Nonlinearly-PT-symmetric systems: spontaneous symmetry breaking and transmission resonances

Abstract

We introduce a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear PT-symmetric dimer generates new types of nonlinear resonances, with the completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically-induced transparency (EIT). The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.

4 pages, 4 figures

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Solitons in PT-symmetric nonlinear lattices

Cited by in corpus (86)

• Non-Hermitian Physics
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• $\mathcal{P}\mathcal{T}$-Symmetry-Breaking Chaos in Optomechanics
• New topological invariants in non-Hermitian systems
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• Observation of Asymmetric Transport in Structures with Active Nonlinearities
• Stability of solitons in PT-symmetric couplers
• Observation of Defect States in PT-Symmetric Optical Lattices
• Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions
• Nonlinear modes in finite-dimensional PT-symmetric systems
• Supersymmetry-generated complex optical potentials with real spectra
• Breathers in PT-symmetric optical couplers
• Optical mesh lattices with PT-symmetry
• Solitons in a chain of PT-invariant dimers
• PT-symmetric optical potentials in a coherent atomic medium
• Tunneling of Obliquely-Incident Waves through PT-Symmetric Epsilon-Near-Zero Bi-Layers
• Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
• PT Symmetric Aubry-Andre Model
• Stability of localized modes in PT-symmetric nonlinear potentials
• Defect Solitons in Parity-Time Symmetric Optical Lattices with Nonlocal Nonlinearity
• Stabilization of solitons in PT models with supersymmetry by periodic management
• Vector solitons in PT-symmetric lattices
• Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• A solvable model for solitons pinned to a PT-symmetric dipole
• Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis
• Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers
• Nonlinear dynamics in PT-symmetric lattices
• Nonlinear PT-symmetric plaquettes
• PT-Symmetric Dimer of Coupled Nonlinear Oscillators
• On the integrability of PT-symmetric dimers
• 2D Solitons in PT-symmetric photonic lattices
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• Optomechanical transistor with mechanical gain
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• PT-symmetry in optics beyond the paraxial approximation
• Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models
• Scattering properties of PT-symmetric layered periodic structures
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• Flat bands and PT-symmetry in quasi-one-dimensional lattices
• Parametric instability of non-Hermitian systems near the exceptional point
• PT-Symmetric Nonlinear Metamaterials and Zero-Dimensional Systems
• Interaction induced dynamical $\mathcal{P}\mathcal{T}$ symmetry breaking in dissipative Fermi-Hubbard models
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Scattering properties of PT-symmetric objects
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Resonant mode conversion in the waveguides with an unbroken and broken PT-symmetry
• Mode pairs in $\mathcal{P}\mathcal{T}$-symmetric multimode waveguides
• Tailoring inhomogeneous $\mathcal{P}\mathcal{T}$-symmetric fiber Bragg grating spectra
• Stable surface solitons in truncated complex potentials
• PT-symmetric lattices with spatially extended gain/loss are generically unstable
• Light dynamics in nonlinear trimers and twisted multicore fibers
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• Solitons in a $\mathcal{P}\mathcal{T}$- symmetric ${\chi }^{(2)}$ coupler
• $\mathcal{P}\mathcal{T}$ symmetry of the Su-Schrieffer-Heeger model with imaginary boundary potentials and next-nearest-neighboring coupling
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• PT-symmetry, indefinite damping and dissipation-induced instabilities
• Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators
• Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers
• Complex Spatiotemporal Modulations and Non-Hermitian Degeneracies in $\mathcal{P}\mathcal{T}$-Symmetric Phononic Materials
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetry Management in Oligomer Systems
• Transport and localization of waves in ladder-shaped lattices with locally $\mathcal{P}\mathcal{T}$-symmetric potentials
• Bistable soliton switching dynamics in a $\mathcal{P}\mathcal{T}$-symmetric coupler with saturable nonlinearity
• Topological protection in nonlinear optical dynamics with parity-time symmetry
• Pseudo PT symmetric lattice
• Systems that become $\mathcal{P}\mathcal{T}$ symmetric through interaction
• Pseudo-conservative dynamics of coupled polariton condensates
• Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides
• Parity-Time Synthetic Laser
• Parity-time-symmetric coupled microring lasers operating around an exceptional point
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Controlling of blow-up responses by a nonlinear $\mathcal{P}\mathcal{T}$ symmetric coupling
• PT-symmetric transport in non-PT-symmetric bi-layer optical arrays
• Sublattice signatures of transitions in a $\mathcal{P}\mathcal{T}$-symmetric dimer lattice
• Nonlinear modes and symmetries in linearly-coupled pairs of PT-invariant dimers
• Solitons and their ghosts in PT-symmetric systems with defocusing nonlinearities
• Frequency comb generation for wave transmission through the nonlinear dimer
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Parity-Time Symmetry Breaking in Coupled Nanobeam Cavities
• Spontaneous Symmetry Breaking In Nonlinear Binary Periodic Systems
• Stability band structure for periodic states in periodic potentials