Probing Modified Gravity with Entanglement of Microspheres

TL;DR

This paper proposes a tabletop experiment using entanglement of mesoscopic quantum masses to test for deviations from Newtonian gravity, potentially revealing modified gravity effects related to dark matter.

Contribution

It introduces a novel experimental setup to detect modified gravity effects via quantum entanglement, including detailed modeling of environmental factors and thermal states.

Findings

Entanglement is enhanced under modified gravity models like MOND.

Observable entanglement can be achieved within environmental decoherence limits.

Temperature tuning allows certification of modified gravity effects without detailed noise analysis.

Abstract

While a wide variety of astrophysical and cosmological phenomena suggest the presence of Dark Matter, all evidence remains via its gravitational effect on the known matter. As such, it is conceivable that this evidence could be explained by a modification to gravitation and/or concepts of inertia. Various formulations of modified gravity exist, each giving rise to several non-canonical outcomes. This motivates us to propose an experiment searching for departures from (quantum) Newtonian predictions in a bipartite setting with gravitational accelerations $\lesssim 10^{-10}$ m/s$^2$, i.e., where the effective force needs to be stronger than Newtonian to account for the Dark Matter effects. Since quantum particles naturally source weak gravitation, their non-relativistic dynamics offers opportunities to test this small acceleration regime. We show that two nearby mesoscopic quantum masses accumulate significantly larger entanglement in modified gravity models, such as the Modified Newtonian Dynamics. Our calculations include Casimir-Polder forces as well as tidal effects next to the surface of the earth, and confirm that entanglement is observable within the limits imposed by environmental decoherence. We demonstrate how the temperature can be fine-tuned such that modified gravity is certified simply by witnessing the entanglement generated from uncorrelated thermal states, eliminating the need for precise noise characterization. Overall, the required parameters could be realized in a tabletop experiment.