The prospect of detecting gravitationally induced entanglement (GIE) in a laboratory setting within the coming decades has prompted considerable debate about what such a finding would imply for our understanding of the quantum nature of gravity. As a step toward grounding this debate in our most fundamental description of matter, we develop a quantum field-theoretic model of GIE between two massive objects in spatial superposition. The masses are described as excitations of a scalar field in an external harmonic potential, allowing for a well-defined notion of relativistic coherent states. Using linearized quantum gravity in the static limit, we derive an effective Hamiltonian that induces entanglement between the field modes occupied by the masses. To probe this entanglement, we construct an observable from field operators that corresponds to the probability density of detecting the center of mass of one of these massive objects. Using this observable, we compute the fringe visibility in the overlap region and find that gravitationally induced entanglement leads to a decrease in visibility, consistent with previous nonrelativistic results. Additionally, we identify relativistic corrections that accelerate the decay of fringe visibility. These results provide a framework for studying weakly relativistic quantum field systems and their gravitational interactions in tabletop experiments.

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• Quantum field theory (low energy)
• Relativistic quantum information