Detecting the Curvature of de Sitter Universe with Two Entangled Atoms

TL;DR

This paper proposes a method to detect spacetime curvature in de Sitter universe by analyzing the resonance Casimir-Polder interaction between two entangled atoms, which varies with curvature and differs from thermal effects in Minkowski space.

Contribution

It introduces a novel approach using RCPI between entangled atoms to distinguish de Sitter spacetime from Minkowski space based on curvature-dependent interaction decay.

Findings

RCPI depends on de Sitter curvature and shows a $1/L^2$ decay beyond a certain length.

In Minkowski space, RCPI is temperature-independent with a $1/L$ decay.

The method can differentiate between de Sitter and Minkowski universes using entangled atoms.

Abstract

Casimir-Polder interaction arises from the vacuum fluctuations of quantum field that depend on spacetime curvature and thus is spacetime-dependent. Here we show how to use the resonance Casimir-Polder interaction (RCPI) between two entangled atoms to detect spacetime curvature. We find that the RCPI of two static entangled atoms in the de Sitter-invariant vacuum depends on the de Sitter spacetime curvature relevant to the temperature felt by the static observer. It is characterized by a $1/L^2$ power law decay when beyond a characteristic length scale associated to the breakdown of a local inertial description of the two-atom system. However, the RCPI of the same setup embedded in a thermal bath in the Minkowski universe is temperature-independent and is always characterized by a $1/L$ power law decay. Therefore, although a single static atom in the de Sitter-invariant vacuum responds as if it were bathed in thermal radiation in a Minkowski universe, using the distinct difference between RCPI of two entangled atoms one can in principle distinguish these two universes.