Electron waveguide as a model of a giant atom with a dressing field

An atom may be characterized as a system in which a discrete spectrum of electrons is coupled with a continuous spectrum of photons. This coupling leads to significant physical effects, such as the dressing of virtual photons in the ground state of the atom, and quantum transitions of an excited atom. For example, the evanescent dressing photons are the origin of the long-range van der Waals force, as well as the Casimir–Polder force. We show that an electron waveguide (or a quantum dot) that consists of a rectangular cavity and straight leads may mimic an atom on a mesoscopic scale. The electron states inside the cavity correspond to the discrete spectrum of an atom, while the electron states in the leads correspond to the continuous spectrum of photons. The advantage of the electron waveguide is that one can control physical parameters that characterize a given atom, like mass and its coupling constant, only by changing the geometry of the waveguide. Hence, the waveguide offers a good device that can test many theoretical predictions in fundamental problems in atomic physics.