arXiv subjects

Jan Wiersig

Publications and source records attributed to Jan Wiersig.

At least 19 recordsLinked to original sources

arXiv2026

Fundamental Limits of Non-Hermitian Sensing from Quantum Fisher Information

Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate. Here, we address this issue within a scattering-matrix formalism for sensing with coherent light, which allows the quantum Fisher information (QFI) to be evaluated directly from experimentally accessible scattering data without introducing additional noise channels beyond those inherent to the scattering process. We analyze both nondegenerate and degenerate scattering-matrix poles, including EPs of arbitrary order, and show that the QFI per incoming photon flux is governed by three key factors: the decay rate of the resonant mode, the strength of the spectral response associated with non-normality, and the adjustment between the scattering states and the information source. For spatially localized perturbations, this implies that the Fisher information is fully determined by the local density of states at the perturbation site. Within this framework, we demonstrate that EPs can enhance the QFI compared to isolated modes or diabolic points with identical decay rates, and that the QFI can be further increased by moving away from the EP toward parameter regimes where non-Hermitian linewidth splitting reduces the decay rate of one mode. We further show that sufficiently small additional internal losses do not alter this overall picture, thereby providing a unified and experimentally relevant perspective on the design of quantum-limited non-Hermitian sensors.

quant-ph↗

arXiv2025

Exceptional Points and Lasing Thresholds: When Lower-Q Modes Win

One of the most fundamental questions in laser physics is the following: Which mode of an optical cavity will reach the lasing threshold first when gain is applied? Intuitively, the answer appears straightforward: When a particular mode is both temporally well confined (i.e., exhibits the highest quality factor) and experiences initially the largest increase of the modal gain, it is naturally expected to lase first. However, in this work, we demonstrate that this intuition can fail in surprising ways. Specifically, we show that in the presence of non-Hermitian degeneracies, known as exceptional points, the expected mode hierarchy can be dramatically altered. These spectral singularities can give rise to counterintuitive mode switching, where a mode with a lower quality factor and initially smaller increase of modal gain reaches the lasing threshold ahead of a more favorable competitor. Remarkably, this effect can occur even under spatially uniform pumping, underscoring the subtle and profound influence of non-Hermitian physics on lasing dynamics.

physics.optics↗

arXiv2025

Higher-order exceptional points in composite non-Hermitian systems

We show that a composite quantum system described by the tensor product of multiple systems each with a leading-order exceptional point (a non-Hermitian degeneracy at which not only eigenvalues but also eigenstates coalesce) exhibits a single leading-order exceptional point, whose order surpasses the order of any constituent exceptional point. The formation of such higher-order exceptional points does not require coupling among the subsystems. We determine explicitly the order and the spectral response strength of this exceptional point. Moreover, we observe that the energy eigenstates that do not merge are entangled. Finally, we demonstrate that general initial states disentangle during time evolution due to the presence of the higher-order exceptional point of the composite system.

quant-ph↗

arXiv2025

Generalized Petermann factor of non-Hermitian systems at exceptional points

The nonorthogonality of modes in open systems significantly modifies their resonant response, resulting in quantitative and qualitative deviations from Breit-Wigner resonance relations. For isolated resonances with a Lorentzian lineshape, the deviations amount to an enhancement of the resonance linewidth by the Petermann factor (PF), given by the overlap of left and right eigenmodes of the underlying effectively non-Hermitian Hamiltonian. The PF diverges at exceptional points (EPs), where resonance frequencies degenerate, and right and left eigenmodes are orthogonal to each other. This divergence signifies a qualitative departure from a Lorentzian lineshape, which has gained recent attention. In this work, we extend this concept to EPs, and describe how this EP PF manifests in a variety of physical scenarios. Firstly, we identify this PF in physical terms as an enhancement of the response of a system to external or parametric perturbations. Utilizing two natural orthogonally projected reference systems based on the right and left eigenvectors, we show that each choice carries a precise geometric interpretation that naturally extends the notion of the PF for isolated resonances to EPs. The two choices can be combined into an overall EP PF, which again can be expressed in purely geometric terms. Secondly, we illuminate the geometric mechanisms that determine the size of the EP PF, by considering the role of modes participating in the degeneracy and those that remain spectrally separated. Thirdly, we design a system to study the EP PF in a specific physical setup, consisting of two microrings coupled to a waveguide with embedded semitransparent mirrors. This example shows our approach yields a more accurate spectral response strength than conventional truncation. These results complete the description of systems at EPs in the same way as the original PF does for isolated resonances.

