  The Jaynes-Cummings model (JCM), one of the paradigms of quantum
electrodynamics, was introduced to describe interaction between light and a
fictitious two-level atom. Recently it was suggested that the JCM Hamiltonian
can be invoked to describe the motional states of electrons trapped on the
surface of liquid helium and subjected to a constant uniform magnetic field
tilted with respect to the surface [Yunusova et al. Phys. Rev. Lett. 122,
176802 (2019)]. In this case, the surface-bound (Rydberg) states of an electron
are coupled to the electron cyclotron motion by the in-plane component of
tilted field. Here we investigate, both theoretically and experimentally, the
spectroscopic properties of surface electrons in a tilted magnetic field and
demonstrate that such a system exhibits a variety of phenomena common to the
light dressed states of atomic and molecular systems. This shows that electrons
on helium realize a prototypical atomic system where interaction between
components can be engineered and controlled by simple means and with high
accuracy, and which therefore can be potentially used as a new flexible
platform for quantum experiments. Our work introduces a pure condensed-matter
system of electrons on helium into the context of atomic, molecular and optical
physics.
