Predictions for laser-cooled Rb clocks

Using information from a recent ${}^{85}$Rb two-color photoassociation experiment, we evaluate the merits of fountain clocks based on ${}^{87}$Rb and ${}^{85}$Rb isotopes as alternatives to ${}^{133}$Cs and find that they offer significant advantages. In the case of ${}^{87}$Rb the collisionally induced fractional frequency shift is 15 times smaller than for ${}^{133}$Cs. This small shift is associated with a small difference in the triplet and singlet scattering lengths for ${}^{87}$Rb. For ${}^{85}$Rb, the shift produced by the two $m_f=0\mathrm{}$ clock states may have opposite signs allowing the shift to be eliminated by controlling the relative populations of these states. We also present collision quantities relevant to atomic fountain clocks containing multiply launched groups of atoms, and for evaporative cooling of ${}^{85}$Rb atoms.