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arXiv:2603.16487

Achieving Sub-Zeptonewton Force Sensitivity and Spin-Motion Entanglement in Levitated Diamond via Pulsed Backaction Evasion

Gayathrini Premawardhana, Jonathan Beaumariage, M. V. Gurudev Dutt, David Pekker, Thomas Purdy, Jacob M. Taylor

quant-phSubmitted Mar 17, 2026• Announced Mar 18, 2026• 0 citations
v1 · Mar 17, 2026v2 · Aug 26, 2026v3 · Sep 30, 2026
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Abstract

We propose a system to achieve sub-zeptonewton force sensing and robust spin-mechanical entanglement in a levitated diamond system. By coupling a Nitrogen-Vacancy (NV) center spin to the motion of its host diamond within a magnetic trap, we develop a platform designed to surpass the standard quantum limit. We develop and compare three distinct pulse sequences--Ramsey, Hahn echo, and Carr-Purcell-Meiboom-Gill (CPMG)--to create increasing amounts of backaction evasion while mitigating the effects of shot noise and thermal decoherence. Our results show that the CPMG sequences yield the most significant performance gains, reaching a force sensitivity of better than $10^{-23} \text{ N}/\sqrt{\text{Hz}}$ for broadband sensing around $10^4 \text{ Hz}$. Furthermore, we derive an entanglement witness protocol that accounts for pulsed dynamical decoupling, proving that spin-motion entanglement remains detectable even when occurring much faster than the mechanical period. These findings provide a more practical path for using levitated nanodiamonds both as high-precision sensors and as non-classical mechanical systems for fundamental tests of quantum mechanics.

Comments
15 pages. 7 figures

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We propose a system to achieve sub-zeptonewton force sensing and robust spin-mechanical entanglement in a levitated diamond system. By coupling a Nitrogen-Vacancy (NV) center spin to the motion of its host diamond within a magnetic trap, we develop a platform designed to surpass the standard quantum limit. We develop and compare three distinct pulse sequences--Ramsey, Hahn echo, and Carr-Purcell-Meiboom-Gill (CPMG)--to create increasing amounts of backaction evasion while mitigating the effects of shot noise and thermal decoherence. Our results show that the CPMG sequences yield the most significant performance gains, reaching a force sensitivity of better than 10−23 N/Hz10^{-23} \text{ N}/\sqrt{\text{Hz}}10−23 N/Hz​ for broadband sensing around 104 Hz10^4 \text{ Hz}104 Hz. Furthermore, we derive an entanglement witness protocol that accounts for pulsed dynamical decoupling, proving that spin-motion entanglement remains detectable even when occurring much faster than the mechanical period. These findings provide a more practical path for using levitated nanodiamonds both as high-precision sensors and as non-classical mechanical systems for fundamental tests of quantum mechanics.
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We perform a detailed theoretical-experimental study of the dynamical decoupling (DD) of the nitrogen-vacancy (NV) center in diamond. We investigate the DD sequences applied to suppress the dephasing of the electron spin of the NV center induced by the coupling to a spin bath composed of the substitutional nitrogen atoms. The decoupling efficiency of various DD schemes is studied, including both periodic and aperiodic pulse sequences. For ideal control pulses, we find that the DD protocols with the Carr-Purcell-Meiboom-Gill (CPMG) timing of the pulses provides best performance. We show that, as the number of control pulses increases, the decoupling fidelity scaling differs qualitatively from the predictions of the Magnus expansion, and explain the origin of this difference. In particular, more advanced symmetrized or concatenated protocols do not improve the DD performance. Next, we investigate the impact of the systematic instrumental pulse errors in different periodic and aperiodic pulse sequences. The DD protocols with the single-axis control do not preserve all spin components in the presence of the pulse errors, and the two-axis control is needed. We demonstrate that the two-axis control sequence with the CPMG timing is very robust with respect to the pulse errors. The impact of the pulse errors can be diminished further by symmetrizing this protocol. For all protocols studied here, we present a detailed account of the pulse error parameters which make the strongest impact on the DD performance. In conclusion, we give specific recommendations about choosing the decoupling protocol for the system under investigation.
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Nitrogen-vacancy (NV) centers in nanodiamond offer a promising platform for quantum information processing due to their room-temperature spin coherence and optical addressability. However, scalable quantum processors remain limited by the challenge of achieving strong, controllable interactions between distant NV spins. Here, we propose a scalable architecture utilizing optically levitated nanodiamond arrays, where torsional vibrations mediate the coherent coupling between the embedded NV centers. By optimizing the shape of ellipsoidal nanoparticles, we achieve a light-induced coupling strength exceeding 119 kHz between torsional modes of the distant levitated nanodiamonds, which are two orders of magnitude larger than the typical decoherence rates in this system. This strong interaction, combined with magnetic-field-enabled spin-torsion coupling, establishes an effective interaction between the spatially separated NV centers in the distant nanodiamonds. Numerical simulations confirm that dynamic decoupling can suppress both thermal noise and spin dephasing, enabling two-qubit gates with fidelity exceeding 99%. This work provides a foundation for reconfigurable quantum hybrid systems, with potential applications in rotational sensing and programmable quantum processing.
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.
Ultimate sensitivity for quantum magnetometry using nitrogen-vacancy (NV) centers in a diamond is limited by a number of NV centers and coherence time. Microwave irradiation with a high and homogeneous power density for a large detection volume is necessary to achieve a highly sensitive magnetometer. Here, we demonstrate a microwave resonator to enhance the power density of the microwave field and an optical system with a detection volume of 1.4 × 10−3 mm3. The strong microwave field enables us to achieve 48 ns Rabi oscillation which is sufficiently faster than the phase relaxation time of NV centers. This system combined with a decoupling pulse sequence, XY16, extends the spin coherence time (T2) up to 27 times longer than that with a spin echo method. Consequently, we obtained an AC magnetic field sensitivity of 10.8 pt/Hz using the dynamical decoupling pulse sequence.