS, RCPI produces a new significantcontribution appearing in the effective Hamiltonian of the total system andthermal bath under consideration. We find that the Lamb Shift is characterizedby a decreasing inverse square power-law behavior, $L^{-2}$, when inter atomicEuclidean distance, $L$, is much larger than a characteristic length scale,$k$, which is the inverse surface gravity of the background De Sitter space. Ifthe background space-time would have been Minkowskian this shift decreases as,$L^{-1}$, and is independent of temperature. Thus, we establish a connectionbetween the curvature of the De Sitter space-time with the Lamb Shiftspectroscopy.

Relating the curvature of De Sitter Universe to Open Quantum Lamb Shift Spectroscopy