Probing massless and massive gravitons via entanglement in a warped extra dimension

Gravity's quantum nature can be probed in a laboratory by witnessing the entanglement between the two quantum systems, which cannot be possible if gravity is a classical entity. In this paper, we will provide a simple example where we can probe the effects of higher dimensions, in particular the warped extra dimension of five-dimensional anti-de Sitter spacetime (AdS5). We assume that the two quantum harmonic oscillators are kept at a distance d on a 3-brane (our 4D world) embedded in AdS5, while gravity can propagate in all five dimensions. We will compute the effective potential due to the massless and massive gravitons propagating in the warped geometry. We will compute the entanglement between position and momentum states for both static and nonstatic cases. The entanglement enhances compared to the four-dimensional massless graviton, and it depends now on the AdS5 radius. We will also show that if we would prepare non-Gaussian superposition states, e.g., spatial superposition of masses of order 10-14-10-15 kg with a superposition size of O(20) micron, we can yield larger concurrence of order O(0.1).