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arXiv:2610.07422

White paper: 1-10 Hz matter-wave interferometer to test the spin entanglement witness for quantum gravity

Sougato Bose, Anupam Mazumdar, Marko Toroš, Tian Zhou, Tadeusz Adach, Niayesh Afshordi, Agya Sewara Alam, Alexandre Arbey, Navdeep Arya, Simon Baier, Peter F. Barker, Angelo Bassi, Ettore Bernardi, Lorenzo Braccini, Robert Brandenberger, Daniel Braun, Guri K. Buza, Luigi Cacciapuoti, Carlo Cepollaro, Lin-Qing Chen, Yanbei Chen, Ralph Jason Costales, Marion Cromb, Álvaro de la Cruz-Dombriz, Catalina Curceanu, Shubhang Dadhich, Debarshi Das, Saurya Das, Pratika Dayal, Subhadeep De, Ema Dimastrogiovanni, Lajos Diósi, Or Dobkowski, Kemal Döner, Brian D'Urso, Gurudev Dutt, Shafaq Gulzar Elahi, Samira Elghaayda, Matteo Fadel, Samuel Fedida, Omer Feldman, Fabiano Feleppa, Ron Folman, Joshua Foo, Paolo Fragolino, Laurent Freidel, Giulio Gasbarri, Marco Genovese, Andrew Geraci, Menachem Givon, Cisco Gooding, Jonathan M. H. Gosling, Piotr T. Grochowski, David Groswasser, Mustafa Gündoğan, Ekim Taylan Hanımeli, Bas Hensen, Dipankar Home, Richard Howl, Yonathan Japha, Maciej T. Jarema, Rainer Kaltenbaek, Adrian Kent, Eva Kilian-Rademacher, M. S. Kim, Jarosław K. Korbicz, Timothy Kovachy, Samuel Kováčik, Ohkyung Kwon, Gaetano Lambiase, Naor Levi, Iarley P. Lobo, Leon Loveridge, Adrian Lupascu, Paolo Luppi, Marta Maria Marchese, Antonino Marcianò, Aaron G. Markowitz, Chiara Marletto, Ryan J Marshman, J. D. D. Martin, Florian Millo, Gavin W. Morley, Maria Muretova, Sebastian Murk, Robin Oberfrank, Daniel K. L. Oi, Jerzy Paczos, Papadopoulos Stylianos, Matteo G. A. Paris, Mauro Paternostro, Alessandro Pesci, Luciano Petruzziello, Fabrizio Piacentini, Tanmay Kumar Poddar, Sofia Qvarfort, Markus Rademacher, Dennis Rätzel, Anna Chiara Rescigno, Ryan Rizaldy, Albert Roura, Carlos Sabín, Barry C. Sanders, Martine Schut, Helen M Sheehy, Suprit Singh, Aninda Sinha, Urbasi Sinha, Peter Skakunenko, Michael E Tobar, Géza Tóth, Hendrik Ulbricht, Gislaine Varão, Vlatko Vedral, Vincent Vennin, Francesca Vidotto, Giuseppe Filiberto Vitale, Marko Vojinović, Chenan Wei, Qian Xiang, Magdalena Zych

quant-phgr-qcSubmitted Oct 5, 2026• Announced Oct 7, 2026• 0 citations
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Abstract

In this white paper, we highlight the importance of the ($1-10~{\rm Hz}$) frequency range for laboratory tests of the quantum nature of gravity using the quantum gravity-induced entanglement of masses (QGEM) protocol. QGEM requires matter-wave interferometers with masses ($m\sim10^{-15}-10^{-14}~{\rm kg}$), brought within separations ($d\sim30-50~μ{\rm m}$), while maintaining spatial superpositions of ($1-20~μ{\rm m}$) and coherence for ($τ\sim 0.1 - 1~{\rm s}$). These requirements make low-frequency environmental noise a central experimental challenge and place QGEM in a regime closely related to the low-frequency goals of the Einstein Telescope (ET) and the Cosmic Explorer (CE). In particular, QGEM is sensitive to relative acceleration noise (RAN) and to gravity-gradient noise (GGN) generated by seismic and other environmental mass-density fluctuations. For representative parameters $m=10^{-14}~{\rm kg}$, $Δx=10~μ{\rm m}$, and $τ=1~{\rm s}$, the differential acceleration-noise amplitude spectral density must be suppressed well below the $10^{-15}~{\rm m\,s^{-2}/\sqrt{Hz}}$ level to keep acceleration-induced dephasing below the relevant experimental scale. Achieving this level of low-frequency noise suppression is therefore a key requirement for QGEM and closely parallels the seismic and gravity-gradient noise challenges that ET and CE address.

