Optical simulation of Majorana physics

Abstract

We show a procedure to classically simulate the Majorana equation in 1+1 dimensions via two one-dimensional photonic crystals. We use a decomposition of the Majorana equation into two Dirac equations and propose a novel approach that uses a bi-chromatic refractive index distribution and nearest neighbor couplings of the type found in Glauber-Fock lattices. This allows us to escape the restriction of staying near the Brillouin zone imposed by the classical simulation of Dirac dynamics with bi-chromatic lattices. Furthermore, it is possible to simulate the evolution of Gaussian wavepackets under the Majorana/Dirac equation with light impinging only into the first waveguide of our bi-chromatic-Glauber-Fock lattice.