Probing the limits to refocusing in spin systems

Out-of-Time-Ordered Correlators (OTOCs) provide a measure of how a local perturbation propagates through an interacting quantum system. They can potentially be used to study many problems in physics such as characterizing phases of matter, the thermalization of quantum systems and determining molecular structure. Refocusing many-body dynamics of a system with high fidelity is key to OTOC measurements. In dipolar-coupled nuclear spin systems this refocusing is done via collective control of the spins. Here we characterize the fidelity of such refocusing as a function of system size and explore the sensitivity of OTOC dynamics to an applied perturbation. We employ a series of phosphine molecules in which the protons form the many-body system while the phosphorus is a local spin used to apply controlled perturbations. We contrast the growth of correlations with and without the perturbation in each case. We complement the experimental studies with numerical simulations and attempt to extract a general scaling behaviour. High sensitivity to small perturbations serves as a proof of failure of refocusing ability in the system and may establish bounds on the efficacy of OTOC-based studies in these systems.