Improving Gravitationally Induced Entanglement in Interferometric Configurations

arXiv:2611.07153v1 Announce Type: new Abstract: Proposals to detect gravitationally induced entanglement between massive particles offer a promising pathway toward probing the quantum nature of gravity. We perform a systematic geometric optimization and comparative analysis of Stern--Gerlach (SG) and Mach--Zehnder (MZ) matter-wave interferometers for this purpose, deriving exact analytical expressions for the gravitational phase of each configuration. Our first key result is that geometric optimization is indispensable. For commonly assumed experimental parameters, neglecting the optimization of geometric ratios can suppress the accumulated phase, and hence the detectability of entanglement, by up to several orders of magnitude.