Van der Waals Interactions among Alkali Rydberg Atoms with Excitonic States

We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the $|ns\rangle$ and $|np\rangle$ states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients, $C_6^{sp}$, can be defined. We calculate the $C_6$ coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several $\mu m$, we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.