  The motion of atoms is at the heart of any chemical or structural
transformation in molecules and materials. Upon activation of this motion by an
external source, several (usually many) vibrational modes can be coherently
coupled, thus facilitating the chemical or structural phase transformation.
These coherent dynamics occur on the ultrafast time scale, as revealed, e.g.,
by nonlocal ultrafast vibrational spectroscopic measurements in bulk molecular
ensembles and solids. Tracking and controlling vibrational coherences locally
at the atomic and molecular scales is, however, much more challenging and in
fact has remained elusive so far. Here, we demonstrate that the vibrational
coherences induced by broadband laser pulses on a single graphene nanoribbon
(GNR) can be probed by femtosecond coherent anti-Stokes Raman spectroscopy
(CARS) when performed in a scanning tunnelling microscope (STM). In addition to
determining dephasing (~ 440 fs) and population decay times (~1.8 ps) of the
generated phonon wave packets, we are able to track and control the
corresponding quantum coherences, which we show to evolve on time scales as
short as ~ 70 fs. We demonstrate that a two-dimensional frequency correlation
spectrum unequivocally reveals the quantum couplings between different phonon
modes in the GNR.