physics.optics↗

arXiv2024

Graph-theoretical approach to the eigenvalue spectrum of perturbed higher-order exceptional points

Exceptional points are special degeneracy points in parameter space that can arise in (effective) non-Hermitian Hamiltonians describing open quantum and wave systems. At an n-th order exceptional point, n eigenvalues and the corresponding eigenvectors simultaneously coalesce. These coalescing eigenvalues typically exhibit a strong response to small perturbations which can be useful for sensor applications. A so-called generic perturbation with strength $ε$ changes the eigenvalues proportional to the n-th root of $ε$. A different eigenvalue behavior under perturbation is called non-generic. An understanding of the behavior of the eigenvalues for various types of perturbations is desirable and also crucial for applications. We advocate a graph-theoretical perspective that contributes to the understanding of perturbative effects on the eigenvalue spectrum of higher-order exceptional points, i.e. n > 2. To highlight the relevance of non-generic perturbations and to give an interpretation for their occurrence, we consider an illustrative example, a system of microrings coupled by a semi-infinite waveguide with an end mirror. Furthermore, the saturation effect occurring for cavity-selective sensing in such a system is naturally explained within the graph-theoretical picture.

quant-ph↗

arXiv2024

Computing eigenfrequency sensitivities near exceptional points

Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly at the exceptional point. Capturing this enhanced sensitivity is crucial for the investigation and optimization of exceptional-point-based applications, such as optical sensors. We present a numerical framework, based on contour integration and algorithmic differentiation, to accurately and efficiently compute eigenfrequency sensitivities near exceptional points. We demonstrate the framework to an optical microdisk cavity and derive a semi-analytical solution to validate the numerical results. The computed eigenfrequency sensitivities are used to track the exceptional point along an exceptional surface in the parameter space. The presented framework can be applied to any kind of resonance problem, e.g., with arbitrary geometry or with exceptional points of arbitrary order.

physics.comp-ph↗

arXiv2023

Moving along an exceptional surface towards a higher-order exceptional point

Open systems with non-Hermitian degeneracies called exceptional points show a significantly enhanced response to perturbations in terms of large energy splittings induced by a small perturbation. This reaction can be quantified by the spectral response strength of the exceptional point. We extend the underlying theory to the general case where the dimension of the Hilbert space is larger than the order of the exceptional point. This generalization allows us to demonstrate an intriguing phenomenon: The spectral response strength of an exceptional point increases considerably and may even diverge to infinity under a parameter variation that eventually increases the order of the exceptional point. This dramatic behavior is in general not accompanied by a divergence of the energy eigenvalues and is shown to be related to the well-known divergence of Petermann factors near exceptional points. Finally, an accurate and robust numerical scheme for the computation of the spectral response strength based on the general theory and residue calculus is presented.

quant-ph↗

arXiv2023

Petermann factors and phase rigidities near exceptional points

The Petermann factor and the phase rigidity are convenient measures for various aspects of open quantum and wave systems, such as the sensitivity of energy eigenvalues to perturbations or the magnitude of quantum excess noise in lasers. We discuss the behavior of these two important quantities near non-Hermitian degeneracies, so-called exceptional points. For small generic perturbations, we derive analytically explicit formulas which reveal a relation to the spectral response strength of the exceptional point. These formulas shed light on the possibilities for enhanced sensing in passive systems. The predictions of the general theory are successfully compared to analytical solutions of a toy model. Moreover, it is demonstrated that the connection between the Petermann factor and the spectral response strength provides the basis for an efficient numerical scheme to calculate the latter. Our theory is also important in the presence of the unavoidable imperfections in the fabrication of exceptional points as it allows to determine of what is left of the sensitivity for such imperfect exceptional points studied in experiments.

