The manipulation of quantum information in large systems requires precise
control of quantum systems that are out-of-equilibrium. As the size of the
system increases, its fragility in response to external perturbations and
intrinsic decoherence processes also increases. The degradation of the system
response makes accurate measurements a challenging and time-consuming task.
Jedoch, quantum information lifetime enhancement can be achieved by dynamical
decoupling techniques (DD), where an external drive with a frequency much
higher than the system’s internal evolution renders signal acquisition with
decay times greater than 1000-fold. In this study, we demonstrate that the
system response during a prethermal period, subject to Floquet control, can be
utilized to probe the multiple quantum evolution of dense and highly connected
spin systems. This approach exhibits an enhanced sensitivity at a reduced
experimental time. The enhanced signal-to-noise ratio achieved enabled the use
of numerical inversion strategies to model the evolution of the excited
multiple quantum coherences, which describe the number of correlated spins
within a cluster. We observed for the first time, to the best of our knowledge,
that the increase in the number of correlated spins with multiple quantum
evolution is accompanied by an increase in the distribution of spin cluster
sizes, which follows a quadratic law.

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