Mass-Independent Gravitationally Induced Entanglement

TL;DR

This paper analytically demonstrates that gravitationally induced entanglement between two matter interferometers is mass-independent and explores how interaction effects can constrain the mass range of experimental systems, considering realistic noise.

Contribution

It provides an exact analytical solution for gravitationally induced entanglement in Stern-Gerlach interferometers, revealing mass independence and experimental bounds on mesoscopic masses.

Findings

Entangling phase is mass-independent for both unitary and open dynamics.

Interaction effects prevent perfect recombination of the center of mass.

Realistic noise tightens bounds on the mass range for experiments.

Abstract

We analytically solve the entangling quantum dynamics of two interacting Stern-Gerlach Interferometers~(SGI). Each SGI exploits an operator-valued force applied by a qubit to create and recombine a non-Gaussian state of matter. The entangling phase between the two qubits generated by the leading-order gravitational interaction of the massive degrees of freedom is found to be mass-independent, both for unitary and open dynamics, irrespective of the temperature and squeezing of the initial states. Further, we show that the solution of the four interferometric paths reveals that the mere presence of the interaction does not allow for a perfect recombination of the centre of mass. This second-order effect, alongside higher-order interaction terms, can be used to bound the mass from above and below, thus restricting the experiment's regime to mesoscopic masses. By solving the open dynamics which includes diffusion and dephasing with initial squeezed thermal states, the bounds are tightened by the inclusion of realistic experimental noise. We discuss diamagnetic levitated masses with embedded NV-centres as a specific physical implementation.