Towards the ν = 1 Pfaffian Fractional Quantum Hall State with Ultracold Bosons in an Optical Lattice

Interesting topological states of matter, such as fractional quantum Hall states, arise from the interplay of charged particles and magnetic fields. We can study these states using ultracold ⁸⁷Rb atoms in an optical lattice by engineering artificial gauge fields to realize the Harper-Hofstadter model. In our previous work [Léonard et al. Nature 619, 495 (2023)], we used this platform to adiabatically prepare the ν = 1/2 fractional quantum Hall state for two particles in a 4x4 lattice. We extend these efforts to study the larger system of three particles in a 5x5 lattice for the ν = 1 bosonic Pfaffian state. We expect to observe pairing of particles by investigating the two- and three-body correlations. Leveraging the approach in the previous work, we perform adiabatic passage to connect a topologically trivial initial state to the target fractional quantum Hall state. We report progress in improving state preparation with adiabatic ramps and identifying Floquet regimes for a fractional quantum Hall state.