Progress toward measuring the $^{85}$Rb $ng$-series quantum defect using $\Delta l = 0$ microwave spectroscopy

We describe progress toward a new measurement of the $^{85}$Rb $ng$-series quantum defect via two-photon microwave spectroscopy of a $\Delta l = 0$ transition using cold Rydberg atoms. Past efforts have used resonant energy transfer\footnote{K.Afrousheh, P.Bohlouli-Zanjani, J.A.Petrus, J.D.D.Martin, PRA, 74, 062712 (2006)} and preliminary microwave spectroscopy of a $\Delta l = 2$ transition\footnote{J.Han, Y.Jamil, D.V.L.Norum, P.J.Tanner, T.F.Gallagher, PRA, 74, 054502 (2006)}, yielding $\delta_g(n=30)=0.00405(6)$ and $\delta_g=0.00400(9)$, respectively. By performing a $\Delta l = 0$ measurement, we hope to eliminate uncertainties due to lower-$l$-state quantum defects and differing Land\'{e}-$g$ factors and thereby achieve an improved precision. Preliminary measurements will be presented, including efforts at resolving fine structure in the spectrum. Applications of this high-$l$ measurement method toward experimentally determining the dipole and quadrupole core polarizabilities of $^{85}$Rb will be discussed, including comparisons with calculated values\footnote{J.Heinrichs, J. Chem. Phys. 52, 6316 (1970)},\footnote{R.M.Sternheimer, PRA 1, 321 (1970)} and preliminary experimental limits$^3$, which yield inconsistent results for the dipole polarizability value.