  The ability to create, manipulate and detect non-classical states of light
has been key for many recent achievements in quantum physics and for developing
quantum technologies. Achieving the same level of control over phonons, the
quanta of vibrations, could have a similar impact, in particular on the fields
of quantum sensing and quantum information processing. Here we present a
crucial step towards this level of control and realize a single-mode waveguide
for individual phonons in a suspended silicon micro-structure. We use a
cavity-waveguide architecture, where the cavity is used as a source and
detector for the mechanical excitations, while the waveguide has a free
standing end in order to reflect the phonons. This enables us to observe
multiple round-trips of the phonons between the source and the reflector. The
long mechanical lifetime of almost 100 $\mu s$ demonstrates the possibility of
nearly lossless transmission of single phonons over, in principle, tens of
centimeters. Our experiment demonstrates full on-chip control over traveling
single phonons strongly confined in the directions transverse to the
propagation axis, potentially enabling a time-encoded multimode quantum memory
at telecom wavelength and advanced quantum acoustics experiments.
