Complex Photonic Systems with Broken Symmetries: Synergetic Effects of Wave Chaos and Non-Hermiticity

Effectively non-Hermitian systems receive substantial interest as they display striking physical phenomena applicable to a wide range of settings, from classical photonic and mechanical systems with gain and loss to open and monitored quantum systems. These phenomena are enhanced at spectral degeneracies, such as exceptional points (EPs), where the system behavior qualitatively changes. At these EPs, multiple degenerate eigenvalues share a single eigenvector making them much more sensitive to external perturbations. This distinctive feature is not displayed by the Hermitian degeneracies such as a Diabolic point (DP) possessing two linearly independent eigenvectors. In this poster, we will introduce partial exceptional points (PEPs): a more complex non-Hermitian degeneracy in which the eigenvectors are only partially degenerate. In addition, we will also describe criteria for their emergence within a rigorous and efficient mathematical framework so-called modes of the adjugate matrix, which can be obtained directly from the Hamiltonian of the system under consideration. We will demonstrate this mathematical framework using a simple example of a non-Hermitian version of the well-known 2D-Lieb lattice, and utilize the above-mentioned conditions to showcase the presence of exceptional rings and lines hosting PEPs in its bulk energy eigenspectrum. Finally, we will quantify the physical as well as the spectral response to external perturbation at these PEPs by using a recently developed uniform expansion of the Green’s function [1]. Using this, we can compute the response strength functions at PEPs directly from the data of the Hamiltonian itself which vary smoothly with energy and external parameters. As an application, we will use this expansion of the Green’s function to design a micro-ring resonator setup operating at a PEP and discuss how the response varies as one approach the PEP. Thus, this provides us a uniform and well-conditioned description of the response at various degenerate scenarios, such as PEPs, and therefore completes the description of NH systems both mathematically as well as physically. [1] S. Bid and H. Schomerus, Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point, Phys. Rev. Research 7, 023062– Published 16 April, 2025.

We are interested in molding complex scattering systems that have few or no symmetries and to uncover new features and applications that have not been previously recognized. By means of multiple tunable reflecting metasurfaces embedded in complex non-Hermitian systems we uncover a rich diversity of scattering phenomena, some of which prove to be of practical utility. These electronically tunable reflecting metasurfaces enable the exploration of large regions of parameter space which can be used to find numerous scattering singularities and determine their topological properties and interactions. Looking at complex time delays derived from components of the scattering matrix, we are able to uncover superuniversal statistical behavior independent of wave propagation dimension, number of ports, loss, and symmetry class. We have also put forward physical interpretations of the real and imaginary parts of complex time delay. Additionally, using coherent perfect absorption (CPA) enabling conditions and injecting arbitrary monochromatic signals into a system, the output signals maintain a fixed relative amplitude and phase. Due to the topological stability of CPA enabling conditions, the relative amplitude and phase of the output signals can also be continuously tuned by varying an embedded tunable parameter. Tunable reflecting metasurfaces create a great deal of control over generic scattering systems, including wave chaotic systems, and enable new applications of singularities to be discovered.

Exceptional points are spectral degeneracies in open systems where not only the eigenvalues but also the corresponding eigenvectors coalesce. The fundamental reason behind the research interest in exceptional points stems from the enhanced system's sensitivity to external perturbations. Specifically, when a system at an exceptional point of order N is perturbed, the involved eigenvalues diverge generically with a characteristic N-root topology. The resulting eigenvalue splitting depends on the specific kind of perturbation and on a quantity--the spectral response strength--which can be assigned independently of the perturbation to a particular exceptional point. The response strength is therefore a quantitative measure for the system's sensitivity to external perturbations and allows to compare different exceptional points of the same order. So far, the theory for the spectral response strength is restricted to non-Hermitian Hamiltonians on finite-dimensional Hilbert spaces which can occur naturally as an effective description, e.g. within coupled-mode theory. On the other hand, realistic systems described by a wave equation give rise to an underlying infinite-dimensional Hilbert space. In this work we present a scheme to calculate the spectral response strength directly from the numerical results of wave simulations. To do so, the relation between the spectral response strength and the Petermann factor of the eigenstates near the exceptional point is exploited. For a validation of our approach, we consider three different photonic systems: a microring dimer, waveguide-coupled microrings, and a weakly deformed microdisk. For all three cases our approach shows an excellent agreement to results provided by an effective Hamiltonian based on coupled-mode theory.

Previous studies have noted the lasing modes whose intensities are localized along stable periodic orbits by pumping selectively along the orbits. The resonant modes localized along unstable periodic orbits called scar modes are well-known in quantum chaos, however, the localization of them was weak. It is shown that the lasing modes pumped selectively along unstable periodic orbits are strongly localized along the orbits by self-organized optimization.

We explain the structure of chaotic resonance states with arbitrary decay rates in scattering systems in the semiclassical limit [1]. It is given by a multifractal measure from classical dynamics. Numerical results are presented for dielectric cavities and the three-disk scattering system. [1] R. Ketzmerick, F. Lorenz, J. R. Schmidt, Semiclassical Limit of Resonance States in Chaotic Scattering, Phys. Rev. Lett. 134, 020404 (2025).

