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We have measured the AC-Stark shift of the $14D_{5/2}$ Rydberg state ofrubidium 87 in an optical dipole trap formed by a focussed CO$_2$-laser. Wefind good quantitative agreement with the model of a free electron experiencinga ponderomotive potential in the light field. In order to reproduce theobserved spectra we take into account the broadening of the Rydberg state dueto photoionization. The extracted cross-section is compatible with previousmeasurements on neighboring Rydberg states.

AC-Stark shift and photoionization of Rydberg atoms in an optical dipole trap