Fig. 2: Förster versus vdW Rydberg interactions.
a, Rb–Cs pairs excited to \({\left\vert 67{S}_{1/2}\right\rangle }_{{\rm{Rb}}}{\left\vert 67{S}_{1/2}\right\rangle }_{{\rm{Cs}}}\) interact through second-order vdW interactions (green). b, Rb–Cs pairs excited to \({\left\vert 68{S}_{1/2}\right\rangle }_{{\rm{Rb}}}{\left\vert 67{S}_{1/2}\right\rangle }_{{\rm{Cs}}}\) undergo resonantly enhanced Förster interactions (pink) due to near-degeneracy with the neighbouring pair state \({\left\vert 67{P}_{1/2}\right\rangle }_{{\rm{Rb}}}{\left\vert 67{P}_{3/2}\right\rangle }_{{\rm{Cs}}}\). c, The vdW interaction strength was extracted from the shift in the Rb Rydberg resonance after exciting the Cs atom to the Rydberg state. The strength increased with decreasing interatomic separation (see e for precise separation values). The vertical axis is offset for clarity, and the data were fitted to Gaussian profiles to extract the centres of the features. d, The Förster interaction strength was extracted similarly but reveals oher features. The two main peaks correspond to the eigenstates \({\left\vert \pm \right\rangle }_{{\rm{pair}}}\) (see text). The smaller peaks at zero detuning correspond to the erroneous cases where the Cs atom was not excited to the Rydberg state. The centre peak at larger spacings stems from other resonant pair states, which can be suppressed by tuning the electric field (Supplementary Information Section 8). e, Measured energy shifts plotted against the interatomic spacing for the Rb–Rb, Cs–Cs and Rb–Cs vdW and Rb–Cs Förster interactions. The theoretically predicted (dashed) curves for the homogeneous pairs were used to calibrate the x axis. By fitting the heterogeneous pair data to the appropriate functional forms (solid lines, Supplementary Information Section 7), we found C3 = 16.4(3) GHz μm3 and C6 = 662(21) GHz μm6, both of which are compatible with theoretically predicted values. The inset shows the interaction strengths plotted on a log-log scale, which define V = ΔE for the vdW interactions and V = (ΔEu − ΔEl)/2 for the Förster interaction. Here, ΔEu(l) denotes the energy of the upper (lower) branch. In e, error bars are statistical fit uncertainties.
