Gravitational entanglement witness through Einstein ring image

TL;DR

This paper proposes a visual method to distinguish quantum gravity models by analyzing Einstein ring images, showing that quantum entanglement leads to multiple rings while classical models produce a single ring.

Contribution

It introduces a novel visual approach to witness gravity-induced entanglement using Einstein ring images, comparing quantum and classical gravity models.

Findings

QG model produces multiple Einstein rings indicating superposition.

SN model yields a single deformed Einstein ring.

The which-path indicator image vanishes in the SN model.

Abstract

We investigate the interplay between quantum theory and gravity by exploring gravitational lensing and Einstein ring images in a weak gravitational field induced by a mass source in spatial quantum superposition. We analyze a quantum massless scalar field propagating in two distinct models of gravity: the first quantized Newtonian gravity (QG) model, which generates quantum entanglement between the mass source and other systems, and the Schr\"odinger-Newton (SN) gravity model, which does not produce entanglement. Visualizing the two-point correlation function of the scalar field, we find that the QG model produces a composition of multiple Einstein rings, reflecting the spatial superposition of the mass source. By contrast, the SN model yields a single deformed ring image, representing a classical spacetime configuration. Furthermore, we introduce a specific quantity named the which-path information indicator and visualize its image. The QG model again reveals multiple Einstein rings, while the image intensity in the SN model notably vanishes. Our findings provide a visual approach to witness gravity-induced entanglement through distinct features in Einstein ring images. This study advances our understanding of quantum effects in general relativistic contexts and establishes a foundation for future studies of other relativistic phenomena.