  Atoms interact with each other through the electromagnetic field, creating
collective states that can radiate faster or slower than a single atom, i.e.
super- and sub-radiance. The generation and control of such states by
engineering the dipolar interactions between atoms can enable new tools for
atomic-based technologies. Atom-atom interactions in free space are limited in
range, since the amplitude of the radiated field decreases inversely with
distance. When the field is confined to one dimension it enables infinite-range
interactions. This has been observed for atoms in an optical cavity, but
remains to be proven in one-dimensional waveguides, where the extent of the
interactions is not limited by the cavity size. Here we present the first
report of infinite-range interactions between macroscopically separated atomic
dipoles mediated by an optical waveguide. This is evidenced by the collective
radiative decay of a single photon distributed between distant atoms. We use
cold $^{87}$Rb atoms in the vicinity of a single-mode optical nanofiber (ONF)
that coherently exchange evanescently coupled photons through the ONF mode. In
particular, we observe super-radiance of a few atoms separated by hundreds of
resonant wavelengths. This effect is not possible for atoms separated by more
than a wavelength interacting through free space. The same platform allows us
to measure sub-radiance, a rarely observed effect, presenting a novel tool for
quantum optics. This result constitutes a proof-of-principle for collective
behavior of macroscopically delocalized atomic states, a crucial element for
new proposals in quantum information and many-body physics. Given the
application of one-dimensional waveguides in photonic-based quantum
technologies, we envision infinite-range interactions as the natural next step
towards interconnecting quantum systems on scales suitable for practical
applications.
