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/L2 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.
Highlights
It is well known that the relativistic motion of the interacting systems, as well as the curvature of the background spacetime can modify the Casimir-Polder interaction
It is known that a single particle interacting with a conformally coupled massless scalar field in the de Sitter invariant vacuum state behaves exactly the same way as the one coupled to thermal bath in Minkowski spacetime[25,26,27,28,29,30,31,32]
Our results show that the resonance interatomic interaction for the de Sitter spacetime case does depend on the spacetime curvature and certain features of resonance Casimir-Polder interaction (RCPI) could in principle be used to distinguish de Sitter universe from the thermal Minkowski spacetime
Summary
It is well known that the relativistic motion of the interacting systems, as well as the curvature of the background spacetime can modify the Casimir-Polder interaction. It is known that a single particle interacting with a conformally coupled massless scalar field in the de Sitter invariant vacuum state behaves exactly the same way as the one coupled to thermal bath in Minkowski spacetime[25,26,27,28,29,30,31,32]. 33 the authors proposed how to use entanglement present in the quantum fields to detect spacetime curvature and showed that using two local particle-detectors interacting with the field can achieve this goal. In the Minkowski spacetime with a quantum field in a thermal state the pair of detectors will be able to extract some entanglement that wouldn’t be present in the corresponding scenario involving de Sitter spacetime. Our results show that the resonance interatomic interaction for the de Sitter spacetime case does depend on the spacetime curvature and certain features of RCPI could in principle be used to distinguish de Sitter universe from the thermal Minkowski spacetime
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