Continuous-Variable Entanglement through Central Forces: Application to Gravity between Quantum Masses

TL;DR

This paper presents a method to analyze gravitational entanglement between quantum masses, emphasizing the importance of non-Gaussian states and force gradients, with applications in quantum gravity experiments.

Contribution

It introduces a complete framework for studying gravitational entanglement via central forces, highlighting the role of non-Gaussian states and providing a closed-form entanglement expression.

Findings

Entanglement sensitivity to initial momentum in non-Gaussian states.

Force gradient dominates position-momentum correlations.

Cubic and quartic potential terms contribute proportionally to momentum and momentum squared.

Abstract

We describe a complete method for a precise study of gravitational interaction between two nearby quantum masses. Since the displacements of these masses are much smaller than the initial separation between their centers, the displacement-to-separation ratio is a natural parameter in which the gravitational potential can be expanded. We show that entanglement in such experiments is sensitive to initial relative momentum only when the system evolves into non-Gaussian states, i.e., when the potential is expanded at least up to the cubic term. A pivotal role of force gradient as the dominant contributor to position-momentum correlations is demonstrated. We establish a closed-form expression for the entanglement gain, which shows that the contribution from the cubic term is proportional to momentum and from the quartic term is proportional to momentum squared. From a quantum information perspective, the results find applications as a momentum witness of non-Gaussian entanglement. Our methods are versatile and apply to any number of central interactions expanded to any order.