Quantum Gravity Witness via Entanglement of Masses: Casimir Screening

A recently proposed experimental protocol for Quantum Gravity induced Entanglement of Masses (QGEM) requires in principle realizable, but still very ambitious, set of parameters in matter-wave interferometry. Motivated by easing the experimental realization, in this paper, we consider the parameter space allowed by a slightly modified experimental design, which mitigates the Casimir potential between two spherical neutral test-masses by separating the two macroscopic interferometers by a thin conducting plate. Although this set-up will reintroduce a Casimir potential between the conducting plate and the masses, there are several advantages of this design. First, the quantum gravity induced entanglement between the two superposed masses will have no Casimir background. Secondly, the matter-wave interferometry itself will be greatly facilitated by allowing both the mass $10^{-16}-10^{-15}$kg and the superposition size $\Delta x \sim 20 \mu$m to be a one-two order of magnitude smaller than those proposed earlier, and thereby also two orders of magnitude smaller magnetic field gradient of $10^4$Tm$^{-1}$ to create that superposition through the Stern-Gerlach effect. In this context, we will further investigate the collisional decoherences and decoherence due to vibrational modes of the conducting plate.