Manifestation of quantum entanglement between harmonic oscillators in de Sitter

TL;DR

This paper investigates quantum entanglement between two harmonic oscillators in an expanding universe, revealing that entanglement is significant within the Hubble horizon but negligible outside it, depending on their frequencies relative to the universe's expansion rate.

Contribution

It demonstrates how quantum entanglement between harmonic oscillators is affected by the universe's expansion and their position relative to the Hubble horizon.

Findings

Entanglement is significant for oscillators within the Hubble horizon.

Entanglement is negligible for oscillators outside the Hubble horizon.

Oscillator frequency relative to the expansion rate determines entanglement strength.

Abstract

Two harmonic oscillators interacting through the exchange of a quantum field leads to non-zero entanglement between the two, which is absent for classical interaction. In this work, we determine the entanglement between two such harmonic oscillators living in an expanding universe. It turns out that, if the oscillators are within the Hubble horizon, with their frequencies are comparable to the rate of expansion of the universe, the entanglement is non-zero and significant. While, for oscillators outside the Hubble horizon, with oscillation frequencies much higher than the expansion rate, the entanglement is negligibly small.