Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities

Abstract

Optical systems combining balanced loss and gain profiles provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time- (PT-) symmetric Hamiltonians and to originate new synthetic materials with novel properties. To date, experimental works on PT-symmetric optical systems have been limited to waveguides in which resonances do not play a role. Here we report the first demonstration of PT-symmetry breaking in optical resonator systems by using two directly coupled on-chip optical whispering-gallery-mode (WGM) microtoroid silica resonators. Gain in one of the resonators is provided by optically pumping Erbium (Er3+) ions embedded in the silica matrix; the other resonator exhibits passive loss. The coupling strength between the resonators is adjusted by using nanopositioning stages to tune their distance. We have observed reciprocal behavior of the PT-symmetric system in the linear regime, as well as a transition to nonreciprocity in the PT symmetry-breaking phase transition due to the significant enhancement of nonlinearity in the broken-symmetry phase. Our results represent a significant advance towards a new generation of synthetic optical systems enabling on-chip manipulation and control of light propagation.

13 Pages, 5 figures, 35 References

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• Analysis of a Triple-cavity Photonic Molecule Based on Coupled Mode Theory
• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• Vertical-Cavity In-plane Heterostructures: Physics and Applications
• Chiral Symmetry Breaking in Micro-Ring Optical Cavity By Engineered Dissipation
• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• Shape-preserving beam transmission through non-Hermitian disordered lattices
• Encircling the Liouvillian exceptional points: a brief review
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Prethermalization and nonreciprocal phonon transport in a levitated optomechanical array
• Scattering properties of PT-symmetric objects
• Observation of flat-band and band transition in the synthetic space
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Non-reciprocal geometric phase in nonlinear frequency conversion
• Critical features of nonlinear optical isolators for improved nonreciprocity
• Ab initio investigation of lasing thresholds in photonic molecules
• Bose-Einstein condensates with balanced gain and loss beyond mean-field theory
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Localized Single Frequency Lasing States in a Finite Parity-Time Symmetric Resonator Chain
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• Non-reciprocity and zero reflection in nonlinear cavities with tailored loss
• Unidirectional zero reflection as gauged parity-time symmetry
• Scattering-free pulse propagation through invisible non-Hermitian disorder
• Interaction effects on $\mathcal{P}\mathcal{T}$-symmetry breaking transition in atomic gases
• Topological Protection in non-Hermitian Haldane Honeycomb Lattices
• Asymmetric Transmission in Photonic Structures with Phase-Change Components
• Entanglement Dynamics in Anti-$\mathcal{P}\mathcal{T}$-Symmetric Systems
• Continuous-variable entanglement generated with a hybrid PT-symmetric system
• Bulk vortices and half-vortex surface modes in parity-time-symmetric media
• Controlling decoherence via $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian open quantum systems
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• Dynamical phase diagram of parity-time symmetry with competing saturable channels
• Magnified imaging based on non-Hermitian nonlocal cylindrical metasurfaces
• Energy-level-attraction and heating-resistant-cooling of mechanical resonators with exceptional points
• Towards perturbative renormalization of ${\varphi }^2(i\varphi {)}^{\epsilon }$ quantum field theory
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Symmetry-induced higher-order exceptional points in two dimensions
• Towards nanoscale multiplexing with parity-time symmetric plasmonic coaxial waveguides
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
• Anomalous Parity-Time Symmetry Transition away from an Exceptional Point
• Chiral state transfer under dephasing
• Anti-parity-time symmetry hidden in a damping linear resonator
• Piecewise Adiabatic Following in Non-Hermitian Cycling
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Broadband and Wide-Angle Nonreciprocity with a Nonhermitian Metamaterial
• Non-reciprocal Optical Mirrors Based on Spatio-Temporal Modulation
• PT-symmetric phase in kagome photonic lattices
• Realization of the unidirectional amplification in a cavity magnonic system
• New perspective on chiral exceptional points with application to discrete photonics
• Nonreciprocal conversion between radio-frequency and optical photons with an optoelectromechanical system
