Experimental exploration of the 1D anyon-Hubbard model via adiabatic state preparation

Anyons are indistinguishable particles whose exchange statistics are neither bosonic nor fermionic. While anyons are known to exist in two dimensions, a one-dimensional (1D) system can also host fractional statistics. In this work, we focus on the 1D anyon-Hubbard model (AHM) which describes anyons on a 1D lattice and has been theorized to host many phenomena. We experimentally realize the AHM with ultracold rubidium-87 atoms in an optical lattice via periodic driving [1]. Leveraging the ability to independently tune Hubbard parameters, we engineer the two-particle ground states of the AHM via adiabatic state preparation, by connecting a Fock state to the ground state of the AHM with arbitrary statistical phase. As the statistical phase increases from 0 to 𝜋, we observe smooth change from bosonic, through anyonic, to pseudo-fermionic density profiles, which manifests a continuous build up of Friedel oscillations. Moreover, we probe the properties of the AHM via expansion dynamics, revealing the existence of chiral bound states induced by quantum statistics. Our work lays a foundation to study many-body phenomena of the AHM, such as a statistically-induced Mott insulator to superfluid phase transition and novel two-component superfluids.

[1] J Kwan, et al., Realization of 1D anyons with arbitrary statistical phase. Preprint on arxiv (2023).