We study the relations between massless Dirac fermions in an electromagneticView original: http://arxiv.org/abs/1103.5297
field and atoms in quantum optics. After getting the solutions of the energy
spectrum, we show that it is possible to reproduce the 2D Dirac Hamiltonian,
with all its quantum relativistic effects, in a controllable system as a single
trapped ion through the Jaynes--Cummings and anti-Jaynes--Cummings models. Also
we show that under certain conditions the evolution of the Dirac Hamiltonian
provides us with Rashba spin-orbit and linear Dresselhaus couplings.
Considering the multimode multiphoton Jaynes-Cummings model interacting with N
modes of electromagnetic field prepared in general pure quantum states, we
analyze the Rabi oscillation. Evaluating time evolution of the Dirac position
operator, we determine the Zitterbewegung frequency and the corresponding
oscillating term as function of the electromagnetic field.