Engineering a Fractional Quantum Hall State of Bosons in an Optical Lattice

Realization of strongly interacting particles under the presence of a magnetic field can lead to novel phases of matter with topological order. Here, we demonstrate adiabatic preparation of the ground state of a two-particle Harper-Hofstadter system under different fluxes with ultracold bosonic ⁸⁷Rb atoms in an optical lattice. A superimposed running lattice of two Raman beams and a magnetic field gradient are utilized to apply a tunable synthetic gauge field on the atoms. With the single-site resolution provided by our quantum gas microscope, we explore the ground-state fidelity of our protocol over the space of multiple parameters. There are more observables being studied to exhibit phase transition into the fractional quantum Hall state. Our study presents characterization of passage towards topological states in optical-lattice experiments.