• Behavior of eigenvalues in a region of broken-PT symmetry
• Quantum centrality testing on directed graphs via PT-symmetric quantum walks
• Scattering properties of anti-parity-time symmetric non-Hermitian system
• Real-time imaging of standing-wave patterns in microresonators
• Eigenvalue dynamics in the presence of non-uniform gain and loss
• Nonreciprocal directional dichroism at telecom wavelengths
• Transforming space with non-Hermitian dielectrics
• Giant frequency-selective near-field energy transfer in active--passive structures
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Non-Hermiticity-Induced Wave Confinement and Guiding in Loss-Gain-Loss Three-Layer Systems
• Coupling-induced nonunitary and unitary scattering in anti-PT-symmetric non-Hermitian systems
• Solitary waves of a PT-symmetric Nonlinear Dirac equation
• Observation of two PT transitions in an electric circuit with balanced gain and loss
• Parity-Time Symmetry in Coherently Coupled Vertical Cavity Laser Arrays
• Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss
• Enhanced response of non-Hermitian photonic systems near exceptional points
• Non-Hermitian Floquet invisibility
• Systematic pathway to $\mathcal{P}\mathcal{T}$ symmetry breaking in scattering systems
• Tunable two-dimensional laser arrays with zero-phase locking
• Dynamical encircling exceptional point in largely detuned multimode optomechanical system
• Symmetry-protected localized states at defects in non-Hermitian systems
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Experimental Observation of Partial Parity-Time Symmetry and Its Phase Transition with a Laser-Driven Cesium Atomic Gas
• Bandpass transmission spectra of a whispering-gallery microcavity coupled to an ultrathin fiber
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• A large-scale single-mode array laser based on a topological edge mode
• Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
• Signature of PT-symmetric non-Hermitian superconductivity in angle-resolved photoelectron fluctuation spectroscopy
• Exceptional points in oligomer chains
• Multimode interference induced optical nonreciprocity and routing in an optical microcavity
• Exponential sensitivity revival of noisy non-Hermitian quantum sensing with two-photon drives
• Controlling slow and fast light and dynamic pulse-splitting with tunable optical gain in a whispering-gallery-mode microcavity
• Bicomplex Hamiltonian systems in Quantum Mechanics
• Nonlinear wave dynamics near phase transition in $\mathcal{P}\mathcal{T}$-symmetric localized potentials
• On-demand Parity-Time symmetry in a lone oscillator through complex, synthetic gauge fields
• Unification of quantum Zeno-anti Zeno effects and parity-time symmetry breaking transitions
• $\mathcal{P}\mathcal{T}$ symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model
• Algebraic treatment of $\mathcal{P}\mathcal{T}$-symmetric coupled oscillators
• Quantum phase transition in a non-Hermitian XY spin chain with global complex transverse field
• Active tuning of hybridized modes in a heterogeneous photonic molecule
• Optical isolation induced by subwavelength spinning particle via spin-orbit interaction
• Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution
• Simulating topological materials with photonic synthetic dimensions in cavities
• Rotation sensing in two coupled whispering-gallery-mode resonators with loss and gain
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
• Connecting dissipation and noncommutativity: A Bateman system case study
• Exceptional point induced lasing dynamics in a non-Hermitian system
• Non-reciprocal mu-near-zero mode in PT-symmetric magnetic domains
• Robust zero modes in non-Hermitian systems without global symmetries
• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
• Unique optical characteristics of a Fabry-Perot resonator with embedded PT-symmetrical grating
• Virtual exceptional points in an electromechanical system
• Exceptional point induced quantum phase synchronization and entanglement dynamics in mechanically coupled gain-loss oscillators
• Cavity solitons in a microring dimer with gain and loss
• Hidden PT Symmetry and quantization of coupled-oscillators model of QASER
• Novel PT-invariant Solutions For a Large Number of Real Nonlinear Equations
• Light propagation in periodically modulated complex waveguides
• Quantum state discrimination in a PT-symmetric system
• Classical Purcell factors and spontaneous emission decay rates in a linear gain medium
• Random matrix ensembles for $PT$-symmetric systems
• Dynamical signature of moire pattern in non-Hermitian ladder
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Laser Mode Bifurcations Induced by $\mathcal{P}\mathcal{T}$-Breaking Exceptional Points
• Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• Dynamic Nonreciprocity with a Kerr Nonlinear Resonator
• Experimentally Accessible Quantum Phase Transition in a non-Hermitian Tavis-Cummings Model Engineered with Two Drive Fields
• Tweaking Spectral Topology and Exceptional Points by Nonlinearity in Non-Hermitian Polariton Systems
• High-order spectral singularity
• Bulk-edge correspondence and stability of multiple edge states of a $\mathcal{P}\mathcal{T}$ symmetric non-Hermitian system by using non-unitary quantum walks
• PT -symmetric rational Calogero model with balanced loss and gain
• Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations
• Exponentially Enhanced non-Hermitian Cooling
• PT-symmetric quantum oscillator in an optical cavity
• Active Polarization Control with a Parity-Time Symmetric Plasmonic Resonator
• Characterizing and Tuning Exceptional Points Using Newton Polygons
• Few-photon optical diode in a chiral waveguide
• Non-Hermitian gauge field theories and BPS limits
• Detecting topological exceptional points in a parity-time symmetric system with cold atoms
• Experimentally-realizable $\mathcal{P}\mathcal{T}$ phase transitions in reflectionless quantum scattering
• Optomechanical devices based on traveling-wave microresonators
• Nonreciprocal quantum phase transition in cavity magnonics
• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• Restricted Hilbert transform for non-Hermitian management of fields
• Nonreciprocal light propagation induced by a subwavelength spinning cylinder
• Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance
• Optomechanically induced transparency and directional amplification in a non-Hermitian optomechanical lattice
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Observation of exceptional point in a PT broken non-Hermitian system simulated using a quantum circuit
• Balanced gain and loss in Bose-Einstein condensates without PT symmetry
• Open quantum systems with loss and gain
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• Quantum transport in non-Hermitian impurity array
• Kerr Nonlinearity Induced Nonreciprocity in dissipatively coupled resonators
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• Excitation of whispering gallery modes with a "point-and-play", fiber-based, optical nano-antenna
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Quantum deleting and cloning in a pseudo-unitary system
• Detecting the effects of quantum gravity with exceptional points in optomechanical sensors
• Universal Route for the Emergence of Exceptional Points in PT-Symmetric Metamaterials with Unfolding Spectral Symmetries
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices
• Nonhermitian defect states from lifetime differences
• Giant non-reciprocity and gyration through modulation-induced Hatano-Nelson coupling in integrated photonics
• Solitary waves in the Nonlinear Dirac Equation
• Unitary Scattering Protected by Pseudo-Hermiticity
• Parity-time symmetry under magnetic flux
• Quantum decay and amplification in a non-Hermitian unstable continuum
• Integrable nonlinear parity-time symmetric optical oscillator
• Faraday effect in rippled graphene: Magneto-optics and random gauge fields
• Amplified and directional spontaneous emission from arbitrary composite bodies: self-consistent treatment of Purcell effect below threshold
• Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Generalized Dimers and their Stokes-variable Dynamics
• Observing a Changing Hilbert-Space Inner Product
• Non-Bloch PT symmetry breaking: Universal threshold and dimensional surprise
• Broadband mixing of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-broken phases in photonic heterostructures with a one-dimensional loss/gain bilayer
• Moving along an exceptional surface towards a higher-order exceptional point
• Helical resonant transport and purified amplification at an exceptional point
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Maxwell's demon-like nonreciprocity by non-Hermitian gyrotropic metasurfaces
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Enhancing the sensitivity of nonlinearity sensors through homodyne detection in dissipatively coupled systems
• Resonant interaction of ${\varphi }^4$ kink with spatially periodic $\mathcal{P}\mathcal{T}$-symmetric perturbation
• PT-symmetric sine-Gordon breathers
• Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling
• The combination of directional outputs and single-mode operation in circular microdisk with broken PT symmetry
• Cavity controlled spectral singularity
• One-Way Optical Transition based on Causality in Momentum Space
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory
• Work statistics in non-Hermitian evolutions with Hermitian endpoints
• Coherent control of magnon-polaritons using an exceptional point
• Direct observation of energy band attraction effect in non-Hermitian systems
