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

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.

18 pages. 8 figures. Updates to v1: Added more explanations. Expanded entanglement witness sections. Corrected analysis for section which looks at combined entanglement witness + thermal force + pulse sequences

arXiv:2603.16487 [quant-ph]

(or arXiv:2603.16487v2 [quant-ph] for this version)