  Recently, experiments aimed at measuring gravity mediated entanglement (GME)
using quantum information techniques have been proposed, based on the
assumption that if two systems get entangled through local interactions with
gravitational field, then this field must be quantum. While there is a debate
about what could be drawn from GME, quantum simulation might provide some
clarification. Here, we present electromagnetic analogy of GME using
magnetic-field mediated interaction between the electron and nucleus in a
single atom. Our work successfully implements the general procedures of GME
experiments and confirms that the mediating field does not support the
mean-field description. It also clarifies that, without considering the
light-crossing time, the GME experiment would not distinguish a
quantum-field-theory description from a quantum-controlled classical field one.
Furthermore, this work provides a novel method to construct two-qubit systems
in a single atom, and providing the first quantum simulation of GME using
material qubits. It helps to conceive the future GME experiments on the scale
of light-crossing time.
