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arXiv:2007.05762 · Physical Review A

Acceleration noise constraints on gravity-induced entanglement

André Großardt

Published Oct 12, 2020• 13 citations
arXivHTMLPDF

Abstract

It has been proposed that quantum features of the gravitational field can be exposed experimentally by employing gravity as a mediator of entanglement. We show that in order to witness this type of entanglement experimentally, strong limits on acceleration noise, which has been neglected in previous work, must be overcome. In the case of two particles of similar mass, Casimir-Polder forces lead to a fundamental limit of tenths of $\mathrm{fm}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}2}/\sqrt{\mathrm{Hz}}$. Limits are between three and six orders of magnitude less strict for two particles of unequal mass, depending on collisional decoherence.

DOI
10.1103/physreva.102.040202

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It has been proposed that quantum features of the gravitational field can be exposed experimentally by employing gravity as a mediator of entanglement. We show that in order to witness this type of entanglement experimentally, strong limits on acceleration noise, which has been neglected in previous work, must be overcome. In the case of two particles of similar mass, Casimir-Polder forces lead to a fundamental limit of tenths of fms\ensuremath−2/Hz\mathrm{fm}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}2}/\sqrt{\mathrm{Hz}}fms\ensuremath−2/Hz​. Limits are between three and six orders of magnitude less strict for two particles of unequal mass, depending on collisional decoherence.
While a wide variety of astrophysical and cosmological phenomena suggest the presence of dark matter, all evidence remains via its gravitational effect on the known matter. As such, it is conceivable that this evidence could be explained by a modification to gravitation and/or concepts of inertia. Various formulations of modified gravity exist, each giving rise to several noncanonical outcomes. This motivates us to propose an experiment searching for departures from (quantum) Newtonian predictions in a bipartite setting with gravitational accelerations $\ensuremath{\lesssim}{10}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}$, i.e., where the effective force needs to be stronger than Newtonian to account for the dark matter effects. Since quantum particles naturally source weak gravitation, their nonrelativistic dynamics offers opportunities to test this small acceleration regime. We show that two nearby mesoscopic quantum masses accumulate significantly larger entanglement in modified gravity models, such as the modified Newtonian dynamics. Our calculations include Casimir-Polder forces as well as tidal effects next to the surface of the Earth, and confirm that entanglement is observable within the limits imposed by environmental decoherence. We demonstrate how the temperature can be fine-tuned such that modified gravity is certified simply by witnessing the entanglement generated from uncorrelated thermal states, eliminating the need for precise noise characterization. Overall, the required parameters could be realized in a tabletop experiment.
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Recently, a theoretical and an experimental protocol known as quantum-gravity-induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses, each placed in a superposition of two locations. If after eliminating all nongravitational interactions between them the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e., graviton. In this paper we explore extensions of the QGEM experiment to multidimensional quantum objects and examine a range of different experiment geometries, in order to determine which would generate entanglement faster. We conclude that when a sufficiently high decoherence rate is introduced, multicomponent superpositions can outperform the two-qubit setup. With low decoherence however, and given a maximum distance $\mathrm{\ensuremath{\Delta}}x$ between any two spatial states of a superposition, a set of two qubits placed in spatial superposition parallel to one another will outperform all other models given realistic experimental parameters. This is further verified with an experiment simulation, showing that O(103)O({10}^{3})O(103) measurements are required to reject the no-entanglement hypothesis with a parallel-qubit setup without decoherence at a 99.999.9%99.9 confidence level. The number of measurements increases when decoherence is introduced. When the decoherence rate reaches 0.125 Hz, six-dimensional qudits are required as the two-qubit system entanglement cannot be witnessed anymore. However, in this case, O(106)O({10}^{6})O(106) measurements will be required. One can group the witness operators to measure in order to reduce the number of measurements (up to tenfold). However, this may be challenging to implement experimentally.
A recently proposed experimental protocol for quantum gravity induced entanglement of masses (QGEM) requires in principle realizable, but still very ambitious, set of parameters in matter-wave interferometry. Motivated by easing the experimental realization, in this paper, we consider the parameter space allowed by a slightly modified experimental design, which mitigates the Casimir potential between two spherical neutral test masses by separating the two macroscopic interferometers by a thin conducting plate. Although this setup will reintroduce a Casimir potential between the conducting plate and the masses, there are several advantages of this design. First, the quantum gravity induced entanglement between the two superposed masses will have no Casimir background. Secondly, the matter-wave interferometry itself will be greatly facilitated by allowing both the mass ${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\phantom{\rule{0.28em}{0ex}}\mathrm{kg}$ and the superposition size $\mathrm{\ensuremath{\Delta}}x\ensuremath{\sim}20\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ to be a one-two order of magnitude smaller than those proposed earlier, and thereby also two orders of magnitude smaller magnetic field gradient of ${10}^{4}\phantom{\rule{0.28em}{0ex}}{\mathrm{Tm}}^{\ensuremath{-}1}$ to create that superposition through the Stern-Gerlach effect. In this context, we will further investigate the collisional decoherences and decoherence due to vibrational modes of the conducting plate.
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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.