We explore the existence and stability of exceptional points (EPs) in finite waveguide arrays subject to single-site dissipation. We show that the EP landscape is dictated by a geometry-dependent parity effect, leading to strictly distinct spectral behaviors for arrays with even versus odd numbers of waveguides. Through analytical derivation and numerical analysis, we define the conditions under which these singularities emerge and evolve. Our findings clarify the mechanisms of symmetry breaking in finite non-Hermitian lattices, offering new guidelines for the design of robust optical structures that exploit or avoid exceptional points.
We explore the existence and stability of exceptional points (EPs) in finite waveguide arrays subject to single-site dissipation. We show that the EP landscape is dictated by a geometry-dependent parity effect, leading to strictly distinct spectral behaviors for arrays with even versus odd numbers of waveguides. Through analytical derivation and numerical analysis, we define the conditions under which these singularities emerge and evolve. Our findings clarify the mechanisms of symmetry breaking in finite non-Hermitian lattices, offering new guidelines for the design of robust optical structures that exploit or avoid exceptional points.
Exceptional points (EPs), indicative of parity-time (PT) symmetry breaking, play a central role in non-Hermitian physics, yet most studies begin from deliberately engineered effective Hamiltonians whose parameters are tuned to exhibit exceptional behavior. In realistic open quantum systems, however, dynamics are governed by Lindblad superoperators whose spectral structure is high-dimensional, symmetry-constrained, and not obviously reducible to minimal non-Hermitian models. A general framework for discovering exceptional dynamics directly from microscopic dissipative models has been lacking. Here we introduce a symmetry-resolved approach for identifying and characterizing exceptional points directly from the full Liouvillian generator. Correlated dissipation induces graph symmetries that decompose Liouville space into low-dimensional invariant sectors, within which minimal non-Hermitian blocks govern the onset of EPs and PT-breaking behavior. We further introduce a numerical diagnostic - the exceptional-point strength E - based on eigenvector conditioning, which quantifies proximity to defective dynamics without requiring analytic reduction. Applied to tight-binding models with correlated dephasing and relaxation, the method reproduces analytically predicted exceptional seams and reveals universal scaling of E near EP manifolds. More broadly, the framework enables systematic discovery of hidden exceptional structure in complex or high-dimensional open systems and is naturally compatible with matrix-free and tensor-network implementations for scalable many-body applications.
Exceptional points (EPs) are non-Hermitian spectral singularities where eigenvalues and eigenvectors coalesce. We propose a geometry-controlled route to EPs in orbital-angular-momentum (OAM) photonics. In an effective torsion-free helicoidal background, the twist supplies a signed, real chiral splitting between opposite-OAM modes, while openness, gain, loss, leakage, or channel coupling, supplies the non-Hermiticity. The EP is reached when the geometric detuning compensates for a residual mode splitting and the linewidth contrast meets the non-Hermitian balance condition; the twist rate is thus the control parameter, not the source of non-Hermiticity. We obtain the OAM slope both for a confined quantum problem and, in the paraxial regime, for a helically twisted guide, and embed the OAM doublet in a multimode mode-space model to show that the EP survives spectator modes. Eigenvalue coalescence, phase-rigidity collapse, linear EP tracking with residual detuning, and branch exchange under geometric encircling provide falsifiable signatures. An OAM-resolved input-output response maps these onto spectroscopy-level observables, including spectral maps and three-dimensional Riemann-surface visualizations. A device-level paraxial simulation of two distinct photonic platforms, one reciprocal and one asymmetric-coupling Wiersig-type platform, reproduces the predicted exceptional point and its linear geometric tracking.
Controlling atom–photon interactions in engineered environments is central to quantum optics and emerging quantum technologies. Non-Hermitian (NH) photonic baths, where dissipation fundamentally reshapes spectral and dynamical properties, provide versatile platforms for such control. Here, we investigate the relaxation dynamics of a single two-level quantum emitter coupled to the edge of a semi-infinite dissipative bosonic lattice with uniform loss. Despite the simplicity of this bath, we uncover rich dynamical phase transitions, i.e., qualitative changes in spontaneous-emission decay as system parameters are varied. In particular, we establish the existence of an optimal dissipative environment for accelerated spontaneous emission. The phase transitions are traced to spectral restructuring of the resolvent, in some cases governed by the coalescence of resonance states on the second Riemann sheet. We identify these coalescences as virtual exceptional points (EPs) of resonance origin, providing a conceptual bridge with EP physics while highlighting distinctive features of infinite-dimensional NH systems. More broadly, our results illustrate how the specific nature of dissipation—whether uniform losses, staggered losses, or dephasing—can profoundly impact emitter relaxation, pointing to dissipation engineering as a versatile tool for quantum technologies.
As an exclusive feature of a non-Hermitian system, the existence of exceptional points (EPs) depends not only on the details of the Hamiltonian but also on the particle-number filling and the particle statistics. In this paper, we study many-particle EPs in a Bose Hubbard chain with two end-site resonant imaginary potentials. Starting from a single-particle coalescing eigenstate, we construct n-particle condensate eigenstates for the cases with zero and infinite U. Compared with the free bosonic case, where the $ n $-particle condensate eigenstate is an (n+1)-th-order coalescing state, the hardcore-boson counterpart is a second-order coalescing state for odd n , while it is not for even n. The difference in particle-number parity results in distinct quenching dynamics of the condensate states, highlighting the role of parity in system behavior. Our finding may stimulate research on the dynamic sensitivity to particle-number parity.
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.
ABSTRACT Exceptional points (EPs), singularities in non‐Hermitian systems where eigenvalues and eigenstates coalesce, exhibit unique spectral responses and enhanced sensitivity. However, in quantum‐interference settings such as two‐photon measurements, the interference transition generally does not occur at the EPs, limiting their applications for quantum sensing. To address this issue, we develop an anti‐parity‐time‐symmetric model based on indirectly coupled waveguides and introduce a cascaded‐waveguide configuration that produces an effective rotation of the system's eigenbasis. This modification shifts the two‐photon bunching‐antibunching transition to coincide with the EP. Near the EP, a small refractive‐index perturbation leads to a sharp change in visibility, which becomes more pronounced by increasing waveguide length. This passive, gain‐free design may minimize noise and offer a feasible route toward EP‐enhanced quantum phase sensing on integrated platforms.