Repulsive Gravitational Force as a Witness of the Quantum Nature of Gravity

We show that a single spatially superposed ‘source’ mass acting on a ‘probe’ matter wavepacket can reveal the quantum nature of the gravitational field. For this we use a specific state preparation and measurement of the superposed source mass, including a postselection, which altogether results in a repulsive gravitational force on the probe particle. A classical gravitational field can never lead to repulsion, as the effect requires quantum interference of two distinct states of gravity. We also present a calculation in the Heisenberg picture under the formalism of weak values that illustrates how repulsion is achieved. Finally, we estimate the range of parameters (masses and the spatio-temporal extent of interference) for which the experiment is feasible.

💡 Research Summary

The paper proposes a novel tabletop test of the quantum nature of gravity that relies on a single massive particle placed in a spatial superposition (the “source”) and a second massive particle that serves as a probe. Unlike earlier proposals based on gravitationally‑induced entanglement (GIE), which require two masses each in a superposition and the detection of entanglement between them, this scheme needs only one superposed mass and does not require any direct measurement of quantum correlations between the two particles.

The authors consider a source particle of mass M prepared in the state
|Ψ_i⟩ = α|A⟩ + β|B⟩,
where |A⟩ and |B⟩ are localized around positions x_A and x_B respectively. The probe particle of mass m is initially in a momentum‑space Gaussian wavepacket ψ(p) with a large momentum uncertainty, so that the interaction only slightly perturbs its internal state but can shift its momentum distribution.

During an interaction time T the gravitational attraction from each possible source location imparts a positive momentum kick δ_A or δ_B to the probe, with
δ_j = G M m T / x_j² (j = A,B).
Thus after the interaction the joint state is a superposition of two terms, each containing a shifted probe wavepacket.

The crucial step is a post‑selection on the source particle after it passes through a Mach‑Zehnder interferometer. The chosen final state is
|Ψ_f⟩ =