Massless Dirac Fermions in Electromagnetic Field

Abstract

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.

15 pages, 3 tables, 1 figure, clarifications and references added, misprints corrected. Version published in JSTAT

References in corpus (9)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• Quantum simulation of the Klein paradox with trapped ions
• Klein tunneling and Dirac potentials in trapped ions
• Relativistic quantum mechanics with trapped ions
• Spin-flip excitations, spin waves, and magneto-excitons in graphene Landau levels at integer filling factors
• Jaynes-Cummings model with a collective atomic mode

Cited by in corpus (5)

• Dunkl-Graphene in constant magnetic field
• Phase-space representation of Landau and electron coherent states for uniaxially strained graphene
• Mapping of the 2+1 q-deformed Dirac oscillator onto the q-deformed Jaynes-Cummings model: It's non-relativistic limit and Zitterbewegung effect
• Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices
• Confined System with Rashba Coupling in Constant Magnetic Field