  Anyons - particles carrying fractional statistics that interpolate between
bosons and fermions - have been conjectured to exist in low dimensional
systems. In the context of the fractional quantum Hall effect (FQHE),
quasi-particles made of electrons take the role of anyons whose statistical
exchange phase is fixed by the filling factor. Here we propose an experimental
setup to create anyons in one-dimensional lattices with fully tuneable exchange
statistics. In our setup, anyons are created by bosons with
occupation-dependent hopping amplitudes, which can be realized by assisted
Raman tunneling. The statistical angle can thus be controlled in situ by
modifying the relative phase of external driving fields. This opens the
fascinating possibility of smoothly transmuting bosons via anyons into fermions
and of inducing a phase transition by the mere control of the particle
statistics as a free parameter. In particular, we demonstrate how to induce a
quantum phase transition from a superfluid into an exotic Mott-like state where
the particle distribution exhibits plateaus at fractional densities.
