Jaynes-Cummings models with trapped electrons on liquid helium

Jaynes-Cummings model is a typical model in quantum optics and has been realized with various physical systems [e.g, cavity quantum electrodynamics (QED), trapped ions, circuit QED, etc.] of two-level atoms interacting with quantized bosonic fields. Here, we propose an implementation of this model by using a single classical laser beam to drive an electron floating on liquid helium. Two lowest levels of the vertical motion of the electron act as a two-level atom and the quantized vibration of the electron along one of the parallel directions, e.g., x direction, serves as the bosonic mode. These two degrees of freedom of the trapped electron can be coupled together by using a classical laser field. If the frequencies of the applied laser fields are properly set, the desirable Jaynes-Cummings models could be effectively realized.