  The most direct approach for characterizing the quantum dynamics of a
strongly-interacting system is to measure the time-evolution of its full
many-body state. Despite the conceptual simplicity of this approach, it quickly
becomes intractable as the system size grows. An alternate framework is to
think of the many-body dynamics as generating noise, which can be measured by
the decoherence of a probe qubit. Our work centers on the following question:
What can the decoherence dynamics of such a probe tell us about the many-body
system? In particular, we utilize optically addressable probe spins to
experimentally characterize both static and dynamical properties of
strongly-interacting magnetic dipoles. Our experimental platform consists of
two types of spin defects in diamond: nitrogen-vacancy (NV) color centers
(probe spins) and substitutional nitrogen impurities (many-body system). We
demonstrate that signatures of the many-body system's dimensionality, dynamics,
and disorder are naturally encoded in the functional form of the NV's
decoherence profile. Leveraging these insights, we directly characterize the
two-dimensional nature of a nitrogen delta-doped diamond sample. In addition,
we explore two distinct facets of the many-body dynamics: First, we address a
persistent debate about the microscopic nature of spin dynamics in
strongly-interacting dipolar systems. Second, we demonstrate direct control
over the spectral properties of the many-body system, including its correlation
time. Our work opens the door to new directions in both quantum sensing and
simulation.
