  One-dimensional anyonic models of the Hubbard type show intriguing
ground-state properties, effectively transmuting between Bose-Einstein and
Fermi-Dirac statistics. The simplest model that one can investigate is an
anyonic version of the bosonic Josephson junction, the repulsive anyon-Hubbard
dimer. In the following we find an exact duality relation to the Bethe-solvable
Bose-Hubbard dimer, which is well known from quantum optics and information
theory and has interesting connections to spin squeezing and entangled coherent
states. Conversely, we show that the anyonic Hubbard dimer has nontrivial
coherence properties that emerge from the anyonic statistics. In particular, we
find that coherences can be suppressed and amplified and show that these
features are remarkably robust against additional repulsive on-site
interactions highlighting the distinct nature of anyons.
