Ripplonic Lamb Shift for Electrons on Liquid Helium

Many-Electron System on Helium and Color Center Spectroscopy

Electrons on the helium surface display sharp resonant absorption lines related to the transitions between the subbands of quantized motion transverse to the surface. A magnetic field parallel to the surface strongly affects the absorption spectrum. We show that the effect results from admixing the intersubband transitions to the in-plane quantum dynamics of the strongly correlated electron liquid or a Wigner crystal. This is similar to the admixing of electron transitions in color centers to phonons. The spectrum permits a direct characterization of the many-electron dynamics and also enables testing the theory of color centers in a system with controllable coupling.

Statistical Mechanics at Strong Coupling: A Bridge between Landsberg's Energy Levels and Hill's Nanothermodynamics

We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill's nanothermodynamics.

Coupling between Rydberg States and Landau Levels of Electrons Trapped on Liquid Helium

We investigate the coupling between Rydberg states of electrons trapped on a liquid helium surface and Landau levels induced by a perpendicular magnetic field. We show that this realizes a prototype quantum system equivalent to an atom in a cavity, where their coupling strength can be tuned by a parallel magnetic field. We determine experimentally the renormalization of the atomic transition energies induced by the coupling to the cavity, which can be seen as an analog of the Lamb shift. When the coupling is sufficiently strong, the transition between the ground and first excited Rydberg states splits into two resonances corresponding to dressed states with vacuum and one photon in the cavity. Our results are in quantitative agreement with the energy shifts predicted by the effective atom in a cavity model where all parameters are known with high accuracy.