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arXiv:2604.20767

Gravity mediated entanglement of phonons in Bose-Einstein condensates

Soham Sen, Sunandan Gangopadhyay, Vlatko Vedral

hep-thgr-qcquant-phSubmitted Apr 22, 2026• Announced Apr 23, 2026• 0 citations
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Abstract

The eigenstates of two test-masses (where each test-mass is placed inside of a harmonic trap) separated by a distance, can get entangled where gravity acts as the mediator of entanglement and it has been argued in \href{https://doi.org/10.48550/arXiv.2511.07348}{arXiv:2511.07348 [quant-ph]} that this entanglement of masses cannot be generated without the underlying quantum nature of gravity. In this work, we consider two non-relativistic Bose-Einstein condensates (formed inside of harmonic trap potentials with identical trapping frequencies) separated by a distance. We take a linearized quantum gravity model and investigate the generation of entanglement while gravitons serve as the mediator of entanglement. The entanglement is generated between the phonon modes of the two condensates, and we observe that for very low separation distance, the entanglement generated is significantly higher than that observed for the quantum gravity induced entanglement of masses or QGEM protocol; however, the fall of entanglement is faster than the two-particle case for two separated Bose-Einstein condensates. We observe that when the number of particles in the condensate is increased, the degree of entanglement for a smaller separation distance becomes substantially higher compared to the case discussed in \href{https://doi.org/10.1103/PhysRevD.105.106028}{Phys. Rev. D 105 (2022) 106028}, which allows for a more robust experimental proposal using this quantum gravity induced entanglement of phonons or QGEP protocol.

Comments
8 pages LATEX with supplementary material. Comments are welcome. Om Thakur Ma

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The eigenstates of two test-masses (where each test-mass is placed inside of a harmonic trap) separated by a distance, can get entangled where gravity acts as the mediator of entanglement and it has been argued in \href{https://doi.org/10.48550/arXiv.2511.07348}{arXiv:2511.07348 [quant-ph]} that this entanglement of masses cannot be generated without the underlying quantum nature of gravity. In this work, we consider two non-relativistic Bose-Einstein condensates (formed inside of harmonic trap potentials with identical trapping frequencies) separated by a distance. We take a linearized quantum gravity model and investigate the generation of entanglement while gravitons serve as the mediator of entanglement. The entanglement is generated between the phonon modes of the two condensates, and we observe that for very low separation distance, the entanglement generated is significantly higher than that observed for the quantum gravity induced entanglement of masses or QGEM protocol; however, the fall of entanglement is faster than the two-particle case for two separated Bose-Einstein condensates. We observe that when the number of particles in the condensate is increased, the degree of entanglement for a smaller separation distance becomes substantially higher compared to the case discussed in \href{https://doi.org/10.1103/PhysRevD.105.106028}{Phys. Rev. D 105 (2022) 106028}, which allows for a more robust experimental proposal using this quantum gravity induced entanglement of phonons or QGEP protocol.
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A recent paper by Aziz and Howl (Nature 2025) argues that, once quantum matter is described at the level of quantum field theory and coupled to a classical gravitational field, higher order processes can generate entanglement between two spatially separated masses. A contemporaneous critical note (Marletto, Oppenheim, Vedral, Wilson, arXiv:2511.07348v1) shows that, in the actual nonrelativistic limit employed there, the interaction becomes ultra local, the total unitary factorizes, and no entanglement is generated from a product input. In this comment we (i) restate the core point of that critique, (ii) give a channel theoretic reformulation that makes the conclusion model independent, and (iii) clarify the distinction between activation of entanglement in already quantum matter and genuine mediation of entanglement by a classical field. Once these clarifications are in place, the standard BMV inference that observation of gravity mediated entanglement strongly indicates nonclassical gravitational degrees of freedom remains intact.
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Recently, a protocol called quantum-gravity-induced entanglement of masses (QGEM) that aims to test the quantum nature of gravity using the entanglement of two qubits was proposed. The entanglement can arise only if the force between the two spatially superposed masses is occurring via the exchange of a mediating virtual graviton. In this paper we examine a possible improvement of the QGEM setup by introducing a third mass with an embedded qubit so that there are now three qubits to witness the gravitationally generated entanglement. We compare the entanglement generation for different experimental setups with two and three qubits and find that a three-qubit setup where the superpositions are parallel to each other leads to the highest rate of entanglement generation within $\ensuremath{\tau}=5\phantom{\rule{4pt}{0ex}}\mathrm{s}$. We show that the three-qubit setup is more resilient to the higher rate of decoherence. The entanglement can be detected experimentally for the two-qubit setup if the decoherence rate $\ensuremath{\gamma}$ is $\ensuremath{\gamma}<0.11\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$ compared to $\ensuremath{\gamma}<0.16\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$ for the three-qubit setup. However, the introduction of an extra qubit means that more measurements are required to characterize entanglement in an experiment. We conduct experimental simulations and estimate that the three-qubit setup would allow detecting the entanglement in the QGEM protocol at a 99.999.9%99.9 certainty with O(104)−−O(105)O({10}^{4})--O({10}^{5})O(104)−−O(105) measurements when $\ensuremath{\gamma}\ensuremath{\in}[0.1,0.15]\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$. Furthermore, we find that the number of needed measurements can be reduced to O(103)−−O(105)O({10}^{3})--O({10}^{5})O(103)−−O(105) if the measurement schedule is optimized using joint Pauli basis measurements. For $\ensuremath{\gamma}>0.06\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$ the three-qubit setup is favorable compared to the two-qubit setup in terms of the minimum number of measurements needed to characterize the entanglement. Thus, the proposed setup here provides a promising avenue for implementing the QGEM experiment.
Gravitationally induced entanglement has been proposed as a probe of the quantum nature of gravity. This work analyzes a system of two particles in harmonic traps interacting only through gravity, considering thermal and two-mode squeezed initial states. For thermal states, a maximum temperature is identified above which entanglement cannot be generated, and for fixed system parameters an optimal trap frequency that maximizes the logarithmic negativity is found. Squeezing the initial state does not further enhance the entanglement generation, but increases the temperature range over which it can be observed. Extending the analysis to general Gaussian states, an upper bound on the achievable entanglement is derived and shown to be saturated, for example, by ground and squeezed states. The results show that the amount of entanglement generated in this setup is extremely small, highlighting the experimental challenges of observing gravitationally induced quantum effects.