Spin dynamical decoupling for generating macroscopic superpositions of a free-falling nanodiamond

Levitated nanodiamonds containing negatively charged nitrogen-vacancy centers (NV-) have been proposed as a platform to generate macroscopic spatial superpositions. Requirements for this include having a long NV- 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-nm-diameter diamond in a superposition with spatial separation of over 250 nm, while incorporating dynamical decoupling. We achieve this by letting a diamond fall for 2.4 m through a magnetic structure, including 1.13 m in an inhomogeneous region generated by magnetic teeth.