Lineshapes of Dipole-Dipole Resonances in a Cold Rydberg Gas

We have examined the lineshapes associated with Stark tuned, dipole-dipole resonances involving Rydberg atoms in a cold gas. Rb atoms in a MOT are laser excited from the 5$p$ level to 32$p_{3/2}$ in the presence of a weak electric field. A fast rising electric field pulse Stark tunes the total energy of two 32$p$ atom pairs so it is (nearly) degenerate with that of the 32$s_{1/2}$+33$s_{1/2}$ states. Because of the dipole-dipole coupling, atom pairs separated by a distance $R$, develop 32$s_{1/2}$+33$s_{1/2}$ character. The maximum probability for finding atoms in $s$-states depends on the detuning from degeneracy and on the dipole-dipole coupling. We obtain the ``resonance'' lineshape by measuring, via state-selective field ionization, the $s$-state population as a function of the tuning field. The resonance width decreases with density due to $R^{-3}$ dependence of the dipole-dipole coupling. In principle, the lineshape provides information about the distribution of Rydberg atom spacings in the sample. For equally spaced atoms, the lineshape should be Lorentzian while for a random nearest neighbor distribution it appears as a cusp. At low densities nearly Gaussian lineshapes are observed with widths that are too large to be the result of inhomogeneous electric or magnetic fields.