Resonant energy transfer Rb ns plus Rb ns+2hυ → Rb np1/2 + Rb np3/2 in a frozen Rydberg gas

We have observed the process Rb ns + Rb ns + 2h upsilon -> Rb np(1/2) + Rb np(3/2) from n = 34 to n = 40 in a frozen gas of Rb Rydberg atoms. It is resonant when the microwave frequency is halfway between the ns -> np(1/2) and ns -> np(3/2) frequencies, which range from 57 to 106 GHz. The process cannot occur in isolated atoms, nor can it occur if the magnetic quantum numbers are unchanged, an implicit assumption of one-dimensional models. A Floquet-Forster model shows that the coupling between the initial and final states involves the absorption of two microwave photons and the dipole-dipole interaction, which leads to a coupling proportional to the product of the density, the microwave field squared, and n*(14), where n* is the effective quantum number of the np(3/2). state. We have experimentally verified these dependences. The observed resonances are asymmetric, with a low-frequency tail, which we attribute to the van der Waals shift of the final np(1/2)np(3/2) state due to its dipole-dipole interaction with the nearby (n + 1)s state. While the van der Waals shift is negligible for most of the atoms in the Rydberg gas, it is not for the pairs of close atoms which undergo this transition.