Gravitational Harmonium: Gravitationally Induced Entanglement in a Harmonic Trap

TL;DR

This paper introduces a non-relativistic quantum model of gravitationally induced entanglement in a harmonic trap, proposing a thought experiment with potential for future experimental verification and providing a foundation for more advanced quantum field theoretical analysis.

Contribution

It presents the first non-relativistic quantum mechanical analysis of gravitational entanglement in a harmonic trap, linking matter wave interference to entanglement measurement and setting the stage for relativistic quantum field theory modeling.

Findings

Entanglement can be inferred from particle position detection probabilities.

The model demonstrates how gravitational interaction induces measurable quantum correlations.

Provides a basis for future relativistic quantum field theoretical studies.

Abstract

Recent work has shown that it may be possible to detect gravitationally induced entanglement in tabletop experiments in the not-too-distant future. However, there are at present no thoroughly developed models for this type of experiment where the entangled particles are treated more fundamentally as excitations of a relativistic quantum field, and with the measurements modeled using expectation values of field observables. Here we propose a thought experiment where two particles (i.e., massive scalar field quanta) are initially prepared in a superposition of coherent states within a common three-dimensional (3D) harmonic trap. The particles then develop entanglement through their mutual gravitational interaction, which can be probed through particle position detection probabilities. The present work gives a non-relativistic quantum mechanical analysis of the gravitationally induced entanglement of this system, which we term the `gravitational harmonium' due to its similarity to the harmonium model of approximate electron interactions in a helium atom; the entanglement is operationally determined through the matter wave interference visibility. The present work serves as the basis for a subsequent investigation, which models this system using quantum field theory, providing further insights into the quantum nature of gravitationally induced entanglement through relativistic corrections, together with an operational procedure to quantify the entanglement.