• Controlling lasing around Exceptional Points in Coupled Nanolasers
• Parity-time symmetry and coherent perfect absorption in a cooperative atom response
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension
• Theory and Numerical Modelling of Parity-Time Symmetric Structures in Photonics: Introduction and Grating Structures in One Dimension
• Single-mode magnon-polariton lasing and amplification controlled by dissipative coupling
• Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry
• Anomalous spontaneous emission dynamics at chiral exceptional points
• $\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function
• Fabrication of a microresonator-fiber assembly maintaining a high-quality factor by CO2 laser welding
• On regular and chaotic dynamics of a non-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
• Transparent Perfect Mirror
• Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{R}\mathcal{T}$ symmetry
• Partially dark optical molecule via phase control
• Controllable distant interactions at bound state in the continuum
• Eigenstates Transition Without Undergoing an Adiabatic Process
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Enhancing the quantum entanglement and EPR steering of a coupled optomechanical system with a squeezed vacuum field
• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• Constructing the scattering matrix for optical microcavities as a nonlocal boundary value problem
• All-optical transistor based on Rydberg atom-assisted opto-mechanical system
• Experimental investigation of uncertainty relations for non-Hermitian operators
• A passive bias-free ultrabroadband optical isolator based on unidirectional self-induced transparency
• Transition from degeneracy to coalescence: theorem and applications
• Universal quantum control by non-Hermitian Hamiltonian
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Exceptional Point modulated by Kerr effect in Anti-Parity-Time Symmetry System
• Floquet topological phase in a generalized PT-symmetric lattice
• Exceptional point in a coupled Swanson system
• Gain assisted controllable fast light generation in cavity magnomechanics
• Observing Parity Time Symmetry Breaking in a Josephson Parametric Amplifier
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Optically induced nonreciprocity by a plasmonic pump in semiconductor wires
• Engineering Optomechanically Induced Transparency by coupling a qubit to a spinning resonator
• $\mathcal{P}\mathcal{T}$ symmetry-protected exceptional cones and analogue Hawking radiation
• Comprehensive understanding of parity-time transitions in $\mathcal{P}\mathcal{T}$ symmetric photonic crystals with an antiunitary group theory
• Integrable coupled Li$\acute{e}$nard-type systems with balanced loss and gain
• Strong magneto-optical response enabled by quantum two level systems
• Quantization of magnetoelectric fields
• Coalescing Majorana edge modes in non-Hermitian PT-symmetric Kitaev chain
• Coherent population oscillations and an effective spin-exchange interaction in a $\mathcal{P}\mathcal{T}$ symmetric polariton mixture
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Wireless energy transfer in non-Hermitian quantum battery
• Taming Hamiltonian systems with balanced loss and gain via Lorentz interaction : General results and a case study with Landau Hamiltonian
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit
• Necklaces of $\mathcal{P}\mathcal{T}$-symmetric dimers
• Tunable atom-cavity interactions with configurable atomic chains
• Parity-time symmetric systems with memory
• Surface plasmon-polaritons in graphene, embedded into medium with gain and losses
• Effects of non-uniform distributions of gain and loss in photonic crystals
• Interaction-Induced Second-Order Skin Effect
• Higher-order interactions in quantum optomechanics: Analytical solution of nonlinearity
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Variational Approach to studying solitary waves in the nonlinear Schrodinger equation with Complex Potentials
• Phase-controlled Optical PT symmetry and asymmetric light diffraction in one- and two-dimensional optical lattices
• Non-Markovian anti-parity-time symmetric systems: theory and experiment
• Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model
• Unconventional Photon blockade in a Photonic Molecule Containing a Quantum Dot
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Linear localization of zero modes in weakly coupled non-Hermitian reservoirs
• Eigenfrequency splitting with EPs order tunability in a coupled triple cavity system
• Oscillating potential well in complex plane and the adiabatic theorem
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Anomalous Hall effect from a non-Hermitian viewpoint
• Parity-time-symmetric coupled microring lasers operating around an exceptional point
