The particular Rydberg P pair states shown in Fig. 3(a–c) feature pronounced potential wells which enable an enhanced Rydberg dressing scheme19. For this purpose, we tune the (two-photon) detuning of the dressing laser such that, in the rotating frame, the energy of the ground pair states (green line in Fig. 3(a,b) for , and yellow line in panel (c)) is close to a potential minimum. This gives rise to pronounced light shifts of the pair ground states at the point of closest approach, as shown in Fig. 3(d), while at the same time producing negligible light shifts elsewhere. The particular Rydberg states in Fig. 3(a–c) are chosen such that the dressed ground state potentials and plotted in Fig. 3(d) show peaks at distances , aL and , commensurate with a square lattice geometry with aL=0.89 μm. Accidental crossings of the doubly excited Rydberg levels with the pair ground state energy give rise to resonances in the dressed state level shifts, but these either occur at distances which are not present in the lattice geometry, or they are of negligible width on behalf of a vanishing laser coupling strength to the crossing states.