  The dynamical properties of a dense horizontally vibrated bidisperse granular
monolayer are experimentally investigated. The quench protocol produces states
with a frozen structure of the assembly, but the remaining degrees of freedom
associated with contact dynamics control the appearance of macroscopic
rigidity. We provide decisive experimental evidence that this transition is a
critical phenomenon, with increasingly collective and heterogeneous
rearrangements occurring at length scales much smaller than the grains'
diameter, presumably reflecting the contact force network fluctuations.
Dynamical correlation time and length scales soar on both sides of the
transition, as the volume fraction varies over a remarkably tiny range ($\delta
\phi/\phi \sim 10^{-3}$). We characterize the motion of individual grains,
which becomes super-diffusive at the jamming transition $\phi_J$, signaling
long-ranged temporal correlations. Correspondingly, the system exhibits
long-ranged four-point dynamical correlations in space that obey critical
scaling at the transition density.
