  Understanding the dynamics of a quantum bit's environment is essential for
the realization of practical systems for quantum information processing and
metrology. We use single nitrogen-vacancy (NV) centers in diamond to study the
dynamics of a disordered spin ensemble at the diamond surface. Specifically, we
tune the density of "dark" surface spins to interrogate their contribution to
the decoherence of shallow NV center spin qubits. When the average surface spin
spacing exceeds the NV center depth, we find that the surface spin contribution
to the NV center free induction decay can be described by a stretched
exponential with variable power n. We show that these observations are
consistent with a model in which the spatial positions of the surface spins are
fixed for each measurement, but some of them reconfigure between measurements.
In particular, we observe a depth-dependent critical time associated with a
dynamical transition from Gaussian (n=2) decay to n=2/3, and show that this
transition arises from the competition between the small decay contributions of
many distant spins and strong coupling to a few proximal spins at the surface.
These observations demonstrate the potential of a local sensor for
understanding complex systems and elucidate pathways for improving and
controlling spin qubits at the surface.
