Ripplonic Lamb shift for electrons on liquid helium

TL;DR

This paper investigates the energy level shifts of electrons on liquid helium caused by their interaction with surface vibrations, resolving a theoretical controversy and aligning predictions with experimental data.

Contribution

It demonstrates the cancellation of divergent terms in the level shift calculation using a Bethe-type approach, clarifying the theoretical understanding.

Findings

Divergent terms cancel out at leading order.

Theoretical predictions match experimental results.

Temperature dependence of the level shift is characterized.

Abstract

We study the shift of the energy levels of electrons on helium surface due to the coupling to the quantum field of surface vibrations. As in quantum electrodynamics, the coupling is known, and it is known to lead to an ultraviolet divergence of the level shifts. We show that there are diverging terms of different nature and use the Bethe-type approach to show that they cancel each other, to the leading-order. This resolves the long-standing theoretical controversy and explains the existing experiments. The results allow us to study the temperature dependence of the level shift. The predictions are in good agreement with the experimental data.