Gravitationally mediated entanglement of fermionic qubits: from static to dynamical limits

TL;DR

This work probes whether gravity can act as a quantum mediator by analyzing entanglement generation between two distant spin-1/2 qubits via graviton exchange. It leverages an extended quantum Boltzmann equation to focus on forward scattering, demonstrating that entanglement arises only when the dynamical (transverse) part of the graviton propagator is included. Two microscopic models yield distinct mass- and spin-dynamics: Model I ties entanglement strength to the particle masses, while Model II ties it to the Larmor frequencies under an external magnetic field, with effects amplified or suppressed by wave-packet size. The results establish concrete conditions under which gravity-mediated entanglement could be observed in tabletop experiments, offering insights into the quantum nature of gravity and guiding experimental tests.

Abstract

We employ the quantum Boltzmann equation to analyze the gravitationally generated entanglement between two remote qubits by considering two explicit microscopic models. A graviton propagator is employed as the mediator of the interactions, while the qubits are considered in a spatial superposition state. Such a setup, in the case of any entanglement generation, could potentially offer experimental evidence for the quantization of gravity. By treating the qubits as spin-1/2 particles in wave packets, we establish that the entanglement arises from forward scattering processes involving graviton exchanges. In our study, we consider both static and dynamical limits of the propagator and show that only in the dynamical limit such entangled states can be generated. We also show that for the microscopic model based on the fermion particles in the background of magnetic field, the amount of entanglement depends on the Larmor frequency of the qubits, rather than their masses. These effects are observed to diminish in both models as the wave packet size increases. Our findings sheds more light into the gravity mediated entanglement between two spin-1/2 particles.

Figures (3)

• Figure 1: Adjacent interferometers probe the quantum nature of gravity: Two test masses are placed adjacently in a spatial superposition of localized states $|L\rangle$ and $|R\rangle$ through two Stern-Gerlach interferometers that split the motional states of the test masses in a spin-dependent manner, preparing states $|L,j\rangle+ |R,j\rangle$ for $j=1,2$.
• Figure 2: Comparison of the Model I (red) and Model II(blue): The top panel gives the accumulated phase for each model as a function of the particle mass. In the bottom panel the logarithmic negativity is shown as a measure of the entanglement built up between the particles. Here, we have considered two set of parameters: $\{d,\tau\}=\{10~\text{nm}, 10^3~\text{s}\}$ solid lines and $\{d,\tau\}=\{0.1~\text{nm}, 10^6~\text{s}\}$ for the dashed lines. In both sets $\Delta x=d/2$ and $B_3=1$ T.
• Figure S1: Logarithmic negativity as a function on the accumulated phases.