arXiv subjects

Nadav Shaibe

Publications and source records attributed to Nadav Shaibe.

7 recordsLinked to original sources

arXiv2026

Measurement and Optimal Targeting of a Hidden Scatterer in a Complex Environment Utilizing Fisher Information

A complex, non-Hermitian scattering system with a high degree of multiple scattering and interference is often treated as a black box, described simply by the relationship between a set of incoming and outgoing waves of a given frequency or energy. The scattering matrix S that describes the system is a non-unique, generally sub-unitary matrix that reveals very little about the microscopic processes that are responsible for the observed scattering. We form the Fisher information operator $F_x$, a Hermitian matrix, utilizing a derivative of S with respect to the value of some varying parameter x of the system, associated with a localized perturbation, and experimentally demonstrate that the principal eigenvector of Fx can be used to quantitatively measure changes in the value of parameter x using only information from the scattering matrix. We propose a "discrete feedback loop" protocol enabled by the knowledge we gain from the Fisher information operator, that repeatedly determines the counter perturbation necessary to return a varying parameter to some fixed benchmark value. A further application of the Fisher information operator for energy focusing that utilizes the principal eigenvector excitation is demonstrated through compelling indirect evidence of targeting within a complex system. These methods are experimentally demonstrated to work even in the presence of time-reversal symmetry breaking due to absorption and/or loss of scattering reciprocity.

physics.optics↗

arXiv2025

Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities

Vortex singularities in speckle patterns formed from random superpositions of waves are an inevitable consequence of destructive interference and are consequently generic and ubiquitous. Singularities are topologically stable, meaning they persist under small perturbations and can only be removed via pairwise annihilation. They have applications including sensing, imaging and energy transfer in multiple fields such as optics, acoustics, and elastic or fluid waves. We generalize the concept of speckle patterns to arbitrary parameter spaces and any complex scalar function that describes wave phenomena involving complicated scattering. In scattering systems specifically, we are often concerned with singularities associated with complex zeros of various functions of the scattering matrix S, such as Coherent Perfect Absorption, Reflectionless Scattering Modes, Transmissionless Scattering Modes, and Exceptional Points. Experimentally, we find that all singularities share a universal statistical property: any quantity that diverges as a simple pole at a singularity has a probability distribution function with a -3 power law tail. The tail of the distribution provides an estimate for the likelihood of finding a given singularity in a generic system. We use these universal statistical results to determine that homogeneous system loss is the most important parameter determining singularity density in a given parameter space of an absorptive scattering system. Finally, we discuss events where distinct singularities coincide in parameter space, which result in higher order singularities that are not topologically protected, and we do not find universal statistical properties for them. We support our empirical results from microwave experiments with Random Matrix Theory simulations and conclude that the statistical results presented hold for all generic non-Hermitian scattering systems.

nlin.CD↗

arXiv2025

Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices

Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved, the impedance matrix becomes a complicated function of the details of the system, in which case a statistical model, such as the Random Coupling Model (RCM) becomes useful. The statistics of the elements of the RCM impedance matrix depend on the excitation frequency, the spectral density of the modes of the enclosed system volume, the average loss factor (Q^{-1}) of the system, and the properties of the coupling ports as given by their radiation impedances. In this paper, properties of the elements of impedance matrices are explored numerically and experimentally. These include the two point frequency correlation functions for the complex impedance of elements and the expected difference in frequencies between which impedance values are approximately repeated. Universal scaling arguments are then given for these quantities, hence these results are generic for all sufficiently complicated scattering systems, including acoustic and optical systems. The experimental data presented in this paper come from microwave graphs, billiards, and three-dimensional cavities with embedded tunable perturbers such as metasurfaces. The data is found to be in generally good agreement with the predictions for the two point frequency correlations and the frequency interval for successive repetitions of impedance matrix elements values.

nlin.CD↗

arXiv2025

Robust Wave Splitters Based on Scattering Singularities in Complex non-Hermitian Systems

