Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems

Abstract

We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for the absence or existence of the prefect reflection at one and two resonant frequencies. Our study can help us to understand the interplay between the Fano resonance and PT symmetry in non-Hermitian discrete systems, which may be realizable in optical waveguide experiments.

arXiv comment6 pages, 6 figures

References in corpus (35)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Fano resonances in nanoscale structures
• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• PT-symmetric laser-absorber
• Visualization of Branch Points in PT-Symmetric Waveguides
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Nonlinear suppression of time-reversals in PT-symmetric optical couplers
• Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
• Observation of Defect States in PT-Symmetric Optical Lattices
• PT-Symmetric Talbot Effects
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Pseudo Parity-Time Symmetry in Optical Systems
• Nonlinear Fano resonance and bistable wave transmission
• Engineering Fano resonances in discrete networks
• Conceptual Problems in Scattering from Localized non-Hermitian Potentials
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• Scattering theory with localized non-Hermiticities
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Gegenbauer-solvable quantum chain model
• Non-Hermitian spectra and Anderson localization
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Discrete PT-symmetric models of scattering
• Hermitian scattering behavior for the non-Hermitian scattering center
• Probability-preserving evolution in a non-Hermitian two-band model
• Fano resonance in discrete lattice models: controlling lineshapes with impurities
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity

Cited by in corpus (7)

• Nonlinear switching and solitons in PT-symmetric photonic systems
• Transport properties in a Non-Hermitian triple-quantum-dot structure
• Scattering properties of anti-parity-time symmetric non-Hermitian system
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Dynamical evolution of an effective two-level system with PT symmetry
• Discretized optical dynamics in one-dimensionally synthetic photonic lattice
• Single-photon scattering controlled by an imperfect cavity