AUTHOR=Saito Shinichi 

TITLE=Photonic quantum chromodynamics

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1225488

DOI=10.3389/fphy.2023.1225488

ISSN=2296-424X

ABSTRACT=<p>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 <italic>m</italic> is orthogonal, in the sense that the overlap integral vanishes among modes with different values of <italic>m</italic>. 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 <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="fraktur">s</mml:mi><mml:mi mathvariant="fraktur">u</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> Lie algebra and the associated SU(3) Lie group to classify the photonic states. We calculated expectation values of eight generators of the <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="fraktur">s</mml:mi><mml:mi mathvariant="fraktur">u</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> 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).</p>