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arXiv:2411.02325 · Physical Review A

Diamagnetic microchip traps for levitated nanoparticle entanglement experiments

Shafaq Gulzar Elahi, Martine Schut, Andrew Dana, Alexey Grinin, Sougato Bose, Anupam Mazumdar, Andrew A. Geraci

Published Oct 6, 2025• 9 citations
arXivHTMLPDF

Abstract

The quantum gravity mediated entanglement protocol offers a method to probe the quantumness of gravitational interactions at nonrelativistic scales. This protocol leverages the Stern-Gerlach effect to create $O(\textmu{}\mathrm{m})$ spatial superpositions of two nanodiamonds (mass $\ensuremath{\sim}{10}^{\ensuremath{-}15}$ kg) with nitrogen-vacancy spins, which are then allowed to interact and become entangled solely through the gravitational interaction. Since electromagnetic interactions such as Casimir-Polder and dipole-dipole interactions dominate at this scale, screening them to ensure the masses interact exclusively via gravity is crucial. In this paper, we propose using magnetic traps based on microfabricated wires, which provide strong gradients with relatively modest magnetic fields to trap nanoparticles for interferometric entanglement experiments. The design consists of a small trap to cool the center-of-mass motion of the nanodiamonds and a long trap with a weak direction suitable for creating macroscopic superpositions. In contrast to permanent-magnet-based long traps, the microfabricated wire-based approach allows fast switching of the magnetic trapping and state manipulation potentials and permits integrated superconducting shielding, which can screen both electrostatic and magnetic interactions between nanodiamonds in a gravitational entanglement experiment. The setup also provides a possible platform for other tests of quantum coherence in macroscopic systems and searches for novel short-range forces.

DOI
10.1103/qdyh-rbyq

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The quantum gravity mediated entanglement protocol offers a method to probe the quantumness of gravitational interactions at nonrelativistic scales. This protocol leverages the Stern-Gerlach effect to create O(\textmum)O(\textmu{}\mathrm{m})O(\textmum) spatial superpositions of two nanodiamonds (mass \ensuremath∼10\ensuremath−15\ensuremath{\sim}{10}^{\ensuremath{-}15}\ensuremath∼10\ensuremath−15 kg) with nitrogen-vacancy spins, which are then allowed to interact and become entangled solely through the gravitational interaction. Since electromagnetic interactions such as Casimir-Polder and dipole-dipole interactions dominate at this scale, screening them to ensure the masses interact exclusively via gravity is crucial. In this paper, we propose using magnetic traps based on microfabricated wires, which provide strong gradients with relatively modest magnetic fields to trap nanoparticles for interferometric entanglement experiments. The design consists of a small trap to cool the center-of-mass motion of the nanodiamonds and a long trap with a weak direction suitable for creating macroscopic superpositions. In contrast to permanent-magnet-based long traps, the microfabricated wire-based approach allows fast switching of the magnetic trapping and state manipulation potentials and permits integrated superconducting shielding, which can screen both electrostatic and magnetic interactions between nanodiamonds in a gravitational entanglement experiment. The setup also provides a possible platform for other tests of quantum coherence in macroscopic systems and searches for novel short-range forces.
We propose a current-carrying-chip scheme for generating spatial quantum superpositions using a levitating nanodiamond with a built-in nitrogen-vacancy (NV) centre defect. Our setup is quite versatile and we aim to create the superposition for a mass range of 10−19 kg<m<10−15 kg10^{-19}~{\rm kg}< m< 10^{-15}~{\rm kg}10−19 kg<m<10−15 kg and a superposition size O(10)μm<Δx<O(1)nm{\cal O}(10) {\rm μm} < Δx < {\cal O}(1){\rm nm}O(10)μm<Δx<O(1)nm, respectively, in t≤0.1t\leq 0.1t≤0.1s, depending on the position we launch from the center of the diamagnetic trap. We provide an in-depth analysis of two parallel chips that can create levitation and spatial superposition along the xxx-axis, while producing a very tight trap in the yyy direction, and the direction of gravity, i.e., the zzz direction. Numerical simulations demonstrate that our setup can create a one-dimensional spatial superposition state along the x-axis. Throughout this process, the particle is stably levitated in the z-direction, and its motion is effectively confined in the y-direction for a Gaussian initial condition. This setup presents a viable platform for a diamagnetically levitated nanoparticle for a table-top experiment exploring the possibility of creating a macroscopic Schrödinger Cat state to test the quantum gravity induced entanglement of masses (QGEM) protocol.
Quantum entanglement provides a novel way to test short-distance quantum physics in a non-relativistic regime. We provide entanglement-based protocols to potentially test the magnetically induced dipole-dipole interaction and the Casimir-Polder potential between the two nano-crystals kept in a Schrodinger Cat state. Our scheme is based on the Stern-Gerlach (SG) apparatus, where we can witness the entanglement mediated by these interactions for the nano-crystal mass m~10^-19 kg with a spatial superposition size of order 0.1 micron in a trap relying on diamagnetic levitation. We show that it is possible to close the SG interferometer in position and momentum with a modest gradient in the magnetic field.
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
Proposed experiments for gravitationally induced entanglement (GIE) typically suppress direct electromagnetic interactions between two massive particles by inserting a conducting Faraday shield. For superconducting particles, their large diamagnetism requires additional magnetic shielding to screen magnetic dipolar interactions. Here, we analyze the effect of residual particle-shield interactions and show that both Casimir and magnetic-dipole interactions can severely limit GIE tests by imprinting large phases. We quantify how run-to-run positional and orientational fluctuations of the setup elements, including the shield, trapping potentials, and detectors, convert these phases into effective decoherence, strongly reducing the detectable bipartite entanglement. In particular, we show that magnetic interactions between the particles and a superconducting shield constitute a major noise source, especially relevant for levitated superconducting particles. Treating the vibrational modes of the shield quantum mechanically, we further find that thermal vibrations generate persistent particle-shield correlations and can even mediate particle-particle entanglement that can mimic a gravitational signal. Finally, we derive quantitative thresholds on the maximum tolerable positional and orientational fluctuations of the setup elements required to observe entanglement, and propose mitigation strategies including geometry optimization and shield cooling to preserve a genuine GIE signature.
The ground-state cooling and quantum control of levitated nanoparticles have become attainable, which makes the enhanced quantum sensing based on the large mass advantage of mesoscopic quantum systems accessible. Here, we propose an enhanced gravity-sensing protocol for a nanodiamond levitated in a linear ion trap, which improves the sensing sensitivity and further reduces device size. By introducing gravitational acceleration into the vibrational state through transient free fall, we achieve a square-accelerated relative phase accumulation, yielding higher sensitivity than the linear accumulation process. The sensitivity reaches the standard quantum limit for a nanodiamond containing multiple nitrogen-vacancy (N-V) centers. Besides, by using phonon-mediated one-axis twisting dynamics induced by magnetic field gradient to squeeze the initial spin state, the sensitivity can further surpass the standard quantum limit as a scaling law of N^{-5/6}. To fully assess the protocol performance, we further analyze the effects of decoherence and control errors, which are negligible under experimentally achievable conditions. Specifically, the sensitivity reaches ∼18 μGal/sqrt[Hz] for the nanodiamond containing only one N-V center over a free-fall distance of ∼20 μm, while exceeds 0.4 μGal/sqrt[Hz] for 100 N-V centers. Our results will further facilitate research on compact and high-sensitivity gravimeters.
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.