arXiv subjects

Steven M. Anlage

Publications and source records attributed to Steven M. Anlage.

At least 19 recordsLinked to original sources

arXiv2026

Creation and Control of Scattering Singularities in non-Hermitian Systems

The ability to controllably manipulate non-Hermitian wave scattering environments has been used to discover exotic scattering phenomena such as scattering exceptional points and coherent perfect absorption, and create numerous applications including signal routing, filtering, imaging, sensing, wireless power transfer, etc. We introduce the concept that many of these applications and phenomena are fundamentally governed by singularities of the scattering matrix. With this understanding, our demonstrated ability to control the location of scattering singularities can be used to enhance current applications and develop new ones. In generic complex scattering systems, there is an abundance of topologically protected scattering singularities corresponding to complex zeros of various functions of the scattering matrix. We show that with just three tunable parameters we are able to create the conditions for nearly any scattering singularity at arbitrary frequencies in such systems. With five tunable parameters, we demonstrate that more complex scenarios can be accomplished, such as making disparate singularities coincident or placing singularities at different frequencies. A benefit of systems with tunable parameters is that generic complex systems can be re-purposed into exhibiting many different useful properties solely by reconfiguring their tunable parameters. A particularly interesting scattering phenomenon is coherent perfect absorption, where a specific wavefront injected into the system is completely absorbed, with no energy reflected or transmitted through any channel. After creating the conditions for this singularity at an arbitrary preselected frequency, we can find and inject the coherent perfect absorption wavefront and demonstrate output-to-input power ratios as low as 1x10^{-10}, 2x10^{-8}, and 3x10^{-8} in a quarter bowtie billiard with two, three, and four ports, respectively.

physics.optics↗

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↗

arXiv2026

Chirped Pulse Analysis and Control in Non-Hermitian Scattering Systems using Complex Time Delay

We theoretically and experimentally establish a connection between linearly chirped pulse propagation properties and the complex generalization of Wigner-Smith time delay for both transmitted and reflected pulses in linear and dispersive reverberant non-Hermitian scattering systems. We demonstrate that the time shift of the chirped pulse depends on both the real and imaginary parts of the complex time delay of the scattering system. We also show that the chirped pulse experiences a center frequency shift that is directly proportional to the imaginary component of complex time delay, similar to that found in Giovannelli and Anlage (2025). Using these insights, we then demonstrate how complex time delay can be harnessed to systematically tune the propagation properties of a chirped pulse such that a near-zero time shift can be achieved for a wide range of pulse center frequencies in a resonant scattering system. Overall, this work broadens the utility and establishes the physical significance of complex time delays in non-Hermitian settings.

physics.optics↗

arXiv2025

Microscopic Investigation of rf Vortex Nucleation in Nb3Sn Films Using a Near-Field Magnetic Microwave Microscope

We use a near-field magnetic microwave microscope to investigate and compare rf vortex nucleation in two superconducting radio-frequency (SRF)-quality Nb3Sn films fabricated by different methods: a conventional vapor-diffused film and an electrochemically plated film followed by thermal annealing, both of which are deposited on Nb substrates. The microscope applies a localized rf magnetic field to the sample surface and measures the resulting third-harmonic response P3f, which is particularly sensitive to rf vortex nucleation triggered by surface defects. Both Nb3Sn films exhibit nontrivial P3f(T) structures below 7 K that display the key signatures associated with rf vortex nucleation at local defects. The electrochemical film additionally shows multiple P3f(T) structures between 14 K and 16 K that are absent in the vapor-diffused sample. Our results highlight the influence of fabrication method on rf vortex penetration properties and demonstrate the utility of third-harmonic response as a local diagnostic tool for surface defects in Nb3Sn films.

cond-mat.supr-con↗

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

Revealing isotropic abundant low-energy excitations in UTe$_2$ through complex microwave surface impedance

