Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-03-28
J.Stat.Mech.:P01021,2012
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, 3 tables, 1 figure, clarifications and references added, misprints corrected. Version published in JSTAT
Scientific paper
We study the relations between massless Dirac fermions in an electromagnetic 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.
Daoud Mohammed
Jellal Ahmed
Mouhafid Abderrahim El
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