We consider a system of N bi-linearly coupled damped harmonic quantum oscillators with time-evolution governed by a Lindblad equation. We show that the corresponding stochastic quantum state diffusion equation can be transformed into a set of N independent damped harmonic oscillators. This offers a great reduction in the basis size and also explains the role of decoupling in the quantum state diffusion formalism. We investigate the numerical performance of the method and find, in particular, scaling laws for the number of stochastic trajectories needed to find a certain accuracy. Ref: J. Moreno, A. Pendse, A. Eisfeld. Appl. Phys. Lett. 124 (16): 161110 (2024).

Spatial localization of coherently propagating waves has been extensively studied under the assumption of homogeneous random media. However, there has been considerably less focus on the phenomenon of wave localization in inhomogeneous media, where the conventional picture of Anderson localization does not apply, as we demonstrate here. We fabricate photonic lattices with inhomogeneous disorder modeled by heavy-tailed alpha-stable distributions. By measuring the light intensity along photonic lattices, we demonstrate that the spatial localization of light is described by a stretched exponential function with a stretching parameter alpha. This localization is asymmetric with respect to the excitation site, contrasting with the symmetric exponential decay observed in standard Anderson localization phenomena. Additionally, we conduct numerical simulations using a tight-binding model to further support our experimental and theoretical findings.

The coupling between the two different polarizations (TE and TM) is a feature in realistic three-dimensional (3D) optical cavities, that is not present in two-dimensional systems. We find the interaction of polarized modes to be governed by a network of exceptional points that reflects the openness, or non-Hermiticity, of the system. The mode coupling is analyzed using an extended 3D Husimi formalism, which maps the wave function on the cavity surface into phase space [1]. To this end we expand the Husimi function method by applying the formalism to 3D systems. We find it to be a comprehensive and useful way to represent the mode structure of 3D microcavities and confirm characteristic features such as exceptional points [2]. [1] Hentschel et al., Europhys. Lett. 62 636 (2003) [2] Rodemund et al., arXiv:2503.12570

The distribution of resonance poles of chaotic scattering systems is investigated in the semiclassical limit at unprecedented small wavelengths. For the paradigmatic three-disk scattering system, we study the spectral gap towards the real axis, the fractal Weyl law, which counts the number of resonance poles, and the distribution of decay rates. These properties are compared to previous analytical results, e.g. from random matrix theory. In contrast to this system with full escape, systems with partial escape have significantly different properties. For the example of a dielectric cavity, we show that results from random matrix theory cannot explain the distribution of decay rates.

Billiard systems are a widely used and common tool for studying nonlinear dynamics. Over the past decades, theoretical studies have been enriched by experimental realizations, such as optical microcavities and ballistic quantum dots. However, these systems are typically isotropic, and chaotic behavior arises only from deviations of the cavity geometry from the perfect circular symmetry. However, an anisotropy, and thus a symmetry breaking in momentum space (as for light in birefringent optical materials or for electrons in bilayer graphene), can induce chaotic dynamics even in circular cavities [1]. We developed a ray-tracing algorithm to model billiard dynamics in anisotropic media and analyze how anisotropy influences the system’s phase space structure [2]. In addition, we investigate the impact of an additional symmetry breaking in real space on the stability of trajectories and quantify the fraction of stable trajectories by calculating Lyapunov exponents [3]. [1] L. Seemann, A. Knothe, M. Hentschel, Phys. Rev. B 107, 205404, 2023 [2] L. Seemann, A. Knothe, M. Hentschel, New J. Phys. 26 103045, 2024 [3] L. Seemann, J. Lukin, M. Häßler, S. Gemming, M. Hentschel, Symmetry 2025, 17(2), 202

We study theoretical models of three coupled wave guides with a PT-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

The main aim of the present paper is to define an active particle in a quantum framework as a minimal model of quantum active matter and investigate the differences and similarities of quantum and classical active matter. Although the field of active matter has been expanding, most research has been conducted on classical systems. Here, we propose a truly deterministic quantum active-particle model with a nonunitary quantum walk [1] as the minimal model of quantum active matter. We aim to reproduce results obtained previously with classical active Brownian particles; that is, a Brownian particle, with finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with nonunitary quantum walks. We introduce new internal states, the ground state and the excited state, and a new nonunitary operator $N(g)$ for an asymmetric transition between the two states. The non-Hermiticity parameter $g$ promotes the transition to the excited state; hence, the particle takes up energy from the environment. For our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a nontrivial manner as we increase the non-Hermiticity parameter $g$, which is similar to the classical active Brownian particle. We also observe three unique features of quantum walks, namely, ballistic propagation of peaks in one dimension, the walker staying on the constant energy plane in two dimensions, and oscillations originating from the resonant transition between the ground state and the excited state both in one and two dimensions. This work is under collaboration with N. Hatano (U. Tokyo) and H. Obuse (Hokkaido U. and U. Tokyo). [1] M. Yamagishi, N. Hatano and H. Obuse, Sci. Rep. 14, 28648 (2024).

Scale-free localization in non-Hermitian systems is a distinctive type of localization where the localization length of certain eigenstates, known as scale-free localized (SFL) states, scales proportionally with the system size. Unlike skin states, where the localization length is independent of the system size, SFL states maintain a spatial profile that remains invariant as the system size changes. We consider a model involving a single non-Hermitian impurity in an otherwise Hermitian one-dimensional lattice. Introducing disorder into this system transforms SFL states into Anderson-localized states. In contrast to the Hatano-Nelson model, where disorder typically leads to the localization of skin states and a size-independent Anderson transition, the scale-free localization in our model causes a size-dependent Anderson transition.