Precision Measurement of the Differential dc Stark Shift of the 5S_1/2to 6S_1/2 Transition in Rb

Using Doppler-free two-photon spectroscopy in a temperature-controlled vapor cell, we measure the static Stark shift for the of the Rb 5S_1/2 to 6S_1/2 transition in both isotopes of rubidium. We lock a tunable microwave-driven EOM sideband of the 993 nm laser to an ultra-stable very high finesse cavity, achieving microwave frequency accuracy for the relative laser tuning. We discuss our progress towards measuring the Stark shift as a function of the applied electric field and determining the differential scalar polarizability of the 5S_1/2 to 6S_1/2 transition.