Gravitationally induced entanglement in a harmonic trap

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 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 nonrelativistic 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.

Automated summary

Recent work suggests the possibility of detecting gravitationally induced entanglement in tabletop experiments. However, there is a lack of developed models for this type of experiment where entangled particles are treated as excitations of a relativistic quantum field and measurements are modeled using expectation values of field observables. In this study, a thought experiment is proposed to investigate entanglement dynamics between two particles prepared in a superposition of coherent states within a 3D harmonic trap. The analysis provides insights into gravitationally induced entanglement and serves as a foundation for further investigation using quantum field theory.