Statistically induced Phase Transitions and Anyons in 1D Optical Lattices

TL;DR

This paper proposes a tunable experimental setup in 1D optical lattices to create and control anyons with fractional statistics, enabling the study of phase transitions between superfluid and Mott-like states.

Contribution

It introduces a novel method to generate and manipulate anyons in 1D lattices using occupation-dependent hopping and external phase control.

Findings

Controlled creation of anyons with tunable statistical angle.

Demonstration of a quantum phase transition induced by particle statistics.

Observation of fractional density plateaus in the Mott-like state.

Abstract

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.