quant-ph↗

arXiv2023

Revisiting the hierarchical construction of higher-order exceptional points

Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is notoriously difficult. Recently, Q. Zhong et al. [Phys. Rev. Lett. 125, 203602 (2020)] have introduced a robust construction where a unidirectional coupling of two subsystems having exceptional points of the same order leads generically to a single exceptional point of twice the order. Here, we investigate this scheme in a different manner by exploiting the nilpotency of the traceless part of the involved Hamiltonians. We generalize the scheme and derive a simple formula for the spectral response strength of the composite system hosting a higher-order exceptional point. Its relation to the spectral response strengths of the subsystems is discussed. Moreover, we investigate nongeneric perturbations. The results are illustrated with an example.

quant-ph↗

arXiv2022

Coherent Perfect Absorption in Chaotic Optical Microresonators for Efficient Modal Control

Non-Hermitian wave engineering has attracted a surge of interest in photonics in recent years. One of the prominent phenomena is coherent perfect absorption (CPA), in which the annihilation of electromagnetic scattering occurs by destructive interference of multiple incident waves. This concept has been implemented in various platforms to demonstrate real-time control of absorption, scattering and radiation by varying the relative phase of the excitation signals. However, so far these studies have been limited to simple photonic systems involving single or few modes at well-defined resonant frequencies. Realizing CPA in more complex photonic systems is challenging because it typically requires engineering the interplay of a large number of resonances featuring large spatial complexity within a narrow frequency range. Here, we extend the paradigm of coherent control of light to a complex photonic system involving more than 1,000 optical modes in a chaotic microresonator. We efficiently model the optical fields within a quasi-normal mode (QNM) expansion, and experimentally demonstrate chaotic CPA states, as well as their non-Hermitian degeneracies, which we leverage to efficiently control the cavity excitation through the input phases of multiple excitation channels. Our results shed light on the universality of non-Hermitian physics beyond simple resonant systems, paving the way for new opportunities in the science and technology of complex nanophotonic systems by chaotic wave interference.

physics.optics↗

arXiv2022

Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems

Exceptional points are non-Hermitian degeneracies in open quantum and wave systems at which not only eigenenergies but also the corresponding eigenstates coalesce. This is in strong contrast to degeneracies known from conservative systems, so-called diabolic points, at which only eigenenergies degenerate. Here we connect these two kinds of degeneracies by introducing the concept of the distance of a given exceptional point in matrix space to the set of diabolic points. We prove that this distance determines an upper bound for the response strength of a non-Hermitian system with this exceptional point. A small distance therefore implies a weak spectral response to perturbations and a weak intensity response to excitations. This finding has profound consequences for physical realizations of exceptional points that rely on perturbing a diabolic point. Moreover, we exploit this concept to analyze the limitations of the spectral response strength in passive systems. A number of optical and photonics systems are investigated to illustrate the theory.

physics.optics↗

arXiv2022

Response strengths of open systems at exceptional points

Open quantum and wave systems exhibit exotic degeneracies at exceptional points in parameter space that have attracted considerable attention in various fields of physics, including optics and photonics. One reason is the strong response of open systems at such degeneracies to external perturbations and excitations. We introduce two characteristics of exceptional points that quantify the response in terms of energy eigenvalues and eigenstates, intensity, and dynamics. The concept is verified for several physically relevant examples. This work provides a new perspective on the physics of exceptional points.

quant-ph↗

arXiv2020

Non-Hermitian scattering on a tight-binding lattice

We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission and absorption coefficients are studied as a function of the strength of this absorbing potential. The system is found to have an exceptional point at a certain strength of the potential. Unusually, all (or nearly all) of the spectrum pairs up into mutually coalescing eigenstate pairs at this exceptional point. At large potential strengths, the absorption coefficient decreases and the effect of the imaginary potential is similar to that of a real potential. We quantify this similarity by utilizing properties of a localized eigenstate.

