  We report on Rydberg spectroscopy of ultracold atoms in an atom-ion hybrid
trap for probing the electric fields in a mixture of atoms and ions. We obtain
spectra which exhibit excitation gaps corresponding to avoided level crossings
in the Stark map. From these measurements we can conclude that the ground state
atoms experience electrical fields of up to 250 V/cm. There is, however, a
difficulty in interpreting the results, because some data indicate that the
electrical fields are produced by the ions while other data indicate that they
stem from the Paul trap. We discuss possible scenarios for explaining the
measured data, provide first measurements to check these scenarios, and propose
methods to finally solve this puzzle.
