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arXiv:2010.05159 · Physical review. D/Physical review. D.

Entanglement and decoherence of massive particles due to gravity

Daisuke Miki, Akira Matsumura, Kazuhiro Yamamoto

Published Jan 25, 2021• 45 citations
arXivHTMLPDF

Abstract

We analyze the dynamics of a gravity-induced entanglement for $N$ massive particles. Considering the linear configuration of these particles, we investigate the entanglement between a specific pair of particles under the influence of the gravitational interaction between the massive particles. As the particle number increases, the specific particle pair decoheres more easily due to the gravitational interaction with other particles. The timescale of the gravity-induced decoherence is analytically determined. We also discuss the entanglement dynamics of initially entangled particles, which exemplify the monogamy of the gravity-induced entanglement.

DOI
10.1103/physrevd.103.026017

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Abstract We investigate the generation rate of the quantum entanglement in a system composed of multiple massive particles with large spin, where the mass of a single particle can be split into multiple trajectories by a generalized Stern–Gerlach interferometer. Taking the coherent spin states as the initial state and considering the gravitational interaction due to Newtonian potential, we compute the generation rate of the entanglement for different configurations of the setup. Explicitly, the optimal polar angles of the spin are found numerically for systems with three and four particles, respectively. We conclude that the amount of the entanglement increases with the number of particles as well as the spin, and the configuration of the prism with a particle at the center generates the best rate of the entanglement.
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We formulate the gravitationally induced quantum decoherence of a massive object prepared in a spatial superposition. Starting from linearized gravity coupled to a massive system particle and an environmental scalar field, we derive a closed-time-path influence functional governing the reduced system dynamics. In the nonrelativistic and quasi-static regime, the decoherence exponent can be written as a bilinear functional of the difference of the system stress-energy tensors and an effective noise kernel obtained by dressing the environmental stress-energy tensor correlator with graviton propagators. We then apply this framework to the Newtonian long-range gravitational interaction and evaluate the resulting decoherence function for a dilute nonrelativistic gas modeled by finite wave packets and coarse-grained in time and space. By performing controlled approximations, we obtain analytic expressions for the cumulative decoherence function and show that the dominant contribution is accumulated logarithmically over a broad range of distances, while remaining subdominant to conventional collisional decoherence under realistic conditions.
Tests of gravity-induced entanglement have been proposed as a route to probing the quantum nature of gravity, but existing schemes rely on free-fall interferometry of massive spatial superpositions, imposing severe experimental constraints. We show that systems exhibiting effectively inertial dynamics in the short-time regime reproduce the same gravitational phase accumulation responsible for entanglement generation. Deviations from the free-fall phase enter at order (τ/T)2(τ/T)^2(τ/T)2, where τττ is the interaction timescale and TTT is the characteristic period of the constrained motion. We analyse a representative mechanically constrained implementation using carbon nanotube pendula and show that the resulting correction to the entangling phase remains small in experimentally relevant regimes, leading to a negligible modification of the interference visibility used to certify entanglement. These results demonstrate that gravity-induced entanglement protocols extend beyond free-fall implementations to a broader class of constrained dynamical systems, complementing existing proposals for experimental realisations of the Bose-Marletto-Vedral protocol.