Here, we propose to couple the and states of Rb and Cs using single photon transitions to the mJ=−1/2 magnetic sublevels of Rydberg P states16173031323334, with laser light that is linearly polarized along the z axis and thus retains the symmetry of the lattice geometry. Figure 3 shows the Rydberg pair energies in the presence of multipole interactions, in the vicinity of (a) the and (b) the Rydberg states of 87Rb and (c) the mixed Rydberg states. The pair potentials are obtained from an exact diagonalization calculation (Supplementary Note 2), including interactions up to quadrupole–quadrupole and dipole–octupole couplings. In the regime of strong interactions, the Rydberg states are mixed by the multipole couplings, and each energy level corresponds to a superposition of Rydberg states with a variety of quantum numbers. The blue colouring in Fig. 3 represents the overlap with the laser targeted mJ=−1/2 states, and is therefore indicative of the effective coupling strength to the pair ground states. Although there are many energy levels in the regime of interest, we see that at distances >0.5 μm only a handful of potential curves is significantly coupled by the dressing laser, while the vast majority of states (grey curves) is only coupled with negligible strengths.