Linear Anyon Model with Rydberg Atoms

Abstract

We propose a scheme for quantum-simulating the one-dimensional anyon-Hubbard model with Rydberg atoms. Starting from the generalized Jordan–Wigner transformation, which trades anyonic exchange statistics for a densitydependent Peierls phase, we encode the truncated local occupations {|0⟩ , |1⟩ , |2⟩} in the internal levels of Rydberg atoms driven by Raman lasers with sitedependent phases. Adiabatically eliminating the far-detuned intermediate states in the dispersive regime yields an effective bond Hamiltonian whose four tunnelling amplitudes we obtain in second-order perturbation theory. First, we show that the Raman scheme allows one to simulate pseudo-fermions with bosons, but not generic anyons: Floquet driving is necessary to engineer a generic statistical phase. In fact, we find that single-tone Floquet driving leads to density-dependent amplitudes, but it is not sufficient to achieve the desired density-dependent tunnelling. This calculation suggests that to achieve the phases one needs a drive with several tones, each resonant with one occupationresolved process and each carrying its own phase, a mechanism similar to the one employed in the recent few-particle realization of the anyon-Hubbard model with ultracold neutral atoms in optical lattices.