Classical simulation of relativistic quantum mechanics in periodic optical structures

Abstract

Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.

Conical intersections for light and matter waves

“…On a more fundamental level, the realization of conical intersections in photonic and matter wave systems allows the direct observation of relativistic quantum analogies not easily visible in systems such as graphene [75], for example the parity anomaly [76], along with the study of surface effects such as edge states that are notoriously hard to control in condensed matter systems [16,17,21,24]. When a conical dispersion is restricted to a finite system, the intersection is replaced by a (small) band gap, due to the vanishing density of states.…”

Nonlinear Optics in Waveguide Arrays and Photonic Nanowires

“…However, it was a common belief that the use of WAs as a model system for quantum mechanics carries the intrinsic drawback of being limited to nonrelativistic phenomena. Only recently, it turns out that binary waveguide arrays -an alternating sequence of two different types of waveguides -can be used to mimic relativistic phenomena typical of quantum field theory, such as Klein tunneling [35,36], the Zitterbewegung [37,38], and fermion pair production [39], which are all based on the properties of the Dirac equation [40]. In this Section we review ours latest works on the optical analogues of the quantum relativistic Dirac solitons in BWAs [49][50][51][52].…”

“…Many fundamental phenomena in nonrelativistic classical and quantum mechanics, such as Bloch oscillations [29,30], Zener tunneling [31,32], optical dynamical localization [33], and Anderson localization in disordered lattices [34] have been simulated both theoretically and experimentally with WAs. Recently, binary waveguide arrays (BWAs) have also been used to mimic relativistic phenomena typical of quantum field theory, such as Klein tunneling [35,36], the Zitterbewegung (trembling motion of a free Dirac electron) [37,38], and fermion pair production [39], which are all based on the properties of the Dirac equation [40]. Although there is as yet no evidence for fundamental quantum nonlinearities, nonlinear versions of the Dirac equation have been studied for a long time.…”

An optical analog of quantum optomechanics

“…Optical analogs of quantum processes [1,2] may become a valuable resource for the design of integrated optics devices [3,4]. In this spirit, a zoo of optical analogs to quantum mechanical systems and the algebraic methods to solve them provide a valuable toolbox for optical designers.…”