Van-der-Waals shifts of rubidium Rydberg states

We present calculations of van der Waals energy shifts of Rb Rydberg-atom pairs for different quantum numbers n, l, j and m$_{\rm j}$, taking into account a large number of perturbing states. For D$_{5/2}$-states we find that over the range of 54 $<$ n $<$ 86 the van-der-Waals shift scaled by $R^6/n^{11}$ is nearly constant, and that the shift does not vary by more than $50\%$ as a function of the relative atomic orientation. This result is consistent with recent experimental work, in which we have studied the effect of a Rydberg-excitation blockade on the probability distribution of the number of Rydberg atoms detected in small atomic ensembles. In these experiments it was found that the counting statistics is sub-poissonian, and that its Mandel Q-parameter exhibits a smooth dependence on n. The calculations further show that the shifts of the D$_{5/2}$, D$_{3/2}$, P$_{3/2}$, P$_{1/2}$ and S$_{1/2}$-levels exhibit qualitatively different behavior. How these differences might effect future experiments will be discussed.