  Rydberg atoms, with their giant electronic orbitals, exhibit dipole-dipole
interaction reaching the GHz range at a distance of a micron, making them a
prominent contender for realizing quantum operations well within their
coherence time. However, such strong interactions have never been harnessed so
far, mainly because of the stringent requirements on the fluctuation of the
atom positions and the necessary excitation strength. Here, using atoms trapped
in the motional ground-state of optical tweezers and excited to a Rydberg state
with picosecond pulsed lasers, we observe an interaction-driven energy
exchange, i.e., a F\"orster oscilation, occuring in a timescale of nanoseconds,
two orders of magnitude faster than in any previous work with Rydberg atoms.
This ultrafast coherent dynamics gives rise to a conditional phase which is the
key resource for an ultrafast controlled-$Z$ gate. This opens the path for
quantum simulation and computation operating at the speed-limit set by
dipole-dipole interactions with this ultrafast Rydberg platform.

Atomic Physics;Quantum Physics