Quantum gravitational contrast in creating Schr\"odinger cat state

TL;DR

This paper explores how a Schrödinger cat state in a matter-wave interferometer can serve as a simple quantum-gravity setup, analyzing matter-gravity interactions and quantum geometric overlaps.

Contribution

It introduces a perturbative effective field theory approach to treat matter and gravity equally, revealing graviton vacuum displacement and matter-gravity entanglement in superpositions.

Findings

Graviton vacuum is displaced as a coherent state due to matter-graviton coupling.

Overlap between matter superpositions relates to gravitational contrast.

Entanglement between matter and gravitons is characterized in the setup.

Abstract

In this paper, we illustrate how a Schr\"odinger cat state created via a matter-wave interferometer can be viewed as the simplest quantum-gravity setup where we can treat both matter and gravity on an equal footing at a perturbative level. Here we treat Einstein's theory of general relativity using an effective field theory approach, quantising the massless spin-2 graviton in the presence of a quantum spatial superposition of matter that creates a matter-wave interferometer in the non-relativistic limit. We show that due to the matter-graviton coupling the graviton vacuum is displaced analogous to the coherent state. We study the contrast/overlap between the coherent states of the left and right superpositions in the matter-wave interferometer. We also study the entanglement between matter and the graviton in this setup and relate it to a gravitational contrast, or the overlap of the quantum geometries led by the coherent states. In the appendix, we provide an example of a time-dependent harmonic oscillator and study the contrast/overlap of such coherent states of the graviton.