• General theory for infernal points in non-Hermitian systems
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons
• Effects of the third-order dispersion on continuous waves in complex potentials
• Non-Hermitian matter wave mixing in Bose Einstein condensates: dissipation induced amplification
• Nonlinear adiabatic optical isolator
• All-optical $\mathcal{P}\mathcal{T}$-symmetric amplitude to phase modulator
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Parity-Time Synthetic Laser
• Quantum correlations in dissipative gain-loss systems across exceptional points
• Photon propagation through linearly active dimers
• A Concept of Linear Thermal Circulator Based on Coriolis forces
• Overcoming the diffraction limit on the size of dielectric resonators using an amplifying medium
• Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Pseudo-conservative dynamics of coupled polariton condensates
• Coherent single-spin electron resonance spectroscopy manifested at an exceptional-point singularity in a doped polyacetylene
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Exceptional point enhanced optical gyroscope in mechanical PT-symmetric system
• PT-symmetric gain and loss in a rotating Bose-Einstein condensate
• Stability of new exact solutions of the nonlinear Schrodinger equation in a Poschl-Teller external potential
• Loss compensation symmetry in dimers made of gain and lossy nanoparticles
• $\mathcal{P}\mathcal{T}$-symmetric currents of a Bose-Einstein condensate in a triple well
• Unconventional steady states and topological phases in an open two-level non-Hermitian system
• Quantum-optical implementation of non-Hermitian potentials for asymmetric scattering
• Optomechanical preparation of photon number-squeezed states with a pair of thermal reservoirs of opposite temperatures
• Two-way enhancement of sensitivity by tailoring higher-order exceptional points
• Impact of non-Hermitian Mode interaction on Inter-cavity Light transfer
• Highly Amplified Light Transmission in Parity-Time Symmetric Multilayered Structure
• Dynamical evolution of an effective two-level system with PT symmetry
• Spacing gain and absorption in a simple $\mathcal{P}\mathcal{T}$-symmetric model: spectral singularities and ladders of eigenvalues and resonances
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Controlling properties of a hybrid Cooper pair box interacting with a nanomechanical resonator in the presence of Kerr nonlinearities and losses
• Diamond Configuration for Non-reciprocal Transmission
• Optical isolators based on non-reciprocal four-wave mixing
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Dynamics of mode entanglement in a system of cavities coupled with a chiral mirror
• Dual-carrier Floquet circulator with time-modulated optical resonators
• Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems
• Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
• Non-Hermitian engineering for brighter broadband pseudothermal light
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Proposal for measuring Newtonian constant of gravitation at an exceptional point in an optomechanical system
• Influence of the bus waveguide on the linear and nonlinear response of a taiji microresonator
• Gain-compensated cavities for the dynamic control of light-matter interactions
• Emergent non-Hermitian physics in generalized Lotka-Volterra model
• Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{P}\mathcal{T}$- and supersymmetric potential
• Enhanced quantum sensing in time-modulated non-Hermitian systems
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Enhancement of signal-to-noise ratio at a high-order exceptional point of coherent perfect absorption
• Stability of exact solutions of the nonlinear Schroedinger equation in an external potential having supersymmetry and parity-time symmetry
• Quantum noise induced nonreciprocity for single photon transport in parity-time symmetric systems
• Enhanced quantum sensing with hybrid exceptional-diabolic singularities
• Controllable non-Hermitian qubit-qubit Coupling in Superconducting quantum Circuit
• Electrical tunability due to coalescence of exceptional points in parity-time symmetric waveguides
• Lopsided optical diffraction in loop electromagnetically induced grating
• Scattering off PT-symmetric upside-down potentials
• Resonant-amplified and invisible Bragg scattering based on spin coalescing modes
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Theory for the spectral splitting exponent of exceptional points
• On-chip optical isolator and nonreciprocal parity-time symmetry induced by stimulated Brillouin scattering
• Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics
• Superoscillatory PT-symmetric potentials
• Radiation families emitted by a discrete soliton in parity-time-symmetric waveguide arrays
