Parameter scanning in a quantum-gravity-induced entanglement of masses (QGEM) experiment with electromagnetic screening

Witnessing the quantum nature of spacetime is an exceptionally challenging task. However, the quantum gravity-induced entanglement of matter (QGEM) protocol proposes such a test by testing entanglement between adjacent matter-wave interferometers. One key obstacle to experimentally realising this protocol is the creation of a spatial quantum superposition with heavy masses. Initially, it was envisaged that the superposition size would have to be of order 200 micron for a mass $10^{-14}$ kg (to obtain the entanglement phase of order unity when the centre of mass of the two interferometers are at a separation of 450 microns). The experimental design has since improved, e.g. by assuming that the two interferometers are separated by an electromagnetic screen, which helps bring the separation distance close to 35 micron. Here, we do parameter scans taking into account the electromagnetic screening, and we consider different geometrical setups; we show superpositions of at least a micron-size for mass $10^{-14}$ kg with a decoherence rate of order $10^{-3}$ Hz are required.