Comments
14 pages, 2 figures

Related papers

Differential and Common Decoherence Modes in Witnessing the Quantum Gravity-Induced Entanglement of Matter

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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 $10^{-14}$ 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 $10^{-14}$ kg with a decoherence rate of order $10^{-3}$ Hz are required.

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Relative accelerations between a mass undergoing matter-wave interference and the associated apparatus, when not tracked, can appear as dephasing. It can be an important limiting factor in interferometry with large masses. Here we advocate taking conceptually the simplest solution: putting both the interfering mass and its associated apparatus in a freely falling capsule, so that the strongest inertial noise components vanish due to the equivalence principle. In this setting, we investigate two of the most important remaining noise sources: (a) the non-inertial jitter of the experimental setup which arises through gas collisions and photon scattering on the experimental apparatus as well as the walls of the enclosing capsule, and (b) the gravity-gradient noise, namely the fluctuating curvature change in a finite sized capsule arising from any untracked motion of external masses. We show that the former can be reduced below desired values by appropriate pressures and temperatures, while the latter can be fully mitigated in a controlled environment. We finally apply the analysis to a recent proposal for testing the quantum nature of gravity [S. Bose et. al. Phys. Rev. Lett 119, 240401 (2017)] through the entanglement of two masses undergoing interferometry. We show that the relevant entanglement witnessing is feasible in a freely falling capsule with achievable levels of relative acceleration noise.

