Prethermal rotating-frame solid echo in a dipolar nuclear-spin network

Abstract

Floquet prethermalization can endow interacting quantum solids with long-lived, approximately conserved quantities, enabling Hamiltonian engineering and new dynamical probes. Using a hyperpolarized network of dipolar-coupled $^{13}$C nuclear spins in diamond driven by pulsed spin-locking, we access a rotating-frame prethermal plateau with quasi-conserved transverse magnetization and cycle-resolved inductive readout. Within this prethermal manifold we observe a robust \emph{rotating-frame solid echo}: after an apparent decay of the rotating-frame free-induction signal over a delay $τ$, the magnetization revives at time $2τ$ following a single $(α)_y$ pulse, with maximum amplitude near $α\simeqπ/2$. The echo envelope decays as a stretched exponential with characteristic time $T_2'\approx 13\,$ms. Analytical arguments and toy-model simulations attribute the revival to Floquet micromotion that transfers coherences between operator subspaces, so that only a subset of the many-body dephasing dynamics is inverted by the $y$ pulse. These results translate classic echo physics into the prethermal rotating frame and point to continuously interrogated prethermal spin ensembles as a versatile platform for high-throughput spectroscopy, Hamiltonian engineering, and long-duration quantum sensing.