Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems

Abstract

Recent progress on nonlinear properties of parity-time ($\mathcal{P}\mathcal{T}$-) symmetric systems is comprehensively reviewed in this article. $\mathcal{P}\mathcal{T}$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\mathcal{P}\mathcal{T}$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\mathcal{P}\mathcal{T}$-symmetric system. The natural inclusion of nonlinearity into these $\mathcal{P}\mathcal{T}$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\mathcal{P}\mathcal{T}$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\mathcal{P}\mathcal{T}$-symmetric systems arising from various physical disciplines are presented; nonlinear properties of these systems are thoroughly elucidated; and relevant experimental results are described. In addition, emerging applications of $\mathcal{P}\mathcal{T}$ symmetry are pointed out.

Review paper; to appear in Reviews of Modern Physics. 65 two-column pages, 46 figures. Link to the abstract online at the RMP site: http://journals.aps.org/rmp/accepted/dd07cE7bE181340ae03857487ac98892c5c69e322

References in corpus (69)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Coherent Perfect Absorbers: Time-reversed Lasers
• Loss-induced suppression and revival of lasing
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Quantum trajectories and open many-body quantum systems
• Unidirectional Nonlinear PT-symmetric Optical Structures
• PT-Symmetric Phonon Laser
• Nonlinear properties of left-handed metamaterials
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Quantum Zeno dynamics: mathematical and physical aspects
• Solitons in PT-symmetric nonlinear lattices
• Spin-orbit coupled Bose-Einstein condensates
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Mathematical and physical aspects of complex symmetric operators
• Bifurcation diagram and pattern formation in superconducting wires with electric currents
• Breathers in PT-symmetric optical couplers
• Beyond mean-field dynamics in open Bose-Hubbard chains
• Stable dark solitons in PT-symmetric dual-core waveguides
• Bragg solitons in nonlinear PT-symmetric periodic potentials
• Optical mesh lattices with PT-symmetry
• Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
• Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity
• Refractive Index Enhancement with Vanishing Absorption in an Atomic Vapor
• Stable localized modes in asymmetric waveguides with gain and loss
• A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
• Families of stationary modes in complex potentials
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Discrete solitons in PT-symmetric lattices
• PT-symmetric Deformations of the Korteweg-de Vries Equation
• The Discrete Nonlinear Schrödinger equation - 20 Years on
• Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
• Symmetry breaking of solitons in two-dimensional complex potentials
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Interactions of Hermitian and non-Hermitian Hamiltonians
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Nonlinear PT-symmetric plaquettes
• Modulation instability in nonlinear complex parity-time (PT) symmetric periodic structures
• PT-symmetry in optics beyond the paraxial approximation
• Perturbation theory of PT-symmetric Hamiltonians
• Multi-stability and condensation of exciton-polaritons below threshold
• Supersolitons: Solitonic excitations in atomic soliton chains
• Discrete solitons and scattering of lattice waves in guiding arrays with a nonlinear $\mathcal{P}\mathcal{T}$-symmetric defect
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Resonant mode conversion in the waveguides with an unbroken and broken PT-symmetry
• CP symmetry in optical systems
• Spectral Singularities and CPA-Laser Action in a Weakly Nonlinear PT-Symmetric Bilayer Slab
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers
• PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
• Generalized Dimers and their Stokes-variable Dynamics
• Global existence of solutions to coupled $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger equations
• PT-symmetric sine-Gordon breathers
• Integrable models from PT-symmetric deformations
• Euler Incognito
• $\mathcal{P}\mathcal{T}$-symmetric ladders with a scattering core
• Some case example exact solutions for quadratically nonlinear optical media with $\mathcal{P}\mathcal{T}$-symmetric potentials
• Bifurcation of nonlinear eigenvalues in problems with antilinear symmetry
• PT-symmetry in macroscopic magnetic structures

