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

Abstract

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.

Figures (2)

• Figure 1: Scheme to test a quantum behaviour of gravity using the quantum interference of force effect correa18. The source quantum massive particle is put in a superposition of two different spatial locations centered in $x_A$ and $x_B$. The quantum superposition of the two possible gravitational attractions in a probe quantum particle, relative to the two possible positions of the source particle, can result in an effective gravitational repulsion, depending on the post-selection of the source particle state. This is a behaviour with no classical analogue.
• Figure 2: Decomposition of the post-selected wavefunction of the probe particle from Eq. (\ref{['psips']}), showing how the superposition of two wavefunctions with average positive momenta can generate a wavefunction with negative average momentum through destructive interference. We considered $\psi(p)\propto\mathrm{Exp}[-p^2W^2/(4\hbar^2)]$, $\beta=0.9$, $\alpha=\sqrt{1-\beta^2}$, $\delta_B=0.1\hbar/W$, and $\delta_A=0.7\hbar/W$.