Bosonic Pfaffian in the Hofstadter-Hubbard model

Applied to bosons at unit magnetic filling, the composite Fermion theory predicts a Fermi sea. However, if the microscopic repulsion between the bosons is over-screened by flux attachment, an effective attractive interaction between the spinless composite fermions can give rise to a superconducting instability: in this case a topological p-wave superconductor of composite fermions may form. This is the celebrated bosonic Moore-Read Pfaffian state.

In a recent LMU / Harvard collaboration we have demonstrated direct signatures for the Moore-Read Pfaffian in the bosonic Hofstadter-Hubbard model. This opens the door for realizing this exotic state with a few ultracold bosons in a quantum gas microscope in the near future.