**
Tassilo Keilmann, Simon Lanzmich, Ian McCulloch, and Marco Roncaglia**

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 laser-assisted Raman tunneling. The statistical angle can thus be controlled in situ by modifying the relative phase of two Raman laser beams. 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.