Spectroscopy of electrons in image-potential-induced surface states outside liquid helium

Abstract

We report a spectroscopic study of electronic transitions from the ground state to several excited states in the potential well lying outside the free surface of liquid helium formed by the long-range attractive-image potential and the short-range electron-atom repulsive potential. These electric dipole transitions were observed at frequencies from 130 to 220 GHz by measuring the microwave absorption derivative at fixed frequency as the splittings between states were tuned to resonance by an applied electric field $\mathcal{E}$. Transitions were observed between the ground state and the first through seventh excited states, and detailed measurements were made of the frequency versus $\mathcal{E}$ relation for transitions to the first and second excited states. Extrapolation of the respective data to $\mathcal{E}=0\mathrm{}$ yields splittings of 125.9 ± 0.2 and 148.6 ± 0.3 GHz and initial Stark-tuning rates of 2.3 ± 0.1 and 5.9 ± 0.4 GHz/(V/cm). The data can be fit satisfactorily by variational calculations based on a simple model potential which takes the origin of the image potential to lie 1.04 Å inside the liquid-helium surface. These calculations show the wave functions to be significantly compressed by the Stark-tuning fields; e.g., the second excited state is compressed at our highest fields to 1/2 of its original size. Measurements of the linewidth of the lowest transition as a function of the helium vapor density are reported. The peak-to-peak line width is 1.0 GHz at a vapor density of 5 × ${10}^{18}$ atoms/${\mathrm{cm}}^3$ and increases approximately linearly with increasing vapor density. A phenomenological theory of several mechanisms contributing to the linewidth is discussed.