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 center of the mode while propagating in a certain direction. Each mode with different topological charges 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 three different modes with left and right vortices and a Gaussian mode without a vortex. These three states are considered to be assigned to different quantum states; thus, we employed the su(3) Lie algebra and the associated SU(3) Lie group to classify the photonic states. We calculated expectation values of eight generators of the su(3) Lie algebra, which should be observable, since the generators are Hermite matrices. We proposed to call these parameters Gell-Mann parameters, named after the theoretical physicist Murray Gell-Mann, who established quantum chromodynamics (QCD) for quarks. The Gell-Mann parameters are represented on the eight-dimensional hypersphere with its radius fixed due to the conservation law of the Casimir operator. Thus, we discussed a possibility of exploring photonic QCD in experiments and classified SU(3) states to embed the parameters in SO(6) and SO(5).