Beyond Entanglement: Diagnosing quantum mediator dynamics in gravitationally mediated experiments

TL;DR

This work analyzes a three-harmonic-oscillator model to emulate gravitational mediation in BMV-type experiments and to diagnose mediator dynamics beyond entanglement. By solving the Gaussian, quadratic Hamiltonian with a tunable mediator $B$, the authors identify heavy-mediator and light-mediator regimes that yield qualitatively different entanglement dynamics between the outer oscillators $A$ and $C$. They show that time-averaged entanglement measures can fail to reveal the mediator’s quantum nature, but the time-averaged dynamical fidelity susceptibility $\langle \chi_F\rangle$ provides clear, regime-dependent signatures. The work suggests experimental protocols in optomechanical and trapped-ion platforms to jointly probe entanglement, discord, and fidelity susceptibility, thereby offering a more robust route to testing quantum gravity-inspired interactions.

Abstract

No experimental test to date has provided conclusive evidence on the quantum nature of gravity. Recent proposals, such as the BMV experiment, suggest that generating entanglement could serve as a direct test. Motivated by these proposals, we study a system of three-harmonic oscillator system, with the mediator oscillator operating in two distinct parameter regimes: a heavy mediator regime and a light mediator regime. These regimes induce qualitatively different entanglement dynamics between the terminal oscillators. Crucially, distinguishing these regimes experimentally remains challenging when relying solely on entanglement measures. We demonstrate that the dynamical fidelity susceptibility offers a viable and sensitive probe to contrast the regimes in practice. Our results provide testable signatures for optomechanical and trapped-ion platforms simulating gravitational interactions, and provide new avenues to characterize quantum-gravity-inspired systems beyond entanglement-based protocols.

Figures (6)

• Figure 1: Schematic diagram of the tripartite HO system. Oscillator B mediates interaction with A and C. Interactions include self-squeezing $(\lambda_A, \lambda_B)$ and inter-oscillator couplings $(g_A, g_B)$, like parametric squeezing and mode mixing.
• Figure 2: Contour plots of the long-time averaged logarithmic negativity $\langle \mathcal{E}_{\mathcal{N}} \rangle$ in the two mediator regimes. Top: (HMR) Bottom: (LMR). Parameter choices and initial squeezed states are specified in the text.
• Figure 3: Normalized time-averaged $\langle \chi_F \rangle$ vs $\omega_B$ for two different initial states (vacuum: left, squeezed: right) with $r_1 = r_3 = 0.5$, $r_2 = 0.2$, $\theta_1 = \theta_2 = \theta_3 = 0$. Fixed parameters: $\omega_A = 5$, $\lambda_A = 0.5\,\omega_A$, $g_A = g_B = 0.6$.
• Figure 4: Contour plots of time-averaged logarithmic negativity $\langle \mathcal{E}_{\mathcal{N}} \rangle$ and Fidelity $\langle \mathcal{F}\rangle$. (a, b)(HMR) use the parameter set $\omega_B = 50$, $\lambda_B = 49.9$, $\lambda_A = 0.001$, $g_B = 2.0$, (c, d)(LMR) use $\omega_A = 5.0$, $\lambda_A = 4.999$, $\lambda_B = \omega_B/1.5$, $g_B = 1.4$
• Figure 5: Contour plots of time-averaged quantum discord $\langle \mathcal{D} \rangle$ in two contrasting mediator regimes. (a, c) Vacuum initial state, corresponding to zero squeezing: $r_1 = r_2 = r_3 = 0$, $\theta_1 = \theta_2 = \theta_3 = 0$; (b, d) Squeezed initial state with $r_1 = (0.1, 0.5)$, $r_2 = (1.0, 2.0)$, $r_3 = (0.1, 0.5)$ and squeezing angles $\theta_1 = (-\pi/3, 0)$, $\theta_2 = (\pi/4, 0)$, $\theta_3 = (\pi/6, 0)$.