Massless Dirac Fermions in Electromagnetic Field

TL;DR

This paper demonstrates how massless Dirac fermions in an electromagnetic field can be simulated using trapped ions, reproducing relativistic quantum effects and analyzing their dynamics through quantum optics models.

Contribution

It introduces a method to emulate 2D Dirac Hamiltonian and relativistic effects in a controllable quantum optical system using trapped ions and Jaynes-Cummings models.

Findings

Reproduction of 2D Dirac Hamiltonian in trapped ions

Simulation of Rashba and Dresselhaus spin-orbit couplings

Analysis of Rabi oscillations and Zitterbewegung frequency

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.