  Matter-wave interferometry provides a remarkably sensitive tool for probing
minute forces and, potentially, the foundations of quantum physics by making
use of interference between spatially separated matter waves. Furthering this
development requires ever-increasing stability of the interferometer, typically
achieved by improving its physical isolation from the environment. Here we
introduce as an alternative strategy the concept of dynamical decoupling
applied to spatial degrees of freedom of massive objects. We show that the
superposed matter waves can be driven along paths in space that render their
superposition resilient to many important sources of noise. As a concrete
implementation, we present the case of matter-wave interferometers in a
magnetic field gradient based on either levitated or free-falling nanodiamonds
hosting a color center. We present an in-depth analysis of potential sources of
decoherence in such a setup and of the ability of our protocol to suppress
them. These effects include gravitational forces, interactions of the net
magnetic and dipole moments of the diamond with magnetic and electric fields,
surface dangling bonds, rotational degrees of freedom, Casimir-Polder forces,
and diamagnetic forces. Contrary to previous analyses, diamagnetic forces are
not negligible in this type of interferometers and, if not acted upon lead to
small separation distances that scale with the inverse of the magnetic field
gradient. We show that our motional dynamical decoupling strategy renders the
system immune to such limitations while continuing to protect its coherence
from environmental influences, achieving a linear-in-time growth of the
separation distance independent of the magnetic field gradient. Hence, motional
dynamical decoupling may become an essential tool in driving the sensitivity of
matter-wave interferometry to the next level.
