Probing many-body noise in a strongly interacting two-dimensional spin ensemble ---- Part II: Theory

Experimentally characterizing the full quantum dynamics of a many-body system requires performing state tomography, which becomes intractable as the system size increases. Nevertheless, studying the fluctuations of a small number of degrees of freedom may already provide important insights into the nature of the underlying dynamics; this notion is at the core of noise spectroscopy. In particular, measuring and controlling the quantum coherence of a probe spin coupled to the system provides a flexible framework for studying such fluctuations. In this talk, we present a framework whereby the decoherence dynamics of probe spins enables the direct extraction of important features of a many-body system. Motivated by recent experimental progress in disordered spin systems, we demonstrate how the details of the decoherence dynamics directly inform us of the system's dimensionality, spin density, and correlation time. Finally, we discuss the impact that the underlying microscopic dynamics --- and the resulting many-body noise --- have on the observed decoherence.