• Nonlinear PT-symmetric models bearing exact solutions
• An attractor dynamics in a non-Hermitian two-level system
• Making the PT symmetry unbreakable
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Perpetual emulation threshold of PT-symmetric Hamiltonians
• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Zero-Threshold PT-Symmetric Polariton-Raman Laser
• Efficient and controlled symmetric and asymmetric Bell-state transfers in a dissipative Jaynes-Cummings model
• Enhanced response at exceptional points in multi-qubit systems for sensing
• Design algorithms of driving-induced nonreciprocal components
• Semi-localization transition driven by a single asymmetrical tunneling
• Purely Quantum Nonreciprocity by Spatially Separated Transmission Scheme
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Nonreciprocity of intense light field and weak quantum signal in optomechanical systems with three-mode parametric interactions
• Nonlinear behaviors of parity-time-symmetric lasers
• Local preservation of no-signaling in multiparty PT-symmetric evolutions
• PT-symmetric microring lasers: Self-adapting broadband mode-selective resonators
• Non-Hermitian physics and engineering in silicon photonics
• PT-symmetry enabled spintronic thermal diode and logic gates
• Topological Engineering of High-Order Exceptional Points through Transformation Optics
• Gap solitons and symmetry breaking in parity-time symmetric microring CROWs
• Chiral-reversing vortex radiation from a single emitter by eigenstates phase locking
• 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
• Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering
• Spectral singularities of a potential created by two coupled microring resonators
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• PT-symmetric transport in non-PT-symmetric bi-layer optical arrays
• PT-Symmetric Model of Immune Response
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• Recent advances in the combination of nonlinearity and exceptional points
• Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid Light-Matter System
• Supersymmetrically bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states
• Quantumness and its hierarchies in PT-symmetric down-conversion models
• Conserved quantities in non-Hermitian systems via vectorization method
• Atom-driven multistability in an optomechanical cavity under broken PT-symmetry
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Monopoles in non-Hermitian systems
• Quantum transport in coupled resonators enclosed synthetic magnetic flux
• Multitype entanglement dynamics induced by exceptional points
• Parallel dynamics between non-Hermitian and Hermitian systems
• Transformation cavities with a narrow refractive index profile
• Engineering wavefront caustics trajectories in $\mathcal{P}\mathcal{T}$-symmetric lattices
• Cavity Continuum
• Manipulating spectral transitions and photonic transmission in a non-Hermitian optical system through nanoparticle perturbations
• Exotic light transition between superluminal and subliminal group velocity in a $\mathcal{P}\mathcal{T}$ coupled slab waveguide
• Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{P}\mathcal{T}-$symmetry
• Opto-thermal dynamics in whispering-gallery microresonators
• Self-induced nonreciprocity from asymmetric photonic topological insulators
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• High-Q longwave infrared microresonators based on a non-epitaxial germanium platform
• Interaction induced non-reciprocal three-level quantum transport
• Dynamic suppression of Rayleigh light scattering in dielectric resonators
• PT-symmetric and antisymmetric nonlinear states in a split potential box
• EP restoration and fast-light edge states in photonic crystal waveguide with glide and time reversal symmetry
• Improved coherence time of a non-Hermitian qubit in a $\mathcal{P}\mathcal{T}$-symmetric Environment
• Effective size of a parity-time symmetric dimer
• Diffusive Topological Transport in Spatiotemporal Thermal Lattices
• Sublattice signatures of transitions in a $\mathcal{P}\mathcal{T}$-symmetric dimer lattice
• Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics
• Wireless whispering-gallery-mode sensor for thermal sensing and aerial mapping
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Thermodynamic properties of non-Hermitian Nambu--Jona-Lasinio models
• Coherent confinement and unidirectional dynamics of a wave packet induced by a non-Hermitian Su-Schrieffer-Heeger segment
• Computation and Verification of Spectra for Non-Hermitian Systems
• Third-order exceptional surface in a pseudo-Hermitian superconducting circuit
• Noisy Stark probes as quantum-enhanced sensors
• Connections Between Complex PT-Invariant Solutions and Complex Periodic Solutions of Several Nonlinear Equations
• Squeezing enhanced sensing at an exceptional point
