Temperature Dependent Energy Levels of Electrons on Liquid Helium

We present measurements of the resonant microwave absorption by the Rydberg energy levels of surface state electrons on the surface of superfluid liquid helium, in the frequency range 165 - 220 GHz. The resonant frequency was strongly temperature dependent from 0.1 to 2 K. The experiments are in agreement with recent theoretical calculations of the renormalisation of the electron energy levels due to zero-point and thermal ripplons, analogous to a condensed matter Lamb shift. The temperature-dependent contribution to the linewidth for excitation to the first excited state at 189.6 GHz is compared with other measurements and theoretical predictions.