Mesoscopic Superposition States in Relativistic Landau Levels

We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin $1/2$ charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily superpositions of coherent states involving the particle orbital quanta in a well-defined mesoscopic regime. We demonstrate that these mesoscopic superpositions have a purely relativistic origin and disappear in the nonrelativistic limit.

Figure 1

Quantum optical representation of the relativistic $e^{-}$ levels coupled by means of a constant magnetic field.

Figure 2

Quantum optical representation of the coupling between the relativistic levels caused by the Lorentz boost.

Figure 3

Blockade of the AJC coupling.