Supersymmetry in Rydberg-dressed lattice fermions

Supersymmetry is a powerful tool that allows the characterization of strongly correlated many-body systems, in particular in the case of supersymmetric extensions of the fermionic Hubbard model. At the same time, these models can exhibit rich and exotic physics on their own, such as flat bands or exponentially large ground state degeneracy. We show that such lattice models can be realized with Rydberg-dressed fermions in optical lattices. Strong interactions within the ground state manifold of the atoms can be realized by admixing a weak contribution of a highly excited Rydberg state. By tuning the experimental parameters away from the supersymmetric point, it is possible to assess the validity of a supersymmetric approach to strongly correlated electrons in a systematic way.