quant-ph↗

arXiv2020

Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies

Recent experiments have demonstrated the feasibility of exploiting spectral singularities in open quantum and wave systems, so-called exceptional points, for sensors with strongly enhanced sensitivity. Here, we study theoretically the influence of classical parametric noise on the performance of such sensors. Within a Lindblad-type formalism for stochastic Hamiltonians we discuss the resolvability of frequency splittings and the dynamical stability of the sensor, and show that these properties are interrelated. Of central importance are the different features of exceptional points in the spectra of the Hamiltonian and the corresponding Liouvillian. Two realistic examples, a parity-time-symmetric dimer and a whispering-gallery microcavity with asymmetric backscattering, illustrate the findings.

quant-ph↗

arXiv2019

Nonorthogonality constraints in open quantum and wave systems

It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an appropriately defined decay operator. Here, we show that the weaker and more realistic condition of positive semi-definiteness is sufficient. We prove also that the bound becomes an equality for the case of single-channel decay. However, we show that the condition of positive semi-definiteness can be spoiled by quantum backflow. Hence, the overlap of quasibound quantum states subjected to outgoing-wave conditions can be larger than expected from the bound. A modified and less stringent bound, however, can be introduced. For electromagnetic systems, it turns out that a modification of the bound is not necessary due to the linear free-space dispersion relation. Finally, a geometric interpretation of the nonorthogonality bound is given which reveals that in this context the complex energy space can seen as a surface of constant negative curvature.

quant-ph↗

arXiv2019

Morphology of wetting-layer states in a simple quantum-dot wetting-layer model

The excitation of semiconductor quantum dots often involves an attached wetting layer with delocalized single-particle energy eigenstates. These wetting-layer states are usually approximated by (orthogonalized) plane waves. We show that this approach is too crude. Even for a simple model based on the effective-mass approximation and containing one or a few lens-shaped quantum dots in a rectangular wetting layer, the wetting-layer states typically show a substantially irregular and complex morphology. To quantify this complexity we use concepts from the field of quantum chaos such as spectral analysis of energy levels, amplitude distributions, and localization of energy eigenstates.

cond-mat.mes-hall↗

arXiv2019

Corrected perturbation theory for transverse-electric whispering-gallery modes in deformed microdisks

The perturbation theory by L. Ge et al. [Phys. Rev. A 87, 023833] for transverse-electric polarized modes in weakly deformed microdisks omits terms related to the variation of the normal derivative of the magnetic field along the boundary. Here we show that these terms are necessary to accurately describe microdisks with a strongly winding boundary. In particular, it is demonstrated that the corrected perturbation theory allows to describe the counterintuitive phenomenon of Q-factor enhancement due to weak boundary deformation. We discuss in detail the microflower cavity and the limacon cavity. Good agreement of the corrected perturbation theory with full numerical results is observed.

physics.optics↗

arXiv2018

Determination of the full statistics of quantum observables using the maximum entropy method

Numerical methods for the description of nonequilibrium many-particle quantum systems such as equation of motion techniques often cannot compute the full statistics of observables but only moments of it, such as mean, variance and higher-order moments. We employ here the maximum entropy method to numerically construct unbiased statistics based on the knowledge of moments. We verify the feasibility of the proposed method by numerical simulation of a simple birth-death model for quantum-dot-microcavity lasers, where the full photon and carrier statistics are available for comparison. We show that not only the constructed statistics but also the computed entropy and the Lagrange multipliers, which appear here as a byproduct, provide valuable insight into the physics of the considered system. For example, the entropy reveals that, in contrast to common wisdom, the photon statistics of the microcavity laser above threshold is better described by a Gaussian distribution than by a Poisson distribution. Our approach is general and can be applied to many other systems emerging in physics and related fields.

cond-mat.stat-mech↗