Experimental exploration of the 1D anyon-Hubbard model in an optical lattice

Using ultracold rubidium-87 atoms in an optical lattice, we use Floquet techniques to engineer one-dimensional (1D) abelian anyons with arbitrary exchange statistics. By modulating a tilted lattice, we engineer a density dependent Peierls phase, effectively realizing the anyon-Hubbard model (AHM). This technique is analogous to flux attachment in 2D systems, where the density dependent phase plays the role of the Aharonov-Bohm phase. In our previous work, we used Hanburry Brown-Twiss interference of two particles to probe the effect of exchange phase on the system dynamics. Now, we make use of the independent control over Hamiltonian parameters our technique offers to engineer the AHM ground state and explore equilibrium physics.

By tuning AHM parameters in a finite 1D chain, we adiabatically ramp into the AHM ground state with a given statistical phase. We then use two probes to explore the ground state behavior. The first is the in situ density profile, where the fermionization of the particles manifests via the buildup of Friedel oscillations as the statistical phase increases from 0 to 𝜋. The second is the asymmetric expansion of particles in the lattice after quenching the confining potential, which occurs at anyonic phases due to the presence of chiral bound states. We further probe this chirality by colliding the expanding ground state with a potential barrier, showing that these bound states are only able to propagate in one direction and will disperse after a collision.

These probes demonstrate that the AHM ground state can be used as a platform to realize continuous fermionization and chiral bounds states. In larger systems, these simple properties likely underlie the development of additional many-body phases, and so our ability to realize and control these small systems opens new opportunities for exploring more complex phenomena.