Radiative processes of two entangled atoms outside a Schwarzschild black hole

TL;DR

This paper investigates how two entangled atoms outside a Schwarzschild black hole interact with quantum fields in various vacuum states, revealing conditions for entanglement generation and degradation influenced by the black hole's horizon.

Contribution

It provides a detailed analysis of entanglement dynamics of two atoms near a black hole, considering different vacuum states and identifying the effects of vacuum fluctuations and radiation reaction.

Findings

Atoms can become entangled in Boulware vacuum within finite time.

Energy variation rate is problematic at the event horizon due to acceleration.

Hartle-Hawking and Unruh vacua enable entanglement from initial separable states.

Abstract

We consider radiative processes of a quantum system composed by two identical two-level atoms in a black-hole background. We assume that these identical two-level atoms are placed at fixed radial distances outside a Schwarzschild black hole and interacting with a quantum electromagnetic field prepared in one of the usual vacuum states, namely the Boulware, Unruh or the Hartle-Hawking vacuum states. We study the structure of the rate of variation of the atomic energy. The intention is to identify in a quantitative way the contributions of vacuum fluctuations and radiation reaction to the entanglement generation between the atoms as well as the degradation of entangled states in the presence of an event horizon. We find that for a finite observation time the atoms can become entangled for the case of the field in the Boulware vacuum state, even if they are initially prepared in a separable state. In addition, the rate of variation of atomic energy is not well behaved at the event horizon due to the behavior of the proper accelerations of the atoms. We show that the thermal nature of the Hartle-Hawking and Unruh vacuum state allows the atoms to get entangled even if they were initially prepared in the separable ground state.