Parity-Time Symmetry in Non-Hermitian Complex Optical Media

Abstract

The explorations of the quantum-inspired symmetries in optical and photonic systems have witnessed immense research interests both fundamentally and technologically in a wide range of subjects of physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory, recently ramified into diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant applications prospects and engineering of novel materials. In addition, it has observed increasing research interests in many emerging directions beyond optics and photonics. This Review paper attempts to bring together the state of the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings along with elucidating key concepts and background and a detailed perspective on new emerging directions. It can be anticipated that this trendy field of interest can be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, opto-electronics and beyond, and offer distinctive applications prospects in novel functional materials.

88 Pages, 18 Figures

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• Majorana Zero Modes and Topological Quantum Computation
• Coherent Perfect Absorbers: Time-reversed Lasers
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• Monolithic Ultrahigh-Q Lithium Niobate Microring Resonator
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• Unidirectional Nonlinear PT-symmetric Optical Structures
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• PT-Symmetric Phonon Laser
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Nanofabricated media with negative permeability at visible frequencies
• Reverse Doppler Effect of Sound
• Thresholdless Nanoscale Coaxial Lasers
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
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• Chiral groundstate currents of interacting photons in a synthetic magnetic field
• Introduction to PT-Symmetric Quantum Theory
• Second-Order Topological Phases in Non-Hermitian Systems
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Observation of parity-time symmetry breaking in a single spin system
• Faster than Hermitian Quantum Mechanics
• Topologically protected midgap states in complex photonic lattices
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Edge Solitons in Nonlinear Photonic Topological Insulators
• $\mathcal{P}\mathcal{T}$-Symmetry-Breaking Chaos in Optomechanics
• New topological invariants in non-Hermitian systems
• Observation of PT phase transition in a simple mechanical system
• Observation of Asymmetric Transport in Structures with Active Nonlinearities
• Artificial Gauge Field for Photons in Coupled Cavity Arrays
• Parity-time-symmetric quantum critical phenomena
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• PT-symmetry with a system of three-level atoms
• Stability of solitons in PT-symmetric couplers
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Nonlinear suppression of time-reversals in PT-symmetric optical couplers
• No exceptional precision of exceptional point sensors
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• Observation of Defect States in PT-Symmetric Optical Lattices
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Antisymmetric PT-photonic structures with balanced positive and negative index materials
• PT Metamaterials via Complex-Coordinate Transformation Optics
• Spontaneous mirror-symmetry breaking in a photonic molecule
• The quantum optical Josephson interferometer
• Supersymmetric Optical Structures
• High-order exceptional points in optomechanics
• The Naimark dilated PT-symmetric brachistochrone
• Supersymmetric mode converters
• Mixed-state evolution in the presence of gain and loss
• Parity-time-symmetric topological superconductor
• Observation of PT-symmetric quantum interference
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Mechanical PT symmetry in coupled optomechanical systems
• Non-Hermitean Localization and De-Localization
• Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
• Local PT symmetry violates the no-signaling principle
• PT-Symmetric Plasmonic Metamaterials
• PT-symmetric scattering in flow duct acoustics
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Topological phase in a non-Hermitian PT symmetric system
• Nonlinear reversal of PT symmetric phase transition in a system of coupled semiconductor micro-ring resonators
• Fluctuations and noise-limited sensing near the exceptional point of $\mathcal{P}\mathcal{T}$-symmetric resonator systems
• Exceptional contours and band structure design in parity-time symmetric photonic crystals
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Effective spontaneous PT-symmetry breaking in hybridized metamaterials
• Optomechanically Induced Transparency at Exceptional Points
• Experimental realization of Floquet PT-symmetric systems
• Supersymmetric Laser Arrays
• Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
• Constant-pressure sound waves in non-Hermitian disordered media
• Stable dark solitons in PT-symmetric dual-core waveguides
• Bragg solitons in nonlinear PT-symmetric periodic potentials
• Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
• $\mathcal{P}\mathcal{T}$-symmetric circuit-QED
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• PT-symmetric optical potentials in a coherent atomic medium
• Nonlinear modal interactions in parity-time ($\mathcal{P}\mathcal{T}$) symmetric lasers
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Unidirectional Localization of Photons
• Flat bands in lattices with non-Hermitian coupling
• Symmetry-protected zero-mode laser with a tunable spatial profile
• $\mathcal{P}\mathcal{T}$-symmetric microring laser-absorber
• Non-Abelian braiding of light
• SUSY-inspired one-dimensional transformation optics
• Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity
• A New Class of non-Hermitian Quantum Hamiltonians with PT Symmetry
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Odd-time reversal $PT$ symmetry induced by anti-$PT$-symmetric medium
• Simulating the exchange of Majorana zero modes with a photonic system
• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• Loss-induced transparency in optomechanics
• Tight-binding methods for general longitudinally driven photonic lattices -- edge states and solitons
• Quantum Geometric Tensor in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Supersymetric laser arrays
• Realizing PT-symmetric non-Hermiticity with ultra-cold atoms and Hermitian multi-well potentials
• Topological Bloch oscillations
• Supersymmetric microring laser arrays
• PT Symmetry via Electromagnetically Induced Transparency
• Theory of the spatial structure of non-linear lasing modes
• Unidirectional Lasing Emerging from Frozen Light in Non-Reciprocal Cavities
• PT Symmetric Floquet Topological Phase
• Half-spectral unidirectional invisibility in non-Hermitian periodic optical structures
• $\mathcal{P}\mathcal{T}$-symmetric slowing-down of decoherence
• Scattering in $\mathcal{P}\mathcal{T}$ and $\mathcal{R}\mathcal{T}$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension
• Controllable Asymmetric Phase-Locked States of the Fundamental Active Photonic Dimer
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
• Peregrine Rogue Wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity
• Optical Lattices with Higher-order Exceptional Points by Non-Hermitian Coupling
• Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers
• Self-hybridization within non-Hermitian plasmonic systems
• One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
• Non-adiabatic Modal Dynamics around Exceptional Points in an All-Lossy Dual-Mode Optical Waveguide: Towards Chirality Driven Asymmetric Mode-Conversion
• Statistical PT-symmetric lasing in an optical fiber network
• Type II Perfect Absorption and Amplification Modes with Controllable Bandwidth in PT-Symmetric/Traditional Bragg Grating Combined Structures
• Tailoring $\mathcal{P}\mathcal{T}$-symmetric soliton switch
• PT-symmetric quantum state discrimination
• On the bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors
• Symmetry in optics and photonics: a group theory approach
• Realizing and manipulating space-time inversion symmetric topological semimetal bands with superconducting quantum circuits
• Solitons in PT-symmetric ladders of optical waveguides
• Supersymmetry-guided method for mode selection and optimization in coupled systems
• Supercharge optical arrays
• Topological cascade laser for frequency comb generation in $\mathcal{P}\mathcal{T}$-symmetric structures
• Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles
• A note on topological insulator phase in non-hermitian quantum systems
• Anomalous Parity-Time Symmetry Transition away from an Exceptional Point
• Towards nanoscale multiplexing with parity-time symmetric plasmonic coaxial waveguides
• Embedding, simulation and consistency of $\mathcal{P}\mathcal{T}$ -symmetric quantum Theory
• Solitary waves in Parity-time (PT) symmetric Bragg-grating structure and the existence of Optical Rogue Waves
• Solitary waves of a PT-symmetric Nonlinear Dirac equation
• Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential
• Non-Hermitian heterostructure for two-parameter sensing
• Topological edge state engineering with high-frequency electromagnetic radiation
• Active Polarization Control with a Parity-Time Symmetric Plasmonic Resonator
• Solitary waves in the Nonlinear Dirac Equation
• Topological Flat Band and Parity-Time Symmetry in a Honeycomb Lattice of Coupled Resonant Optical Waveguides
• Asymmetric soliton mobility in competing linear-nonlinear PT-symmetric lattices

