Confined System with Rashba Coupling in Constant Magnetic Field

We study a two dimensional system of electrons with Rashba coupling in the constant magnetic field $B$ and confining potential. We algebraically diagonalize the corresponding Hamiltonian to end up with the solutions of the energy spectrum. In terms of two kinds of operator we construct two symmetries and discuss the filling of the shells with electrons for strong and weak $B$. Subsequently, we show that our system is sharing some common features with quantum optics where the exact operator solutions for the basics Jaynes-Cummings variables are derived from our results. An interesting limit is studied and the corresponding quantum dynamics is recovered.