Quantum-classical gravity distinction in reservoir-engineered massive quantum system

Abstract

Massive quantum systems have emerged as compelling tabletop interface-systems for testing the quantum nature of gravity. However, conventional schemes that focus on directly using gravity to induce entanglement suffer from overwhelming environmental decoherence: maintaining entanglement between two oscillators requires an impractically high mechanical quality factor. In this work, we put forward an alternative reservoir-engineered scheme, whose core function is to quantify how gravity modifies (rather than prepares) the steady-state entanglement. Compared to quantum gravity, classical gravity introduces additional dissipative channels, which in turn give rise to distinct entanglement characteristics and thus enable the discrimination between the two types of gravity. Notably, this entanglement difference can still be maintained even when the mechanical quality factor is far below the threshold required by conventional schemes. Moreover, it demonstrates significant robustness against non-gravitational couplings, specifically, those like Casimir and Coulomb forces that are inherent in experimental setups. Our scheme relaxes the experimental requirements for verifying quantum gravity, thereby paving a new path toward its near-term realization.

Figures (3)

• Figure 1: The proposed experiment setup. (a) A pair of spherical gold masses is connected to the plates of a capacitor and loaded onto membrane oscillators. The plates act as part of a microwave cavity formed by an on-chip superconducting circuit, mediating coupling between the mechanical oscillation and the cavity modes. The red wave represents the pump beam, which excites the mode in the microwave cavity through electromagnetic induction. (b) A schematic of the oscillator when its oscillation displaces it from equilibrium. The blue wavy line denotes the gravitational interaction between the masses. At equilibrium, the center-to-center distance of the two spheres is $d$, each sphere has radius $r$, and the separation of the membranes is $d – 2r$.
• Figure 2: Simulated entanglement differences between quantum and classical gravity models under our scheme and the conventional one, respectively, plotted against mechanical quality factor $Q_m$. The gray thick vertical dashed line marks the threshold for the existence of entanglement in the conventional scheme. We choose the parameters such that, while the mechanical quality $Q_m$ equals $2.5\times 10^{10}$, the single-photon optomechanical couplings $g/(2\pi)= 1~Hz$ and the pump beam amplitude $|\mathcal{E}_+| = 10^2~\mathrm{Hz}$, $|\mathcal{E}_-| = 2\times 10^2~\mathrm{Hz}$. The phases of $\mathcal{E}_{\pm}$ are set such that $\overline{c}_{\pm}$ are real numbers. The pump amplitude will be changed while $Q_m$ increases, due to the parameter adjusting rule.
• Figure 3: Ratio $\mathcal{R}$ of the entanglement contributed by non-gravitational coupling to the entanglement difference between quantum and classical gravity models, plotted against the non-gravitational coupling strength (normalized by the gravitational coupling strength). The numerator of the ratio was simulated under both quantum and classical gravity models, but the difference between them is negligible. The gray thick horizontal dashed line marks the $0.1$ level of the ratio, below which the non-gravitational coupling can be regarded as insignificant. Here, $Q_m$ is set to $2.5\times 10^{10}$, consistent with the reference value shown in Fig. \ref{['fig:gap']}.