Photonic quantum chromodynamics - Saito, Shinichi (Frontiers in Physics, 2023)
Twisted photons with finite orbital angular momentum have a distinct mode profile with topological charge at the centre of the mode, while propagating in a certain direction. Each mode with different topological charge of m is orthogonal, in the sense that the overlap integral vanishes among modes with different values of m. Here, we theoretically consider a superposition state among 3 different modes with left-and right-vorticies and a Gaussian mode without a vortex. These 3 states are considered to be assigned to different quantum states, thus, we have employed the su(3) Lie algebra and the associated SU(3) Lie group to classify the photonic states.We have calculated expectation values of 8 generators of the su(3) Lie algebra, which should be observable, since the generators are Hermite. We proposed to call these parameters as Gell-Mann parameters, named after the theoretical physicist, Murray Gell-Mann, who established Quantum Chromo-Dynamics (QCD) for quarks. The Gell-Mann parameters are represented on the 8-dimensional hypersphere with its radius fixed due to the conservation law of the Casimir operator. We have discussed a possibility to explore photonic QCD in experiments and classified SU(3) states to embed the parameters in SO(6) and SO(5).