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

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 ${10}^{-23}\text{ N}\mathrm{/}\sqrt{\text{Hz}}$ 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.