Realization of One-dimensional Anyons with Arbitrary Statistical Phases

Anyons are indistinguishable particles whose many-body wavefunction acquires a phase between 0 and π when exchanging their positions. We realize a one-dimensional Anyon-Hubbard model (AHM) with ultracold Rubidium 87 atoms in a tilted optical lattice.To engineer the desired Hamiltonian, we use a novel three-tone lattice amplitude modulation technique that allows us to continuously tune the exchange statistical phase of two particles. This Floquet driving technique effectively realizes a Bose-Hubbard model with an occupation-dependent hopping phase that maps onto the AHM. As a benchmark, signatures of anyonic statistics are observed in interferometric two-particle quantum walks. We prepare two particles sitting on adjacent sites and allow them to expand in a chain under the Floquet Hamiltonian. From density correlation functions, we observe slower density expansion and manifestation of pairing for non-zero statistical phases, even in the absence of on-site interactions. We also demonstrate the ability to vary the on-site interaction strength by detuning the modulation frequencies. For non-zero interaction energy, we observe asymmetric density transport which suggests broken inversion symmetry in the AHM. Our technique paves a way to study fractional statistics and explore statistically induced phase transitions.