Quantum Simulation of Dynamics in the 1D Anyon Hubbard Model

We present an experimental realization of the 1D Anyon Hubbard Model (AHM), where we use two-particle quantum walks to explore dynamics with a tunable, arbitrary statistical phase. Through a generalized Jordan-Wigner transformation, the AHM can be represented as a bosonic Hubbard model with a density-dependent tunneling phase. Using Rubidium-87 atoms in an optical lattice, we engineer this dynamical gauge field via three-tone lattice amplitude modulation. This Floquet method provides independent control of the statistical phase, tunneling amplitude, and interaction energy.

Based on the expansion dynamics and two-body density correlations of two-particle quantum walks, we demonstrate continuous tuning of the particle statistics from bosonic (zero phase) to pseudo-fermionic (π phase) through the intermediate anyonic regime. Throughout this process, we track the formation of statistically induced bound pairs of non-interacting particles. In the presence of non-zero interaction energy, we also observe asymmetric transport, a consequence of the broken inversion symmetry in the AHM Hamiltonian. Together, these results confirm our realization of 1D anyons in a quantum simulator, laying the foundation for future explorations of the broader phase diagram.