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 $\ddot{I}„$, the magnetization revives at time $2\ddot{I}„$ following a single $(\hat{I}\pm {)}_y$ pulse, with maximum amplitude near $\hat{I}\pm \simeq \ddot{I}€/2$. The echo envelope decays as a stretched exponential with characteristic time $T_2^{\prime }\approx 13$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.

6 pages, 6 figures