arXiv subjects

Alexander Stegmaier

Publications and source records attributed to Alexander Stegmaier.

11 recordsLinked to original sources

arXiv2025

Odd electrical circuits

Non-reciprocal interactions in elastic media give rise to rich non-equilibrium behaviors, but controllable experimental realizations of such odd elastic phenomena remain scarce. Building on recent breakthroughs in electrical analogs of non-Hermitian solid-state systems, we design and analyze scalable odd electrical circuits (OECs) as exact analogs of an odd solid. We show that electrical work can be extracted from OECs via cyclic excitations and trace the apparent energy gain back to active circuit elements. We show that OECs host oscillatory modes that resemble recent experimental observations in living chiral crystals and identify active resonances that reveal a perspective on odd elasticity as a mechanism for mechanical amplification.

cond-mat.soft↗

arXiv2024

Simulating Holographic Conformal Field Theories on Hyperbolic Lattices

We demonstrate how table-top settings combining hyperbolic lattices with nonlinear dynamics universally encode aspects of the bulk-boundary-correspondence between gravity in anti-de-Sitter (AdS) space and conformal field theory (CFT). Our concrete and broadly applicable holographic toy model simulates gravitational self-interactions in the bulk and features an emergent CFT with nontrivial correlations on the boundary. We measure the CFT data contained in the two- and three-point functions and clarify how a thermal CFT is simulated through an effective black hole geometry. As a concrete example, we propose and simulate an experimentally feasible protocol to measure the holographic CFT using electrical circuits.

cond-mat.mes-hall↗

arXiv2024

Topological Edge State Nucleation in Frequency Space and its Realization with Floquet Electrical Circuits

We build Floquet-driven capactive circuit networks to realize topological states of matter in the frequency domain. We find the Floquet circuit network equations of motion to reveal a potential barrier which effectively acts as a boundary in frequency space. By implementing a Su-Shrieffer-Heeger Floquet lattice model and measuring the associated circuit Laplacian and characteristic resonances, we demonstrate how topological edge modes can nucleate at such a frequency boundary.

cond-mat.mes-hall↗

arXiv2023

Realizing efficient topological temporal pumping in electrical circuits

Quantized adiabatic transport can occur when a system is slowly modulated over time. In most realizations however, the efficiency of such transport is reduced by unwanted dissipation, back-scattering, and non-adiabatic effects. In this work, we realize a topological adiabatic pump in an electrical circuit network that supports remarkably stable and long-lasting pumping of a voltage signal. We further characterize the topology of our system by deducing the Chern number from the measured edge band structure. To achieve this, the experimental setup makes use of active circuit elements that act as time-variable voltage-controlled inductors.

cond-mat.other↗

arXiv2023

Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states.

cond-mat.mes-hall↗

arXiv2022

Simulating hyperbolic space on a circuit board

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a "hyperbolic drum", and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter.

cond-mat.other↗

arXiv2022

Observation of cnoidal wave localization in non-linear topolectric circuits

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of non-linearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a non-linear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the non-linear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the non-linear regime, where the cnoidal eccentricity decreases from edge to bulk.

cond-mat.mes-hall↗

arXiv2022

Universality of Hofstadter butterflies on hyperbolic lattices

Motivated by recent experimental breakthroughs in realizing hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. By utilizing large hyperbolic lattices with periodic boundary conditions, we obtain the true hyperbolic bulk spectrum that is unaffected by contributions from boundary states. Our results reveal that the butterfly spectrum with large extended gapped regions prevails and that its shape is universally determined by the number of edges of the fundamental tile, while the fractal structure is lost in such a non-Euclidean case. We explain how these intriguing features are related to the nature of Landau levels in hyperbolic space, and how they could be verified experimentally.

cond-mat.mes-hall↗

arXiv2021

Active topolectrical circuits

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.

cond-mat.other↗

arXiv2020

Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits

We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $\mathcal{PT}$ and chiral symmetry anti-$\mathcal{PT}$ ($\mathcal{APT}$). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $\mathcal{PT}$ symmetric gain and loss on localized edge and defect states in a non-Hermitian Su--Schrieffer--Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the $\mathcal{APT}$ symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel $\mathcal{PT}$ symmetric $\mathbb{Z}_2$ invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not $\mathcal{PT}$ symmetric, the topological defect state disappears and only reemerges when $\mathcal{APT}$ symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.

physics.app-ph↗

arXiv2020

Efficient Light Funneling based on the non-Hermitian Skin Effect

In the last two decades, the ubiquitous effect of dissipation has proven to entail astonishing non-Hermitian features, rather than just being an inescapable nuisance. As an alternative route to non-Hermiticity, we tailor the anisotropy of a lattice, which constitutes an, up to now, barely exploited degree of freedom. In this case, the appearance of an interface dramatically alters the entire eigenmode spectrum, leading to the exponential localization of all modes at the interface, which goes beyond the expectations for Hermitian systems. This effect is dubbed "non-Hermitian skin effect". We experimentally demonstrate it by studying the propagation of light in a large scale photonic mesh lattice. For arbitrary excitations, we find that light is always transported to the interface, realizing a highly efficient funnel for light.

physics.optics↗