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We show an implementation of a -deformed Dirac equation in tight-binding arrays of photonic waveguides. This is done with a special configuration of couplings extending to second-nearest neighbors. Geometric manipulations can control these evanescent couplings. A careful study of wave packet propagation is presented, including the effects of deformation parameters on Zitterbewegung or trembling motion. In this way, we demonstrate how to emulate the effects of a flat noncommutative spacetime—i.e., -Minkowski spacetime—in simple experimental setups. ©2021 American Physical Society
Photonic realization of the -deformed Dirac equation
Couplings; Deformation parameter; Dirac equations; Evanescent coupling; Geometric manipulation; Minkowski space-time; Photonic waveguides; Second-nearest-neighbor; Wave packet propagation; Linear equations
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AG100819, IN113620; Consejo Nacional de Ciencia y Tecnología, CONACYT: 254515, A1-S-18696; Universidad Nacional Autónoma de México, UNAM