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• Spacing gain and absorption in a simple $\mathcal{P}\mathcal{T}$-symmetric model: spectral singularities and ladders of eigenvalues and resonances
• Complex entanglement entropy for complex conformal field theory
• Topological gap solitons in a 1D non-Hermitian lattice
• Chiral phase modulation and tunable broadband perfect absorber using the coherent cold atomic ensemble
• Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions
• Origin of robust exceptional points: a restricted bulk zero mode
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Analytic eigenvalue structure of a coupled oscillator system beyond the ground state
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• Exceptional second-order topological insulators
• Modes and exceptional points in waveguides with impedance boundary conditions
• Krein signature for instability of $\mathcal{P}\mathcal{T}$-symmetric states
• Composite Quantum Phases in Non-Hermitian Systems
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Non-Hermitian off-diagonal disordered optical lattices
• $\mathcal{P}\mathcal{T}$-symmetric photonic lattices with type-II Dirac cones
• Optical solitons in periodically managed PT-symmetric media
• Impurity in a Fermi gas under non-Hermitian spin-orbit coupling
• Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Making the PT symmetry unbreakable
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Continuous families of non-Hermitian surface solitons
• Simultaneous Quantum Squeezing of Light Polarizations and Atomic Spins in a Cold Atomic Gas
• Non-Hermitian physics and engineering in silicon photonics
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Exceptional Points in Gyrator-Based Circuit and Nonlinear High-Sensitivity Oscillator
• Polarization dynamics of trapped polariton condensates with $\mathcal{P}\mathcal{T}$-symmetry
• Quantum phases transition revealed by the exceptional point in Hopfield-Bogoliubov matrix
• Adjusting exceptional points using saturable nonlinearities
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry
• Nonlinear behaviors of parity-time-symmetric lasers
• Exact States in Waveguides With Periodically Modulated Nonlinearity
• Gain engineering and atom lasing in a topological edge state in synthetic dimensions
• Controllable suppression of Non-Hermitian skin effects
• Hybrid patterns and solitonic frequency combs in non-Hermitian Kerr Cavities
• Resonant scattering of two-dimensional honeycomb PT dipole structure
• Mechanochemical feedback drives complex inertial dynamics in active solids
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Non-linear Schr$\ddot{o}$dinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Quantumness and its hierarchies in PT-symmetric down-conversion models
• Defect-driven incoherent skin localization
• Recent advances in the combination of nonlinearity and exceptional points
• Unidirectional segregation of Bright-Bright soliton through a $\mathcal{P}\mathcal{T}$-symmetric potential
• Manipulating Quantum Spins by a Spin-Polarized Current: An Approach Based Upon PT-Symmetric Quantum Mechanics
• Negative Gilbert damping in cavity optomagnonics
• Creating moving gap solitons in spin-orbit-coupled Bose-Einstein condensates
• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Nonlinear Schrödinger equations with amplitude-dependent Wadati potentials
• Non-Hermitian Hopf insulators
• Existence and Stability of Dissipative Solitons in a Dual-Waveguide Lattice with Linear Gain and Nonlinear Losses
• Can a photonic thermalization gap arise in disordered non-Hermitian Hamiltonian systems?
• Global search for localised modes in scalar and vector nonlinear Schrödinger-type equations
• On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system
• Stability restoration by asymmetric nonlinear states in non-Hermitian double-well potentials
• A systematic construction of parity-time ($\mathcal{P}\mathcal{T}$)-symmetric and non-$\mathcal{P}\mathcal{T}$-symmetric complex potentials from the solutions of various real nonlinear evolution equations
• Dynamic transition of the density-matrix topology under parity-time symmetry
• PT-symmetric and antisymmetric nonlinear states in a split potential box
• Dual opposing quadrature-PT symmetry
• Fundamental issues with light propagation through $\mathcal{P}\mathcal{T}$-symmetric systems
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Self-trapped spatially localized states in combined linear-nonlinear periodic potentials
• Beyond the Petermann limit: can exceptional points increase sensor precision?
• Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I Symmetry preserving and symmetry breaking solutions
• Long time asymptotic behavior for the nonlocal nonlinear Schrödinger equation with weighted Sobolev initial data
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Bosonic Holes in Quadratic Bosonic Systems
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
• Quantum transport in nonlinear Rudner-Levitov models
• Soliton dynamics and stability in the ABS spinor model with a PT-symmetric periodic potential
• A Hermitian bypass to the non-Hermitian quantum theory
• Bright solitons in a PT-symmetric chain of dimers
• Classical Hamiltonian Systems with Balanced loss and gain
• Propagation of light through amplifying honeycomb photonic lattice
• Spontaneous symmetry emergence in a Hermitian system of coupled oscillators without symmetry
• On general rogue waves in the parity-time-symmetric nonlinear Schrodinger equation
• Tunable photon blockade in a whispering-gallery-mode microresonator coupled with two nanoparticles
• Synthetic high-order PT symmetry in a single coil resonator
• On non-existence of continuous families of stationary nonlinear modes for a class of complex potentials
• Superexponential amplification, power blowup, and solitons sustained by non-Hermitian gauge potentials
• Broadband quasi-PT Symmetry Sustained by Inhomogeneous Broadening of the Spectral Line
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry
• Characteristics of rogue waves in the scalar and vector nonlocal nonlinear Schrödinger equations
• A unified inverse scattering transform and soliton solutions of the nonlocal modified KdV equation with non-zero boundary conditions
• Non-Hermitian superintegrable systems
• A class of 2x2 correlated random-matrix models with Brody spacing distribution
• Localization with non-Hermitian off-diagonal disorder
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics
• Gain-loss-engineering: a new platform for extreme anisotropic thermal photon tunneling
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Stability band structure for periodic states in periodic potentials
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• State Diagram of the Non-Reciprocal Cahn-Hilliard Model and the Effects of Symmetry
• Floquet multiple exceptional points with higher-order skin effect
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing
• Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations
• Characteristic influence of exceptional points in quantum dynamics
• Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials
• Darboux transformations and solutions of nonlocal Hirota and Maxwell-Bloch equations
• Reductions of nonlocal nonlinear Schrödinger equations to Painlevé type functions
• Linear and integrable nonlinear evolution of the qutrit
• Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with PT-symmetry
• Theory of light diffusion through amplifying photonic lattice
• Large Chern numbers in a dissipative dice model
• Non-linear and weak-coupling expansion in Quantum Field Theory
• Pursuing complex optical energy through Exceptional Points of Degeneracy (EPDs)
• Solitary waves in the resonant nonlinear Schrödinger equation: stability and dynamical properties
• Construction of non-PT-symmetric complex potentials with all-real spectra
• Editorial (a preface to a Special Issue of journal Applied Sciences on "Guided-Wave Optics")
• Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity