arXiv subjects

Anton Montag

Publications and source records attributed to Anton Montag.

9 recordsLinked to original sources

arXiv2026

Higher-order exceptional points in a multimode continuum optoacoustic system

Exceptional points appear in non-Hermitian systems as degeneracies, where not only eigenvalues but also eigenvectors coalesce. They are of great theoretical and experimental interest due to their exotic topological properties and enhanced sensitivity to perturbations. Experimental realizations of higher-order exceptional points, where more than two eigenvectors coalesce, rely on highly fine-tuned setups. Recently, stimulated Brillouin scattering has been employed to generate second-order exceptional points in a fabrication-free setup by leveraging off-resonant scattering. In this work we generalize this approach, and we develop an off-resonant, multimode theory for stimulated Brillouin scattering as an avenue towards realizing symmetry-induced exceptional points of any order. We present the experimental implementation of our program in an accompanying paper. Our multimode theory could also be employed in applications in optoacoustic sensing, synthetic neuromorphic computing, microwave photonic filters, and optoacoustic quantum signal processing.

physics.optics↗

arXiv2026

Multi-dimensional parameter space of higher-order exceptional points induced by Brillouin optoacoustics

Exceptional points (EPs) are degeneracies in the spectrum of non-Hermitian systems, where both the eigenvalues and eigenvectors coalesce. In the vicinity of an n-th order EP, the eigenvalues generally show n-th-root dependence on the system parameters, making EPs potentially promising candidates for ultra-sensitive measurements. Usually EPs are implemented in precisely fabricated nano- and microstructures. In this work, we instead show the experimental implementation of a third-order EP (EP3) using the synthetic dimension in a single-mode optical fiber, leveraging multi-frequency Brillouin scattering. We perform a multi-dimensional scan of the parameter space revealing not only an EP3 but also additional topological structures connected to it. Our work paves the way toward fabrication-free realizations of exceptional points of arbitrary order.

physics.optics↗

arXiv2026

Non-Hermitian Landau Levels

We formulate non-Hermitian Landau levels in two-dimensional systems under a complex perpendicular magnetic field. In the symmetric gauge, we derive their discretely spaced, highly degenerate complex spectra and biorthogonal eigenstates, and clarify the role of non-unitary gauge transformations. A non-Hermitian Harper-Hofstadter lattice model confirms the continuum theory and reveals Gaussian wave packet dynamics governed by semiclassical equations with a complex Lorentz force, pointing to possible experimental realizations of complex magnetic fields.

quant-ph↗

arXiv2025

Quantum geometrical effects in non-Hermitian systems

We explore the relation between quantum geometry in non-Hermitian systems and physically measurable phenomena. We highlight various situations in which the behavior of a non-Hermitian system is best understood in terms of quantum geometry, namely the notion of adiabatic potentials in non-Hermitian systems and the localization of Wannier states in periodic non-Hermitian systems. Further, we show that the non-Hermitian quantum metric appears in the response of the system upon time-periodic modulation, which one can use to experimentally measure the non-Hermitian quantum metric. We validate our results by providing numerical simulations of concrete exemplary systems.

quant-ph↗

arXiv2025

The analytically tractable zoo of similarity-induced exceptional structures

Exceptional points (EPs) are non-Hermitian spectral degeneracies marking a simultaneous coalescence of eigenvalues and eigenvectors. Despite the fact that multiband $n$-fold EPs (EP$n$s) generically emerge as special points on manifolds of EP$m$s, where $m<n$, EP$n$s as well as their topological properties have hitherto been studied as isolated objects. In this work we address this issue and carefully map out the emerging properties of multifold exceptional structures in three and four dimensions under the influence of one or multiple generalized similarities, revealing diverse combinations of EP$m$s in direct connection to EP$n$s. We find that simply counting the number of constraints defining the EP$n$s is not sufficient in the presence of similarities; the constraints can also be satisfied by the EP$m$-manifolds obeying certain spectral symmetries in the complex eigenvalue plane, reducing their dimension beyond what is expected from counting the number of constraints. Furthermore, the induced spectral symmetries not always allow for any EP$m$-manifold to emerge in $n$-band systems, making the plethora of exceptional structures deviate further from naive expectations. We illustrate our findings in simple periodic toy models. By relying on similarity relations instead of the less general symmetries, we simultaneously cover several physically relevant scenarios, ranging from optics and topolectrical circuits, to open quantum systems. This makes our predictions highly relevant and broadly applicable in modern research, as well as experimentally viable within various branches of physics.