•Jul 29, 2020•2 citations
In this white paper, we highlight the importance of the (1−10 Hz1-10~{\rm Hz}1−10 Hz) frequency range for laboratory tests of the quantum nature of gravity using the quantum gravity-induced entanglement of masses (QGEM) protocol. QGEM requires matter-wave interferometers with masses (m∼10−15−10−14 kgm\sim10^{-15}-10^{-14}~{\rm kg}m∼10−15−10−14 kg), brought within separations (d∼30−50 μmd\sim30-50~μ{\rm m}d∼30−50 μm), while maintaining spatial superpositions of (1−20 μm1-20~μ{\rm m}1−20 μm) and coherence for (τ∼0.1−1 sτ\sim 0.1 - 1~{\rm s}τ∼0.1−1 s). These requirements make low-frequency environmental noise a central experimental challenge and place QGEM in a regime closely related to the low-frequency goals of the Einstein Telescope (ET) and the Cosmic Explorer (CE). In particular, QGEM is sensitive to relative acceleration noise (RAN) and to gravity-gradient noise (GGN) generated by seismic and other environmental mass-density fluctuations. For representative parameters m=10−14 kgm=10^{-14}~{\rm kg}m=10−14 kg, Δx=10 μmΔx=10~μ{\rm m}Δx=10 μm, and τ=1 sτ=1~{\rm s}τ=1 s, the differential acceleration-noise amplitude spectral density must be suppressed well below the 10−15 m s−2/Hz10^{-15}~{\rm m\,s^{-2}/\sqrt{Hz}}10−15 ms−2/Hz​ level to keep acceleration-induced dephasing below the relevant experimental scale. Achieving this level of low-frequency noise suppression is therefore a key requirement for QGEM and closely parallels the seismic and gravity-gradient noise challenges that ET and CE address.
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.
Matter-wave interferometry is a striking quantum phenomenon that differs fundamentally from classical mechanics. In the quantum regime, matter behaves like a wave and can exist in spatial superpositions, allowing a single quantum object to move along multiple trajectories simultaneously. Similar to optical interferometers, such quantum matter systems act as interferometers themselves, with the differential phase that encodes information about external forces experienced during their evolution. This makes matter-wave interferometry a powerful platform for quantum sensing across various applications: (i) One of the most direct applications is precision measurement. Atomic interferometers can measure local acceleration and have already been implemented in devices such as accelerometers, seismometers, gravimeters, and gradiometers. (ii) Atomic interferometers are proposed as complementary tools for future gravitational-wave observatories, including ongoing projects MIGA, MAGIS-100, AION and ZAIGA. (iii) Matter-wave interferometry also offers a promising platform for probing quantum aspects of gravity. Numerous tabletop proposals aim to test quantum gravity models, investigate collapse mechanisms, study gravity-induced decoherence, and search for gravity-mediated quantum entanglement. The Stern-Gerlach interferometer (SGI) is a type of matter-wave interferometer that manipulates spatial superpositions using magnetic-field gradients. The witness of an SGI can be designed via its spin, enabling more precise measurements of the differential phase. Recent developments in atomic chip technology have enabled the generation of highly controlled magnetic fields on compact platforms, allowing for precise manipulation of spin states and making SGIs experimentally realizable. Robustness is a critical challenge for matter-wave interferometers. In real experiments, various sources of classical noises arise from mechanical vibrations, seismic motions, inertial forces, tidal forces, magnetic field fluctuations and so on. These noises can disturb the spin and spatial degrees of freedom of the test mass, resulting in witness loss of the interferometer. While spin decoherence is relatively well understood and can be formulated by the Bloch-Redfield master equation, the impact on spatial degrees of freedom still requires systematic investigation. This thesis therefore aims to explore witness loss in an SGI induced by stochastic noises acting on spatial degrees of freedom. As investigated by this thesis, the witness gets lost via several mechanisms: (i) Dephasing. The spatial phase is fluctuated by stochastic noise, resulting in a random phase factor eiδϕ, whose ensemble average contributes a decay factor e−Γ to the spin density matrix and leads to a loss of witness. As is demonstrated by the thesis, this decay factor is a linear response to the external noise, with a transfer function as the Fourier transform of the unperturbed classical trajectories. (ii) Humpty-Dumpty problem. The classical trajectories are also disturbed by stochastic noise, resulting in a non-closure problem of the interferometer, known as the Humpty-Dumpty problem. The resulting witness loss is usually characterized by the contrast of the final states ⟨ψ1|ψ2⟩, which equals the phase-space distance |α1 − α2|2 when the test mass is in coherent states. (iii) Position localization decoherence. Due to the randomness of the noise, the spatial wavefunction of the test mass is thus also stochastic, of which the ensemble average experiences decoherence characterized by the power spectrum density of external noise. However, as illustrated by this thesis, this type of decoherence does not affect spin-based witnesses in most practical scenarios. The general theoretical framework is mainly constructed in chapter 3 of this thesis. The subsequent chapters analyze several representative noise sources: (i) Gravitational and electrostatic noise. Molecules in the surrounding gas move randomly due to thermal motion, generating stochastic gravitational accelerations and electrostatic forces that can be expanded in multipole series. Since the random motion follows Maxwell’s distribution and approximately has a cylindrical symmetry, the resulting noise power spectrum density takes the form of Bessel functions. (ii) Inertial acceleration noise. The mechanical support of the experimental apparatus is always fluctuated by vibrational noise, resulting in random inertial force on the test mass. In practice, dephasing can be mitigated through destructive interference by introducing appropriate coupling between different directional components. (iii) Inertial torsion noise. In suspended experiments, the experimental apparatus is fluctuated by torsional noise, leading to another inertial noise on the test mass. The power spectrum density of the inertial torsion noise is formulated by the selfconvolution of the original noise, resulting in the peak frequencies that are doubled. Taken together, these analyses build a comprehensive picture of how stochastic noise affects the spatial dynamics of an SGI and leads to the loss of spin-based witnesses. Future work may include more realistic noise sources such as magnetic noise and trap-potential noise. These insights will be valuable for future experimental implementations, particularly in precision sensing for quantum gravity, where preserving coherence and maintaining reliable witness signals are essential.
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.
Relative accelerations between a mass undergoing matter-wave interference and the associated apparatus, when not tracked, can appear as dephasing. It can be an important limiting factor in interferometry with large masses. Here we advocate taking conceptually the simplest solution: putting both the interfering mass and its associated apparatus in a freely falling capsule, so that the strongest inertial noise components vanish due to the equivalence principle. In this setting, we investigate two of the most important remaining noise sources: (a) the non-inertial jitter of the experimental setup which arises through gas collisions and photon scattering on the experimental apparatus as well as the walls of the enclosing capsule, and (b) the gravity-gradient noise, namely the fluctuating curvature change in a finite sized capsule arising from any untracked motion of external masses. We show that the former can be reduced below desired values by appropriate pressures and temperatures, while the latter can be fully mitigated in a controlled environment. We finally apply the analysis to a recent proposal for testing the quantum nature of gravity [S. Bose et. al. Phys. Rev. Lett 119, 240401 (2017)] through the entanglement of two masses undergoing interferometry. We show that the relevant entanglement witnessing is feasible in a freely falling capsule with achievable levels of relative acceleration noise.