Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this universal concept to non-Hermitian systems by defining topological chirality, an invariant that emerges whenever an exceptional-points (EP) pair is present. Built from the non-commutative fundamental group and its braid representation, topological chirality acts as a singularity selector: clockwise EP loops occupy a homotopy class that avoids EPs, whereas counter-clockwise mirrors are equivalent only if they cross the EPs themselves. We confirm this binary rule in an optical microcavity and a non-Hermitian topological band. The same two-sheeted topology governs EP pairs in spin systems, photonic crystals and hybrid light-matter structures, where EP encirclements have already been demonstrated, so the framework transfers without alteration and confirms its experimental viability. Our findings lay the cornerstone for interpreting loop-sensitive observables such as spectral vorticity, the complex Berry phase and the non-Abelian holonomy. Finally, a gluing-of-planes construction extends the invariant to an n-sheeted surface hosting 2m EPs, unifying higher-order EP pairs.
Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this universal concept to non-Hermitian systems by defining topological chirality, an invariant that emerges whenever an exceptional-points (EP) pair is present. Built from the non-commutative fundamental group and its braid representation, topological chirality acts as a singularity selector: clockwise EP loops occupy a homotopy class that avoids EPs, whereas counter-clockwise mirrors are equivalent only if they cross the EPs themselves. We confirm this binary rule in an optical microcavity and a non-Hermitian topological band. The same two-sheeted topology governs EP pairs in spin systems, photonic crystals and hybrid light-matter structures, where EP encirclements have already been demonstrated, so the framework transfers without alteration and confirms its experimental viability. Our findings lay the cornerstone for interpreting loop-sensitive observables such as spectral vorticity, the complex Berry phase and the non-Abelian holonomy. Finally, a gluing-of-planes construction extends the invariant to an n-sheeted surface hosting 2m EPs, unifying higher-order EP pairs.
Non-Hermitian systems exhibit a variety of unique features rooted in the presence of exceptional points (EPs). The distinct topological structure in the proximity of an EP gives rise to counterintuitive behaviors absent in Hermitian systems, which emerge after encircling the EP either quasistatically or dynamically. However, experimental exploration of EP encirclement in quantum systems, particularly those involving high-order EPs, remains challenging due to the difficulty of coherently controlling more degrees of freedom. In this work, we experimentally investigate the eigenvalue braiding and state transfer arising from the encirclement of EP in a three-dimensional non-Hermitian quantum system using superconducting circuits. We characterize the second- and third-order EPs through the coalescence of eigenvalues. Then we reveal the topological structure near the EP3 by quasistatically encircling it along various paths with three independent parameters, which yields the eigenvalue braiding described by the braid group B 3 . Additionally, we observe chiral state transfer between three eigenstates under a fast driving scheme when no EPs are enclosed, while time-symmetric behavior occurs when at least one EP is encircled. Our findings offer insights into understanding non-Hermitian topological structures and the manipulation of quantum states through dynamic operations.
We theoretically investigate the interplay of topology and localized non-Hermiticity in a finite Su-Schrieffer-Heeger chain characterized by non-Hermitian potentials at its boundaries. By tuning the boundary gain and loss parameters, we exploit the finite-size hybridization of two mid-gap topological edge states to analytically derive the exact coordinates of boundary-induced exceptional points (EPs), ΓEP=±ivN/wN−1, at which these states undergo coalescence. We demonstrate that dynamically encircling these boundary EPs facilitates a robust, chiral edge state-transfer protocol. Depending on the orientation of the encircling loop, this protocol allows a topological edge state localized at one boundary to be either transferred to the opposite edge with perfect fidelity or returned to its starting position through a double switching process. Importantly, since the non-Hermiticity remains strictly confined to the boundaries, this chiral transport occurs without affecting the energy spectrum of the bulk bands. These results establish a minimal framework for a large-scale topological chiral switch that is experimentally verifiable and capable of being controlled through boundary non-Hermitian driving.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.
Physical systems with gain and loss can be described by a non-Hermitian Hamiltonian, which is degenerated at the exceptional points (EPs). Many new and unexpected features have been explored in the non-Hermitian systems with a great deal of recent interest. One of the most fascinating features is that chiral state conversion appears when one EP is encircled dynamically. Here, we propose an easy-controllable levitated microparticle system that carries a pair of EPs and realize slow evolution of the Hamiltonian along loops in the parameter plane. Utilizing the controllable rotation angle, gain and loss coefficients, we can control the structure, size and location of the loops in situ. We demonstrate that, under the joint action of topological structure of energy surfaces and nonadiabatic transitions, the chiral behavior emerges both along a loop encircling an EP and even along a straight path away from the EP. This work broadens the range of parameter space for the chiral state conversion, and proposes a useful platform to explore the interesting properties of exceptional points physics.
Exceptional points (EPs) in non-Hermitian systems give rise to enhanced sensitivity and chiral state transfer, which are important for quantum technologies. Although parameter trajectories encircling EPs can control symmetric and chiral state transfer, their robustness against practical perturbations and their role in quantum sensing remain largely unexplored. Here, we study three time-modulated parameter loops in a non-Hermitian two-level system to show how trajectory design governs state-transfer symmetry, robustness, and sensing performance. Trajectories avoiding the EP support robust symmetric transfer, while those encircling the EP yield chiral transfer governed by the topological winding number, whose robustness depends on the distance to the EP and the encircling direction. For quantum sensing, trajectory engineering enables tuning of sensitivity amplitude, time window, and parameter selectivity in both eigenvalue-based and eigenstate-based sensors. Notably, eigenstate-based sensing achieves full parameter selectivity that is unattainable with eigenvalue-based methods. Our results establish a quantitative connection between trajectory topology and system dynamics, providing a unified framework for robust state-transfer protocols and high-performance quantum sensors.
Non-Hermitian operators are now routinely used to describe few-mode systems such as optical resonators and superconducting qubits, and exceptional points (EPs) are defective spectral singularities of such non-Hermitian operators. In contrast, the scattering-theoretic formulation of EP physics for unbounded Hamiltonians remains less settled. In this work, we formulate the geometric phase associated with encircling an EP when the underlying eigenstates are quantum resonances within a one-dimensional scattering model. To do this, we employ the complex-scaling method, where resonance poles of the S matrix are realized as discrete eigenvalues of the non-Hermitian dilated Hamiltonian, to construct situations in which resonant and scattering states coalesce into an EP in the complex energy plane, that is, the resonance pole is embedded into the continuum spectrum. We analyze the self-orthogonality in the vicinity of an EP, the Berry phase, and the Chern characteristic. Our results clarify how EP branch structure and geometric holonomy arise directly from resonance poles in scattering theory, thereby connecting non-Hermitian spectral topology with the traditional theory of quantum resonances.