physics.optics↗

arXiv2024

Robust gap closing and reopening in topological-insulator Josephson junctions

In the seminal proposal by Fu and Kane, the superconducting proximity effect is used to realize topological superconductivity in the topological surface state (TSS) of a 3D topological insulator (TI). In a line Josephson junction made on the TI surface, the spin-momentum locking of the TSS guarantees the existence of a pair of spin-non-degenerate, perfectly transmitted Andreev modes. These modes lead to robust gap closing and parity alteration as a function of the superconducting phase difference $φ$ across the junction. Here, we report the observation of the predicted gap closing at $φ= (2n+1)π$ in a TI Josephson junction ($n$ integer), where the local density of states is probed via tunnel contacts and $φ$ is controlled by a flux loop. This phenomenon is robust for a wide range of chemical potentials, supporting its TSS origin. Under an applied perpendicular magnetic field, Josephson vortices form, making $φ$ position-dependent. In this case, the gap closing occurs locally at the Josephson vortex cores where $φ= (2n+1)π$, which we also observe. Our results confirm the fundamental role of spin-momentum locking in the Andreev physics in the TSS, which implies that the observed gap closing and reopening has a topological nature.

cond-mat.supr-con↗

arXiv2024

Essential implications of similarities in non-Hermitian systems

In this paper, we show that three different generalized similarities enclose all unitary and anti-unitary symmetries that induce exceptional points in lower-dimensional non-Hermitian systems. We prove that the generalized similarity conditions result in a larger class of systems than any class defined by a unitary or anti-unitary symmetry. Further we highlight that the similarities enforce spectral symmetry on the Hamiltonian resulting in a reduction of the codimension of exceptional points. As a consequence we show that the similarities drive the emergence of exceptional points in lower dimensions without the more restrictive need for a unitary and/or anti-unitary symmetry.

quant-ph↗

arXiv2024

Spectral Riemann Sheet Topology of Gapped Non-Hermitian Systems

We show topological configurations of the complex-valued spectra in gapped non-Hermitian systems. These arise when the distinctive EPs in the energy Riemann sheets of such models are annihilated after threading them across the boundary of the Brillouin zone. This results in a non-trivially closed branch cut that is protected by an energy gap in the spectrum. Their presence or absence establishes topologically distinct configurations for fully non-degenerate systems and tuning between them requires a closing of the gap, forming exceptional point degeneracies. We provide an outlook toward experimental realizations in metasurfaces and single-photon interferometry.

quant-ph↗

arXiv2024

Symmetry-induced higher-order exceptional points in two dimensions

Exceptional points of order $n$ (EP$n$s) appear in non-Hermitian systems as points where the eigenvalues and eigenvectors coalesce. They emerge if $2(n-1)$ real constraints are imposed, such that EP2s generically appear in two dimensions (2D). Local symmetries have been shown to reduce this number of constraints. In this work, we provide a complete characterization of the appearance of symmetry-induced higher-order EPs in 2D parameter space. We find that besides EP2s only EP3s, EP4s, and EP5s can be stabilized in 2D. Moreover, these higher-order EPs must always appear in pairs with their dispersion determined by the symmetries. Upon studying the complex spectral structure around these EPs, we find that depending on the symmetry, EP3s are accompanied by EP2 arcs, and two- and three-level open Fermi structures. Similarly, EP4s and closely related EP5s, which arise due to multiple symmetries, are accompanied by exotic EP arcs and open Fermi structures. For each case, we provide an explicit example. We also comment on the topological charge of these EPs, and discuss similarities and differences between symmetry-protected higher-order EPs and EP2s.

cond-mat.mes-hall↗