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 ($\rm AdS_5$). We assume that the two quantum harmonic oscillators are kept at a distance $d$ on a 3-brane (our 4D world) embedded in $\rm AdS_5$, 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 non-static cases. The entanglement enhances compared to the four-dimensional massless graviton, and it depends now on the $\rm AdS_5$ 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 ${\cal O}(20)$ micron, we can yield larger concurrence of order ${\cal O}(0.1)$.