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arXiv:2601.06608 · Physical Review A

Magnetic levitation and spatial superposition of a nanodiamond with a current-carrying chip

Qian Xiang, Shafaq Gulzar Elahi, Andrew Geraci, Sougato Bose, Anupam Mazumdar

quant-phSubmitted Jan 10, 2026• Announced Jan 13, 2026• 0 citations
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Abstract

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 $10^{-19}~{\rm kg}< m< 10^{-15}~{\rm kg}$ and a superposition size ${\cal O}(10) {\rm μm} < Δx < {\cal O}(1){\rm nm}$, respectively, in $t\leq 0.1$s, 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 $x$-axis, while producing a very tight trap in the $y$ direction, and the direction of gravity, i.e., the $z$ 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.

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16 pages, 7 figures

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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.
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.
There is significant interest in potential experimental tests of macroscopic quantum effects, both to test potential modifications to quantum theory and to probe the quantum nature of gravity. A proposed platform with which to generate the required macroscopic quantum spatial superposition is a nanodiamond containing a negatively charged nitrogen vacancy (NV-) centre. In this review, methods to fabricate nanodiamonds containing NV­suitable for these quantum applications are discussed. The proposed probes of the macroscopic limits of quantum theory are presented along with the spin physics of the NV- centre relevant to those tests.
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.
Levitated nanodiamonds containing negatively charged nitrogen-vacancy centers $({\text{NV}}^{\ensuremath{-}})$ have been proposed as a platform to generate macroscopic spatial superpositions. Requirements for this include having a long ${\text{NV}}^{\ensuremath{-}}$ spin coherence time, which necessitates formulating a dynamical decoupling strategy in which the regular spin flips do not cancel the growth of the superposition through the Stern-Gerlach effect in an inhomogeneous magnetic field. Here, we propose a scheme to place a $250\text{\ensuremath{-}}\mathrm{n}\mathrm{m}$-diameter diamond in a superposition with spatial separation of over 250nm250\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}250nm, while incorporating dynamical decoupling. We achieve this by letting a diamond fall for 2.4m2.4\phantom{\rule{0.16em}{0ex}}\mathrm{m}2.4m through a magnetic structure, including 1.13m1.13\phantom{\rule{0.16em}{0ex}}\mathrm{m}1.13m in an inhomogeneous region generated by magnetic teeth.
Creating macroscopic spatial quantum superposition with a nanoparticle has a multitude of applications, ranging from testing the foundations of quantum mechanics, matter-wave interferometer for detecting gravitational waves and probing the electromagnetic vacuum, dark matter detection and quantum sensors to testing the quantum nature of gravity in a lab. In this paper, we investigate the role of rotation in a matter-wave interferometer, where we show that imparting angular momentum along the direction of a defect, such as one present in the nitrogen-vacancy centre of a nanodiamond can cause an enhancement in spin contrast for a wide-ranging value of the angular momentum, e.g. 103−10610^{3}-10^{6}103−106~Hz for a mass of order 10−14−10−1710^{-14}-10^{-17}10−14−10−17 Kg nanodiamond. Furthermore, the imparted angular momentum can enhance the spatial superposition by almost a factor of two and possibly average out any potential permanent dipoles in the nanodiamond.
In the scheme recently proposed by M. Scala et al. [Phys. Rev. Lett. 111, 180403 (2013)], a gravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trapped nanodiamond by the interaction between its magnetic moment and the quantized motion of the particle. This provides a way to detect spatial quantum superpositions by means of only spin measurements. Here, the effect of unwanted coupling with other motional degrees of freedom is considered, and we show that it does not affect the validity of the scheme. Both this coupling and the additional error source due to misalignment between the quantization axis of the NV center spin and the trapping axis are shown not to change the qualitative behavior of the system, so that a proof-of-principle experiment can be neatly performed. Our analysis, which shows that the scheme retains the important features of not requiring ground-state cooling and of being resistant to thermal fluctuations, can be useful for several schemes which have been proposed recently for testing macroscopic superpositions in trapped microsystems.