  Quantum simulation aims to simulate a quantum system using a controble
laboratory system that underline the same mathematical model. Cavity QED
lattice system is that prescribe system to simulate the relativistic quantum
effect. We quantum simulate the Dirac fermion mode, Majorana fermion mode and
Majorana-Weyl fermion mode and a crossover between them in cavity QED lattice.
We also present the different analytical relations between the field operators
for different mode excitations.
