Encircling an Exceptional Point

Abstract

We calculate analytically the geometric phases that the eigenvectors of a parametric dissipative two-state system described by a complex symmetric Hamiltonian pick up when an exceptional point (EP) is encircled. An EP is a parameter setting where the two eigenvalues and the corresponding eigenvectors of the Hamiltonian coalesce. We show that it can be encircled on a path along which the eigenvectors remain approximately real and discuss a microwave cavity experiment, where such an encircling of an EP was realized. Since the wavefunctions remain approximately real, they could be reconstructed from the nodal lines of the recorded spatial intensity distributions of the electric fields inside the resonator. We measured the geometric phases that occur when an EP is encircled four times and thus confirmed that for our system an EP is a branch point of fourth order.

RevTex 4.0, four eps-figures (low resolution)

References in corpus (11)

• Repulsion of Resonance States and Exceptional Points
• Geometric phase in open systems
• The Chirality of Exceptional Points
• Observation of a Chiral State in a Microwave Cavity
• Phases of Wave Functions and Level Repulsion
• First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
• Off-Diagonal Geometric Phases
• Berry phase in a non-isolated system
• Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems
• Resource Letter GPP-1: Geometric Phases in Physics
• Exceptional points and double poles of the S matrix

Cited by in corpus (138)

• Non-Hermitian Physics
• The physics of exceptional points
• Topological Band Theory for Non-Hermitian Hamiltonians
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Non-reciprocal phase transitions
• Non-Hermitian Topology and Exceptional-Point Geometries
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Critical non-Hermitian Skin Effect
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Signatures of three coalescing eigenfunctions
• Experimental observation of exceptional surface in synthetic dimensions with magnon polaritons
• Perspective on topological states of non-Hermitian lattices
• Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Topological classification of non-Hermitian systems with reflection symmetry
• Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
• Observation of an exceptional point in a non-Hermitian metasurface
• Observation of Chiral State Transfer Without Encircling an Exceptional Point
• Non-Hermitian exceptional Landau quantization in electric circuits
• Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre
• Encircling exceptional points in a Riemann sphere for efficient asymmetric polarization-locked devices
• Projective Hilbert space structures at exceptional points
• Non-Hermitian phase transition from a polariton Bose-Einstein condensate to a photon laser
• Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions
• Chirality of wave functions for three coalescing levels
• Topological Modes in a Laser Cavity through Exceptional State Transfer
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Exceptional Bound States and negative Entanglement Entropy
• Exceptional Points and Asymmetric Mode Switching in Plasmonic Waveguides
• Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides
• Rabi Oscillations at Exceptional Points in Microwave Billiards
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Stochastic pump effect and geometric phases in dissipative and stochastic systems
• Topological quantum state control through exceptional-point proximity
• Magnetic suppression of non-Hermitian skin effects
• Parity-time symmetry in optical microcavity systems
• Spectral singularities in PT-symmetric periodic finite-gap systems
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Direct Measurement of Topological Properties of an Exceptional Parabola
• High order exceptional points in ultracold Bose gases
• Symmetry protected topological phases characterized by isolated exceptional points
• Self-dual Spectral Singularities and Coherent Perfect Absorbing Lasers without PT-symmetry
• Resolving the topology of encircling multiple exceptional points
• Parity-time symmetric coupled asymmetric dimers
• Exceptional points in the spectra of atoms in external fields
• Dynamical regimes of a quantum swap gate beyond the Fermi Golden Rule
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• Exotic interactions mediated by a non-Hermitian photonic bath
• Hybrid exceptional point created from type III Dirac point
• Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Inversion symmetric non-Hermitian Chern insulator
• Response strengths of open systems at exceptional points
• Spectral Singularities of a General Point Interaction
• Non-adiabatic Modal Dynamics around Exceptional Points in an All-Lossy Dual-Mode Optical Waveguide: Towards Chirality Driven Asymmetric Mode-Conversion
• Noise Constraints for Nonlinear Exceptional Point Sensing