• An asymptotic field approach for the control of dipole emission in integrated structures
• Homodyne Measurement of a Non-Hermitian Qubit Undergoing Fluorescence
• Non-Hermitian topological filters
• Universal quantum control over non-Hermitian continuous-variable systems
• Enhancing Nonreciprocity through Squeezing-Induced Symmetry Breaking
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
• Tunable chiral spiral phases in a non-Hermitian Ising-Gamma spin chain
• Purity oscillations in coupled Bose-Einstein condensates
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Synchronization in PT-symmetric optomechanical resonators
• Classical Hamiltonian Systems with Balanced loss and gain
• Electrically Pumped Single Transverse-Mode Coupled Waveguide Lasers by Parity-time (PT) Symmetry
• Optical trimer: A theoretical physics approach to waveguide couplers
• Multiphoton controllable transport between remote resonators
• Sign-Reversal Coupling in Coupled-Resonator Optical Waveguide
• Real spectra and phase transition of skin effect in nonreciprocal systems
• A tale of two kinds of exceptional point in a hydrogen molecule
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Broadband non-reciprocal transmission of sound with invariant frequency
• Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems
• Observation of parity-time symmetry in electrically pumped FP laser
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: I. Inherited and genuine singularities
• Stronger sum uncertainty relations for non-Hermitian operators
• Pursuing complex optical energy through Exceptional Points of Degeneracy (EPDs)
• Complex dynamical properties of coupled Van der Pol-Duffing oscillators with balanced loss and gain
• Parity-Time Symmetry Breaking in Coupled Nanobeam Cavities
• Nonclassical light at exceptional points of a quantum PT-symmetric two-mode system
• Non-linear and weak-coupling expansion in Quantum Field Theory
• Genetic optimization Invents non-Hermitian potentials for Asymmetric Reflectivity
• Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems
• Properties and Application of Gaussian Quantum Processes
• Nonreciprocal Coupling Induced Non-Hermitian Entanglement in Optomechanical Systems
• Tunable photon blockade in a two-mode second-order nonlinear system embedded with a two-level atom
• One-directional polarization transport in electron/nuclear spin chains with loss and gain
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials
• Robust photon transmission in nonlinear parity-time-symmetric cavities
• Stability via symmetry breaking in interacting driven systems
• Three-level Λ-type atomic systems with a Pseudo-Hermitian PT-symmetric Hamiltonian
• Widely tunable optoelectronic oscillator based on selective parity-time-symmetry breaking
• Localization of states, Bloch wave and quantum phase transitions in SUSY deformed potentials in non-Hermitian optical systems
• Nonreciprocal electrical transport in linear systems with balanced gain and loss in the bulk
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Computing eigenfunctions and eigenvalues of boundary value problems with the orthogonal spectral renormalization method
• Molecular-optomechanical phonon laser
• Compound symmetries and double antisymmetry groups in linear time-invariant photonic systems
• Recurrence method in Non-Hermitian Systems
• Environment-assisted squeezing in a coherently driven non-Hermitian degenerate parametric oscillator
• Nonreciprocal photon bundle emission
• Synthetic high-order PT symmetry in a single coil resonator
• Out-of-time-order correlators for Swanson Hamiltonian with interaction terms
• Quantization of pseudo-hermitian systems
• Covariant formulation of the Berry connection in non-Hermitian systems
• Impact of noise on nonlinear-exceptional-point-based sensors
• The $\mathcal{P}\mathcal{T}$-symmetry-breaking transition in a chain of trapped interacting ions
• Enhancement of quantum sensing in a dissipatively coupled two-mode system
• Stability band structure for periodic states in periodic potentials
• Exploring Nonreciprocal Noise Transfer under Onsager-Casimir Symmetry in Synthetic-Field Optomechanics
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: II. Nonconventional PT-symmetric dynamics and unidirectional coupling
• Dissipation-induced bound states as a two-level system
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology
• Higher-order exceptional lines in a non-Hermitian JaynesCummings triangle
• Topology with broken parity-time symmetry
• A photonic integrated circuits with reconfigurablenonreciprocal transmission and all-opticalfunctionalities
• Construction of non-PT-symmetric complex potentials with all-real spectra
• Emergence of Hermitian topology from non-Hermitian knots
• Generalized Parity-Time Symmetry Condition for Enhanced Sensor Telemetry