  A vertically shaken granular medium hosts a blade rotating around a fixed
vertical axis, which acts as a mesorheological probe. At high densities,
independently from the shaking intensity, the blade's dynamics show strong
caging effects, marked by transient sub-diffusion and a maximum in the velocity
power density spectrum (vpds), at a resonant frequency $\sim 10$ Hz.
Interpreting the data through a diffusing harmonic cage model allows us to
retrieve the elastic constant of the granular medium and its collective
diffusion coefficient. For high frequencies $f$, a tail $\sim 1/f$ in the vpds
reveals non-trivial correlations in the intra-cage micro-dynamics. At very long
times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in
the most extreme cases. Consistently, the distribution of slow velocity
inversion times $\tau$ displays a power-law decay, likely due to persistent
collective fluctuations of the host medium.
