Mass-Independent Gravitationally Induced Entanglement

TL;DR

This work develops a density-matrix description of two non-Gaussian Stern-Gerlach interferometers entangling through a leading-order Gaussian gravitational interaction, yielding analytic solutions for both unitary and open dynamics. A central result is that the leading-order entangling phase is mass-independent, enabling entanglement detection via qubit measurements across a wide range of initial CV states; a four-path interferometer analysis reveals a residual operator-valued deflection that prevents perfect recombination, introducing mass bounds that place the experiment in the mesoscopic regime. When open dynamics with diffusion and dephasing are included, the authors derive tightened bounds for realistic noise and initial squeezed thermal states, providing concrete guidance on experimental isolation and coherence requirements. The paper also connects the formalism to practical implementations, notably NV-centres in diamagnetic nanospheres, illustrating how the entangling phase scales with magnetic gradients and trap distance. Overall, the results delineate a mass-independent GIE detection regime in the mesoscopic range and offer actionable parameter spaces for experimental exploration of gravitationally induced entanglement and, more broadly, non-classical gravity effects.

Abstract

We analytically solve the entangling quantum dynamics of two interacting Stern-Gerlach Interferometers~(SGI). Each SGI exploits an operator-valued force applied by a qubit to create and recombine a non-Gaussian state of matter. The entangling phase between the two qubits generated by the leading-order gravitational interaction of the massive degrees of freedom is found to be mass-independent, both for unitary and open dynamics, irrespective of the temperature and squeezing of the initial states. Further, we show that the solution of the four interferometric paths reveals that the mere presence of the interaction does not allow for a perfect recombination of the centre of mass. This second-order effect, alongside higher-order interaction terms, can be used to bound the mass from above and below, thus restricting the experiment's regime to mesoscopic masses. By solving the open dynamics which includes diffusion and dephasing with initial squeezed thermal states, the bounds are tightened by the inclusion of realistic experimental noise. We discuss diamagnetic levitated masses with embedded NV-centres as a specific physical implementation.

Figures (5)

• Figure 1: Two SGIs entangling via a Gaussian quantum interaction: the four interferometric paths of the two NPs are in green ($\omega_g =\sqrt{1 -2g}$, $f_q = 1$, $g=0.1$).
• Figure 2: Negativity as function of the unitless parameter space for unitary dynamics with ground-states.
• Figure 3: Constraint negativity (a) for different initial states and (b) for a squeezed thermal state ($n_p = 10^{2},\;s = 10^{-4}$) undergoing diffusive dynamics as function of the entangling coupling $g$.
• Figure 4: Negativity as function of the unitless parameter space for unitary dynamics with different initial states: (a) Ground state, (b) thermal states, and (c) squeezed thermal states ($n_p =100$).
• Figure 5: Negativity as function of the unitless parameter space for open dynamics with different diffision rates.