Abstract
We have measured the AC-Stark shift of the \$14D\_5/2\$ Rydberg state of
rubidium 87 in an optical dipole trap formed by a focussed CO\$\_2\$-laser. We
find good quantitative agreement with the model of a free electron experiencing
a ponderomotive potential in the light field. In order to reproduce the
observed spectra we take into account the broadening of the Rydberg state due
to photoionization. The extracted cross-section is compatible with previous
measurements on neighboring Rydberg states.
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