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arXiv:2006.06931 · Physical Review A

Quantum gravity witness via entanglement of masses: Casimir screening

Thomas W. van de Kamp, Ryan J. Marshman, Sougato Bose, Anupam Mazumdar

Published Dec 4, 2020• 113 citations
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Abstract

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.

DOI
10.1103/physreva.102.062807

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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−15kg{10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\phantom{\rule{0.28em}{0ex}}\mathrm{kg}10\ensuremath−16−−10\ensuremath−15kg and the superposition size \ensuremathΔx\ensuremath∼20\ensuremathμm\mathrm{\ensuremath{\Delta}}x\ensuremath{\sim}20\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}\ensuremathΔx\ensuremath∼20\ensuremathμm 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 104Tm\ensuremath−1{10}^{4}\phantom{\rule{0.28em}{0ex}}{\mathrm{Tm}}^{\ensuremath{-}1}104Tm\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.
The quantum gravity-induced entanglement of masses (QGEM) protocol for testing quantum gravity using entanglement witnessing utilizes the creation of spatial quantum superpositions of two neutral, massive matter-wave interferometers kept adjacent to each other, separated by a distance d . The mass and the spatial superposition should be such that the two quantum systems can entangle solely via the quantum nature of gravity. Despite being charge-neutral, many electromagnetic backgrounds can also entangle the systems such as the dipole-dipole and Casimir-Polder interactions. To minimize electromagnetic-induced interactions between the masses, it is pertinent to isolate the two superpositions by a conducting plate. However, the conducting plate will also exert forces on the masses and hence the trajectories of the two superpositions would be affected. To minimize this effect, we propose to trap the two interferometers such that the trapping potential dominates over the attraction between the conducting plate and the matter-wave interferometers. The superpositions can still be created via the Stern-Gerlach effect in the direction parallel to the plate, where the trapping potential is negligible. The combination of trapping and shielding provides a better parameter space for the parallel configuration of the experiment, where the requirement on the size of the spatial superposition, to witness the entanglement between the two masses purely due to their quantum nature of gravity, decreases by at least two orders of magnitude as compared to the original protocol paper. Published by the American Physical Society 2024
To test the quantum nature of gravity in a laboratory requires witnessing the entanglement between the two test masses (nanocrystals) solely due to the gravitational interaction kept at a distance in a spatial superposition. The protocol is known as the quantum-gravity-induced entanglement of masses (QGEM). One of the main backgrounds in the QGEM experiment is electromagnetic (EM) -induced entanglement and decoherence. The EM interactions can entangle the two neutral masses via dipole-dipole vacuum-induced interactions, such as the Casimir-Polder interaction. To mitigate the EM-induced interactions between the two nanocrystals, we enclose the two interferometers in a Faraday cage and separate them by a conducting plate. However, any imperfection on the surface of a nanocrystal, such as a permanent dipole moment, will also create an EM background interacting with the conducting plate in the experimental box. These interactions will further generate EM-induced dephasing, which we wish to mitigate. In this paper, we will consider a parallel configuration of the QGEM experiment, where we will estimate the EM-induced dephasing rate and run-by-run systematic errors which will induce dephasing, and also provide constraints on the size of the superposition in a model-independent way of creating the spatial superposition.
In the context of the QGEM (Quantum Gravity-induced Entanglement of Masses) experiment, we consider two adjacent matter-wave interferometers in linear and parallel configurations that interact solely via gravity. If gravity were quantum, then the two matter-wave interferometers would become entangled via the virtual excitation of the massless graviton. In this paper, we consider witnessing this entanglement by considering a generic experimental scenario where the two interferometers are subject to different global phases and different decoherence rates. In this context, we show that the individual global phases do not affect the witness, discuss common and differential decoherence modes, and perform the parameter search optimal for different masses. We provide a mathematical framework for these asymmetric decoherence rates and then search for parameters that determine the entanglement witness. We have kept the inter-separation distance between the two closest superpositions of the interferometers' masses fixed while varying the experimental time from τ=0.1τ=0.1τ=0.1 s to τ=1τ=1τ=1 s. Finishing the experiment at $ τ=0.1$ s has many advantages from the point of view of protecting the experiment from random acceleration noise. However, witnessing the entanglement also suffers from ⟨W⟩∼−O(10−2)\langle W\rangle \sim -{\cal O}(10^{-2})⟨W⟩∼−O(10−2) for m=10−14m=10^{-14}m=10−14~kg, for decoherence rate in the ranges of O(10−1−1){\cal O}(10^{-1}-1)O(10−1−1)~Hz for τ=0.1τ=0.1τ=0.1 s experiment. However, as we show, increasing the mass of the matter-wave interferometer may improve the witness considerably.
Witnessing the quantum nature of spacetime is an exceptionally challenging task. However, the quantum gravity-induced entanglement of matter (QGEM) protocol proposes such a test by testing entanglement between adjacent matter-wave interferometers. One key obstacle to experimentally realising this protocol is the creation of a spatial quantum superposition with heavy masses. Initially, it was envisaged that the superposition size would have to be of order 200 micron for a mass 10−1410^{-14}10−14 kg (to obtain the entanglement phase of order unity when the centre of mass of the two interferometers are at a separation of 450 microns). The experimental design has since improved, e.g. by assuming that the two interferometers are separated by an electromagnetic screen, which helps bring the separation distance close to 35 micron. Here, we do parameter scans taking into account the electromagnetic screening, and we consider different geometrical setups; we show superpositions of at least a micron-size for mass 10−1410^{-14}10−14 kg with a decoherence rate of order 10−310^{-3}10−3 Hz are required.
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.
The recently introduced quantum gravity-induced entanglement of masses (QGEM) protocol aims to test the quantum nature of gravity by witnessing the entanglement produced by the virtual exchange of a graviton between two spatially superposed masses. Shortly after the original proposal, further improvements upon the experiment were suggested, including the addition of a third mass, showing that three-qubit setups can be more resilient to higher rates of decoherence caused by the interaction of the system with the environment. In this work, we investigate the type of tripartite entanglement generated in these three-qubit QGEM experiments when considering the effects of decoherence. We show that the gravitational interaction between the qubits is able to generate genuine tripartite entanglement between them, studying the corresponding parameter spaces and comparing the performance of the possible experimental configurations of the three qubits at allowing for the detection of genuine entanglement via an entanglement witness.