High Resolution Rydberg Spectroscopy of ultracold Rubidium Atoms
  We present experiments on two-photon excitation of ${\rm ^{87}}$Rb atoms to Rydberg states. For this purpose, two continuous-wave (cw)-laser systems for both 780 nm and 480 nm have been set up. These systems are optimized to a small linewidth (well below 1 MHz) to get both an efficient excitation process and good spectroscopic resolution. To test the performance of our laser system, we investigated the Stark splitting of Rydberg states. For n=40 we were able to see the hyperfine levels splitting in the electrical field for different finestructure states. To show the ability of spatially selective excitation to Rydberg states, we excited rubidium atoms in an electrical field gradient and investigated both linewidths and lineshifts. Furthermore we were able to excite the atoms selectively from the two hyperfine ground states to Rydberg states. Finally, we investigated the Autler-Townes splitting of the 5S$_{1/2}$$\to$5P$_{3/2}$ transition via a Rydberg state to determine the Rabi frequency of this excitation step. 
Axel Grabowski, Rolf Heidemann, Robert L\"ow, J\"urgen Stuhler, and   Tilman Pfau