  For decades, searches for exotic spin interactions have used
increasingly-precise laboratory measurements to test various theoretical models
of particle physics. However, most searches have focused on interaction length
scales greater than 1 mm, corresponding to hypothetical boson masses less than
0.2 meV. Recently, quantum sensors based on Nitrogen-Vacancy (NV) centers in
diamond have emerged as a promising platform to probe spin interactions at the
micrometer scale, opening the door to explore new physics at this length scale.
Here, we propose experiments to search for several hypothetical interactions
between NV electron spins and moving masses. We focus on potential interactions
involving the coupling of NV spin ensembles to both spin-polarized and
unpolarized masses attached to vibrating mechanical oscillators. For each
interaction, we estimate the sensitivity, identify optimal experimental
conditions, and analyze potential systematic errors. Using multi-pulse quantum
sensing protocols with NV spin ensembles to improve sensitivity, we project new
constraints that are ~5 orders-of-magnitude improvement over previous
constraints at the micrometer scale. We also identify a spin-polarized test
mass, based on hyperpolarized 13C nuclear spins in a thin diamond membrane,
which offers a favorable combination of high spin density and low stray
magnetic fields. Our analysis is timely in light of a recent preprint
(arXiv:2010.15667) reporting a surprising non-zero result of micrometer-scale
spin-velocity interactions.
