  Dynamical decoupling techniques constitute an integral part of many quantum
sensing platforms, often leading to orders-of-magnitude improvements in
coherence time and sensitivity. Most AC sensing sequences involve a periodic
echo-like structure, in which the target signal is synchronized with the echo
period. We show that for strongly interacting systems, this construction leads
to a fundamental sensitivity limit associated with imperfect interaction
decoupling. We present a simple physical picture demonstrating the origin of
this limitation, and further formalize these considerations in terms of concise
higher-order decoupling rules. We then show how these limitations can be
surpassed by identifying a novel sequence building block, in which the signal
period matches twice the echo period. Using these decoupling rules and the
resulting sequence building block, we experimentally demonstrate significant
improvements in dynamical decoupling timescales and magnetic field sensitivity,
opening the door for new applications in quantum sensing and quantum many-body
physics.

Quantum Physics;Disordered Systems and Neural Networks