• Time behaviour near to spectral singularities
• Parametric instability of non-Hermitian systems near the exceptional point
• Collectively induced exceptional points of quantum emitters coupled to nanoparticle surface plasmons
• Manipulating non-Hermitian skin effect via electric fields
• Third-order Exceptional Point and Successive Switching among Three States in a Degenerate Optical Microcavity
• Topology of multipartite non-Hermitian one-dimensional systems
• Experimental observation of exceptional bound states in a classical circuit network
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance
• Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
• Revisiting the hierarchical construction of higher-order exceptional points
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Interacting non-Hermitian ultracold atoms in a harmonic trap: Two-body exact solution and high-order exceptional point
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Non-hermitian exciton dynamics in a photosynthetic unit system
• Non-linear dynamics of the non-Hermitian Su-Schrieffer-Heeger model
• Non-Hermitian eigenvalue knots and their isotopic equivalence
• Pontryagin-Optimal Control of a non-Hermitian Qubit
• Harmonic inversion analysis of exceptional points in resonance spectra
• Nonlinearity Induced Anomalous Mode Collapsing and Non-chiral Asymmetric Mode Switching around multiple Exceptional Points
• Emergence of tunable exceptional points in altermagnet-ferromagnet junctions
• Higher order topological degeneracies and towards unique successive state-switching in a four-level open system
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Novel Topology and Manipulation of Scattering Singularities in Complex non-Hermitian Systems
• Tweaking Spectral Topology and Exceptional Points by Nonlinearity in Non-Hermitian Polariton Systems
• Detecting topological exceptional points in a parity-time symmetric system with cold atoms
• Non-orthogonal cavity modes near exceptional points in the far field
• Exceptional points in two simple textbook examples
• Probing Dark Universe with Exceptional Points
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Moving along an exceptional surface towards a higher-order exceptional point
• Formation of Exceptional Points in pseudo-Hermitian Systems
• Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems
• Information constraint in open quantum systems
• Experimental observation of exceptional points in coupled pendulums
• Quantization of magnetoelectric fields
• Universal quantum control by non-Hermitian Hamiltonian
• Floquet Protocols of Adiabatic State-Flips and Re-Allocation of Exceptional Points
• Non-Hermitian semi-Dirac semi-metals
• Exotic quantum holonomy induced by degeneracy hidden in complex parameter space
• Exceptional points treatment of cavity spectroscopies
• Spectral Singularities and Zero Energy Bound States
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Nonadiabatic Modal Dynamics Around a Third-order Exceptional Point in a planar waveguide
• Resonance scattering and singularities of the scattering function
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory
• Topological Phase Transition of A Non-Hermitian Crosslinked Chain
• Loss revives bistable state near the exceptional point in a non-Hermitian microwave photonic meta-molecule
• Spectral Singularities with Directional Sensitivity
• Non-hermitian time evolution: from static to parametric instability
• Nonadiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric two-level systems
• Correlations at higher-order exceptional points in non-Hermitian models
• Realization of geometric phase topology induced by multiple exceptional points
• Correlated Nonreciprocity around Conjugate Exceptional Points
• Dynamically encircling an exceptional point through phase-tracked closed-loop control
• Recent advances in the combination of nonlinearity and exceptional points
• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Instabilities, nonhermiticity and exceptional points in the cranking model
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Topological spin textures in electronic non-Hermitian systems
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
• Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System
• Exceptional points and defective resonances in an acoustic scattering system with sound-hard obstacles
• Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities
• Characterizing Liouvillian Exceptional Points Through Newton Polygons and Tropical Geometry
• Non-orientable Exceptional Points in Twisted Boundary Systems
• Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems
• Characteristic influence of exceptional points in quantum dynamics
• Dynamical switching of lasing emission by exceptional point modulation in coupled microcavities
• Geometric origin of self-intersection points in non-Hermitian energy spectra