Cited by in corpus (28)

• Topological photonic crystals: physics, designs and applications
• Fermion doubling theorems in 2D non-Hermitian systems for Fermi points and exceptional points
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• High-order exceptional points in supersymmetric arrays
• Hybrid exceptional point created from type III Dirac point
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Spectral Properties of Disordered Interacting Non-Hermitian Systems
• Spatial Kramers-Kronig relation and controlled unidirectional reflection in cold atoms
• Third-order Exceptional Point and Successive Switching among Three States in a Degenerate Optical Microcavity
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• On-demand Parity-Time symmetry in a lone oscillator through complex, synthetic gauge fields
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Unitary Scattering Protected by Pseudo-Hermiticity
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Anderson localization induced by complex potential
• Pseudo-conservative dynamics of coupled polariton condensates
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential
• Resonant-amplified and invisible Bragg scattering based on spin coalescing modes
• $\mathcal{P}\mathcal{T}$-symmetric photonic lattices with type-II Dirac cones
• Quantumness and its hierarchies in PT-symmetric down-conversion models
• Scattering symmetry of diffusive systems
• Stability restoration by asymmetric nonlinear states in non-Hermitian double-well potentials
• Exceptional spectrum and dynamic magnetization
• Synthetic high-order PT symmetry in a single coil resonator