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In the simulation, two Dirac equations with opposite masses are simulated in two parallel planar photonic waveguide lattices, and combined to recover the “unphysical” solution of the Majorana equation. [Image: Keil et al., Optica, doi: 10.1364/OPTICA.2.000454]

The celebrated Majorana equation—a modification of Dirac’s relativistic quantum wave expression—has preoccupied particle physicists for decades. Among other things, the equation predicts a neutrally charged particle that is its own antiparticle (and thus could shed light on the mysterious neutrino). But the equation also allows for solutions that, under fundamental physical laws, can’t be realized or observed in nature.
Now, a multinational group of scientists has fashioned a method for simulating this “unphysical” behavior using classical light (Optica, doi: 10.1364/OPTICA.2.000454). The team believes that the framework will prove useful not only in illuminating the physics of Majorana fermions, but also as a platform for “investigating theories beyond the standard model in a compact laboratory setting.”
Devised by Ettore Majorana in the 1930s, the Majorana equation for a relativistic particle—compactly rendered as iγμμψ – mψc = 0—includes terms for both the particle wavefunction (ψ) and its charge conjugate (ψc). The expression suggests that these particles constitute their own antiparticles. It also suggests that such particles, dubbed Majorana fermions, must be neutrally charged (i.e., ψ = ψc), or the system would violate charge conservation. Indeed, Majorana himself suggested that the equation might be used to describe the characteristics of neutrinos, the virtually massless neutral particles that had been proposed a few years earlier by Wolfgang Pauli, Enrico Fermi and others to fill certain holes in the theory of beta decay.
Could the equation’s “unphysical” solution, a charged Majorana particle (called a Majoranon), shed any interesting light on potential new physics? Maybe—but only if the behavior of these unphysical entities could somehow be simulated in the lab (as even the physical solution, uncharged Majorana fermions, have proved devilishly elusive to find in nature).
To create such a simulator, a research team led by Alexander Szameit of Friedrich-Schiller-Universität Jena, Germany, and Dimitris Angelakis of the Technical University of Crete, Greece, turned to classical light. Specifically, they created a system of two photonic lattices, each consisting of an array of coupled waveguides, and used a “photonic analogue” of the Dirac equation to simulate the particle wavefunction with classical light waves. Then, they sent beams through the waveguides with simulated masses of opposite signs, and coherently combined the beams to retrieve the Majorana wavefunction under the “unphysical” case of a charged Majoranon. Observing the intensity distribution of the output beam allowed them a readout of the Majorana equation’s unphysical solutions that could be compared with numerical calculations.
The scientists suggest that simulating such unphysical dynamics by exploiting the analog between particle and light wavefunctions “provides an entirely new approach for probing and understanding exotic phenomena and particles that cannot exist in nature.” And, they suggest, the new platform they’ve demonstrated could “stimulate many exciting proposals that utilize the freedom of going beyond the ‘physical’ operations in areas such as exotic particle physics and quantum information processing.”