Quantum gravitational contrast in creating Schr\"odinger cat state

Anupam Mazumdar; Tian Zhou

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arXiv · 2605.05153

Quantum gravitational contrast in creating Schr\"odinger cat state

Anupam Mazumdar·Tian Zhou

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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.

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Anupam Mazumdar, Tian Zhou. 2026-05-06. Quantum gravitational contrast in creating Schr\"odinger cat state. https://arxiv.org/abs/2605.05153

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