We have discovered specific conditions for generic scattering systems to act as wave splitters that are robust to any change in relative amplitude or phase of an arbitrary injected waveform. Specifically for complex systems with tunable parameters, these conditions for robust splitting (RS) are abundant, and by using multiple tunable parameters the relative amplitude and phase of the output signals can also be tuned. The splitting property of the systems works for all possible input phase differences and amplitude ratios and does not require a particular coherent input signal. We show experimentally that the fixed splitting ratios and output phases at RS conditions are robust to 100 dB of relative power and 2$π$ phase changes of the input waves to a complex non-Hermitian two-port system. We also demonstrate that the splitting power ratio can be tuned by multiple orders of magnitude and the RS conditions can be tuned to any desired frequency with suitable tunable perturbations embedded in the system. Although this phenomenon is realized in two-port systems and involves some degree of attenuation, tunable robust splitting can be achieved between any two ports of multiport systems. These results are general to all wave scattering phenomena (electromagnetic, acoustic, etc.) and hold in generic complex scattering systems.

cond-mat.mes-hall↗

arXiv2025

Novel Topology and Manipulation of Scattering Singularities in Complex non-Hermitian Systems

The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks, wavefront shaping protocols, active metasurface development, and more. At their core, these achievements rely on our ability to engineer the resonant spectrum of the underlying physical structures which is conventionally accomplished by carefully imposing geometrical and/or dynamical symmetries. In contrast, by taking active control over the boundary conditions in complex scattering environments which lack artificially-imposed geometric symmetries, we demonstrate via microwave experiments the ability to manipulate the spectrum of the scattering operator. This active control empowers the creation, destruction and repositioning of exceptional point degeneracies (EPD's) in a two-dimensional (2D) parameter space. The presence of EPD's signifies a coalescence of the scattering eigenmodes, which dramatically affects transport. The scattering EPD's are partitioned in domains characterized by a binary charge, as well as an integer winding number, are topologically stable in the two-dimensional parameter space, and obey winding number-conservation laws upon interactions with each other, even in cases where Lorentz reciprocity is violated; in this case the topological domains are destroyed. Ramifications of this understanding is the proposition for a unique input-magnitude and phase-insensitive 50:50 in-phase/quadrature (I/Q) power splitter. Our study establishes an important step towards complete control of scattering processes in complex non-Hermitian settings.

cond-mat.mes-hall↗

arXiv2025

Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems

The Wigner-Smith time-delay of flux conserving systems is a real quantity that measures how long an excitation resides in an interaction region. The complex generalization of time-delay to non-Hermitian systems is still under development, and its statistical properties in the short-wavelength limit of complex chaotic scattering systems have not been investigated. From the experimentally measured multi-port scattering ($S$)-matrices of one-dimensional graphs, a two-dimensional billiard, and a three-dimensional cavity, we calculate the complex Wigner-Smith, as well as each individual reflection and transmission time-delays. The complex reflection time-delay differences between each port are calculated, and the transmission time-delay differences are introduced for systems exhibiting non-reciprocal scattering. Large time-delays are associated with scattering singularities such as coherent perfect absorption, reflectionless scattering, slow light, and uni-directional invisibility. We demonstrate that the large-delay tails of the distributions of the real and imaginary parts of each time-delay quantity are superuniversal, independent of experimental parameters: wave propagation dimension $\mathcal{D}$, number of scattering channels $M$, Dyson symmetry class $β$, and uniform attenuation $η$. The tails determine the abundance of the singularities in generic scattering systems, and the superuniversality is in direct contrast with the well-established statistics of unitary systems, where the distribution tail depends explicitly on the values of $M$ and $β$. We relate the statistics to the topological properties of the corresponding singularities. Although the results presented here are based on classical microwave experiments, they are applicable to any non-Hermitian wave-chaotic scattering system in the short-wavelength limit, such as optical or acoustic resonators.

nlin.CD↗

arXiv2024

Asymmetric Transmission Through a Classical Analogue of the Aharonov-Bohm Ring

It has been predicted that new physics and technology are enabled for quantum systems that suffer from partial decoherence, in the intermediate range between coherent quantum evolution and incoherent classical physics. We explore the asymmetric transmission through a classical analogue of the Aharonov-Bohm (AB) mesoscopic ring that supports a 3:1 asymmetry in transmission times, augmented with lossy features that act preferentially on the longer-lingering waves. Such a device is realized as a linear microwave graph utilizing a gyrator to create the 3:1 transmission time delay asymmetry, along with both homogeneous and localized losses, to produce an imbalance in wave transmission through the device. We demonstrate asymmetric transmission through the microwave-ring graph as a function of loss in both simulation and experiment, and in both the frequency- and time-domain. The microwave ring-graph results are compared to a numerical simulation representative of a class of recent models proposing dephasing-induced transport asymmetry in few-channel quantum systems, and parallels are noted.

quant-ph↗