Relaxation of experimental parameters in a quantum-gravity-induced entanglement of masses protocol using electromagnetic screening

To test the quantum nature of gravity in a laboratory requires witnessing the entanglement between the two test masses (nanocrystals) solely due to the gravitational interaction kept at a distance in a spatial superposition. The protocol is known as the quantum-gravity-induced entanglement of masses (QGEM). One of the main backgrounds in the QGEM experiment is electromagnetic (EM) -induced entanglement and decoherence. The EM interactions can entangle the two neutral masses via dipole-dipole vacuum-induced interactions, such as the Casimir-Polder interaction. To mitigate the EM-induced interactions between the two nanocrystals, we enclose the two interferometers in a Faraday cage and separate them by a conducting plate. However, any imperfection on the surface of a nanocrystal, such as a permanent dipole moment, will also create an EM background interacting with the conducting plate in the experimental box. These interactions will further generate EM-induced dephasing, which we wish to mitigate. In this paper, we will consider a parallel configuration of the QGEM experiment, where we will estimate the EM-induced dephasing rate and run-by-run systematic errors which will induce dephasing, and also provide constraints on the size of the superposition in a model-independent way of creating the spatial superposition.