Sudden Decoherence by Resonant Particle Excitation for Testing Gravity-Induced Entanglement

TL;DR

This work proposes a resonance-enhanced test of gravity-induced entanglement between a particle in a shallow potential and a harmonic oscillator whose frequency is coherently controlled. By preparing the oscillator in a superposition of two frequencies and leveraging the resonant gravitational coupling, the bound particle can be excited with a probability growing linearly in time, and detecting this excitation collapses the oscillator’s quantum state, producing a sudden loss of interference visibility if gravity is quantized. The authors quantify the gravity-induced entanglement via a negativity that scales with the excitation probability and contrast it with Schrödinger-Newton gravity, which yields excitation without sudden decoherence. An optomechanical-type experimental realization is discussed, highlighting both feasibility and challenges, and the framework provides a clear criterion to distinguish quantum from semiclassical gravity in the Newtonian regime. Repeating experiments to accumulate small probabilities offers a practical path to test gravity-induced entanglement without requiring ultra-long coherence per run.

Abstract

We propose a novel method to probe gravity-induced entanglement. We consider the gravitational interaction between a particle trapped in a shallow potential and a harmonic oscillator. The harmonic oscillator is in a quantum superposition of two frequencies and only one of these states can excite the trapped particle via resonance. Once the excited particle is detected, the quantum state of the oscillator is collapsed, which can be observed as the sudden disappearance of the superposition of oscillator frequencies. Thus, the sudden decoherence, which is only triggered by particle detection, can be a smoking gun evidence of gravity-induced entanglement. Since the probability of particle excitation increases linearly with time, the total probability is multiplied by repeating experiments. We will also discuss experimental implementations using optomechanics.

Figures (5)

• Figure 1: An easily excitable particle in a shallow potential (green blob on right side) interacting gravitationally with a harmonic oscillator (black blob on left side). The oscillator has two superposed oscillation frequencies $\Omega_0$ and $\Omega_1$ for the control qubit states $|0\rangle$ and $|1\rangle$, respectively (leftmost arrow and harmonic potential in red and blue colors). The particle will be entangled with the oscillator system through gravitational interaction after time evolution.
• Figure 2: Particle detection triggers the sudden disappearance of interference visibility
• Figure 5: An implementation of our setup using optomechanics. A single photon enters cavities 1 and 2 as a quantum superposed states through a half mirror, which corresponds to the control qubit system introduced in the section \ref{['sec:setup']} (see Fig. \ref{['fig:setup1']}). Only in the former case, the eigenfrequency of the oscillator is modified by the radiation pressure. The oscillator, which is thereby in a superposition of two frequencies, gravitationally couples to a particle trapped in a shallow potential.
• Figure 6: The eigensystem of the particle in the Pöschl-Teller potential. The gray line shows the form of the Pöschl-Teller potential. Thick blue lines show the bound state wavefunction; the solid line shows the real part, while the dotted line shows the imaginary part. A translucent blue line on the background shows the bound energy. Similarly, the other lines show the case of the excited states for various $k$.
• Figure 7: The observation time dependence of the particle's excitation probability $P_\text{ex}$. The red and blue lines show the result for $\Omega_1=1.01|\omega_b|$ and $\Omega_1=1.50|\omega_b|$, respectively. Solid lines are the numerical results, while the dashed lines and dotted lines are the analytical form obtained from the saddle-point approximation as the case (i) and (ii) in Eq. \ref{['eq:excitation_probability_saddlepoint']}, respectively. The vertical lines correspond to the saturation time scale $t_\text{sat}$ for each $\Omega_1$.