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 N/sqrt{Hz} for broadband sensing around 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.