  We experimentally and theoretically investigate collective radiative effects
in an ensemble of cold atoms coupled to a single-mode optical nanofiber. Our
analysis unveils the microscopic dynamics of the system, showing that
collective interactions between the atoms and a single guided photon gradually
build-up along the atomic array in the direction of propagation of light. These
results are supported by time-resolved measurements of the light transmitted
and reflected by the ensemble after excitation via nanofiber-guided laser
pulses, whose rise and fall times are shorter than the atomic lifetime.
Superradiant decays more than one order of magnitude faster than the
single-atom free-space decay rate are observed for emission in the
forward-propagating guided mode, while at the same time no speed-up of the
decay rate are measured in the backward direction. In addition,
position-resolved measurements of the light that is transmitted past the atoms
are performed by inserting the nanofiber-coupled atomic array in a 45-m long
fiber ring-resonator, which allow us to experimentally reveal the progressive
growth of the collective response of the atomic ensemble. Our results highlight
the unique opportunities offered by nanophotonic cold atom systems for the
experimental investigation of collective light-matter interaction.
