Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems

Abstract

Zitterbewegung (ZB) is a phenomenon in relativistic quantum systems where the electron wave packet exhibits a trembling or oscillating behavior during its motion, caused by its interaction or coupling with the negative energy state. To directly observe ZB in electronic systems is difficult, due to the challenges associated with the atomic scale wavelength of the electron. Photonic systems offer an alternative paradigm. We exploit the concept of pseudo parity-time (pseudo PT ) symmetry to study ZB in non-Hermitian quantum systems implemented as an experimentally feasible optical waveguide array. In particular, the non-Hermitian Hamiltonian is realized through evanescent coupling among the waveguides to form a one-dimensional lattice with periodic modulations in gain and loss along the guiding direction. As the modulation frequency is changed, we obtain a number of phenomena including periodically suppressed ZB trembling, spatial energy localization, and Hermitian-like ZB oscillations. We calculate phase diagrams indicating the emergence of different types of dynamical behaviors of the relativistic non-Hermitian quantum system in an experimentally justified parameter space. We provide numerical results and a physical analysis to explain the distinct dynamical behaviors revealed by the phase diagrams. Our findings provide a deeper understanding of both the relativistic ZB phenomenon and non-Hermitian pseudo-PT systems, with potential applications in controlling/harnessing light propagation in waveguide-based optical systems.

arXiv comment24 pages, 6 figures

References in corpus (44)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Topological Insulators
• Topological insulators and superconductors
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Topological Photonics
• Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics
• Electronic transport in two dimensional graphene
• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Complex Extension of Quantum Mechanics
• Imaging topological edge states in silicon photonics
• Robust optical delay lines via topological protection
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Topological Acoustics
• Colloquium: The transport properties of graphene: An introduction
• Spawning rings of exceptional points out of Dirac cones
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Observation of dynamic localization in periodically-curved waveguide arrays
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• Observation of Asymmetric Transport in Structures with Active Nonlinearities
• Topological creation and destruction of edge states in photonic graphene
• PT-symmetry in honeycomb photonic lattices
• Robust light transport in non-Hermitian photonic lattices
• Optical realization of relativistic non-Hermitian quantum mechanics
• Pseudo Parity-Time Symmetry in Optical Systems
• Discrete gap solitons in modulated waveguide arrays
• Photonic analogue of Zitterbewegung in binary waveguide arrays
• Bragg solitons in nonlinear PT-symmetric periodic potentials
• Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures
• PT spectroscopy of the Rabi problem
• Stabilizing Non-Hermitian Systems by Periodic Driving
• PT-symmetric Rabi model: Perturbation theory
• Diffraction control in PT-symmetric photonic lattices: from beam rectification to dynamic localization
• Tight-binding lattices with an oscillating imaginary gauge field
• Optical simulation of neutrino oscillations in binary waveguide arrays