Confined System with Rashba Coupling in Constant Magnetic Field

TL;DR

This paper analyzes a 2D electron system with Rashba coupling in a magnetic field and confinement, deriving exact solutions and exploring quantum optical analogies and dynamics.

Contribution

It provides an algebraic diagonalization of the Hamiltonian for the system, revealing symmetries and connections to quantum optics.

Findings

Exact energy spectrum solutions obtained.

Identified symmetries related to electron shell filling.

Established parallels with Jaynes-Cummings model in quantum optics.

Abstract

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.