Abstract
We are using optical- and microwave-fields to excite Rydberg states in trapped cold 40Ca+ ions. We employ a single ion and observe spectroscopically in the manifold of a principal quantum number n=49 the dressing of Rydberg states of angular momentum states S and P. We compare our experimental spectra with a multi-level calculation of dressed states and find good agreement. The results are important for controlling the interaction of single ions in Rydberg states with electric fields of the ion trap, and for tailoring the interactions in an ion crystal in Rydberg states.