The complex surface impedance is a well-established tool to study the super- and normal-fluid responses of superconductors. Fundamental properties of the superconductor, such as the pairing mechanism, Fermi surface, and topological properties, also influence the surface impedance. We explore the microwave surface impedance of spin-triplet UTe$_2$ single crystals as a function of temperature using resonant cavity perturbation measurements employing a novel multi-modal analysis to gain insight into these properties. We determine a composite surface impedance of the crystal for each mode using resonance data combined with the independently measured normal state dc resistivity tensor. The normal state surface impedance reveals the weighting of current flow directions in the crystal of each resonant mode. For UTe$_2$, we find an isotropic $Δλ(T) \sim T^α$ power-law temperature dependence for the magnetic penetration depth for $T\le T_c/3$ with $α< 2$, which is inconsistent with a single pair of point nodes on the Fermi surface under weak scattering. We also find a similar power-law temperature dependence for the low-temperature surface resistance $R_s(T) \sim T^{α_R}$ with $α_R < 2$. We observe a strong anisotropy of the residual microwave loss across these modes, with some modes showing loss below the universal line-nodal value, to those showing substantially more. We compare to predictions for topological Weyl superconductivity in the context of the observed isotropic power-laws, and anisotropy of the residual loss.

cond-mat.supr-con↗

arXiv2025

A Physical Interpretation of Imaginary Time Delay

The scattering matrix $S$ linearly relates the vector of incoming waves to outgoing wave excitations, and contains an enormous amount of information about the scattering system and its connections to the scattering channels. Time delay is one way to extract information from $S$, and the transmission time delay $τ_T$ is a complex (even for Hermitian systems with unitary scattering matrices) measure of how long a wave excitation lingers before being transmitted. The real part of $τ_T$ is a well-studied quantity, but the imaginary part of $τ_T$ has not been systematically examined experimentally, and theoretical predictions for its behavior have not been tested. Here we experimentally test the predictions of Asano, et al. [Nat. Comm. 7, 13488 (2016)] for the imaginary part of transmission time delay in a non-unitary scattering system. We utilize Gaussian time-domain pulses scattering from a 2-port microwave graph supporting a series of well-isolated absorptive modes to show that the carrier frequency of the pulses is changed in the scattering process by an amount in agreement with the imaginary part of the independently determined complex transmission time delay, $\text{Im}[τ_T]$, from frequency-domain measurements of the sub-unitary $S$ matrix. Our results also generalize and extend those of Asano, et al., establishing a means to predict pulse propagation properties of non-Hermitian systems over a broad range of conditions.

physics.optics↗

arXiv2025

Microwave Microscope Studies of Trapped Vortex Dynamics in Superconductors

Trapped vortices in superconductors introduce residual resistance in superconducting radio-frequency (SRF) cavities and disrupt the operation of superconducting quantum and digital electronic circuits. Understanding the detailed dynamics of trapped vortices under oscillating magnetic fields is essential for advancing these technologies. We have developed a near-field magnetic microwave microscope to study the dynamics of a limited number of trapped vortices under the probe when stimulated by a localized rf magnetic field. By measuring the local second-harmonic response ($P_\mathrm{2f}$) at sub-femto-Watt levels, we isolate signals exclusively arising from trapped vortices, excluding contributions from surface defects and Meissner screening currents. Toy models of Niobium superconductor hosting vortex pinning sites are introduced and studied with Time-Dependent Ginzburg-Landau (TDGL) simulations of probe/sample interaction to better understand the measured second-harmonic response. The simulation results demonstrate that the second-harmonic response of trapped vortex motion under a localized rf magnetic field shares key features with the experimental data. This measurement technique provides access to vortex dynamics at the micron scale, such as depinning events and spatially-resolved pinning properties, as demonstrated in measurements on a Niobium film with an antidot flux pinning array.

cond-mat.supr-con↗

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

Microscopic Examination of SRF-quality Nb Films through Local Nonlinear Microwave Response

The performance of superconducting radio-frequency (SRF) cavities is sometimes limited by local defects. To investigate the RF properties of these local defects, especially those that nucleate RF magnetic vortices, a near-field magnetic microwave microscope is employed. Local third harmonic response (P3f) and its temperature-dependence and RF power-dependence are measured for one Nb/Cu film grown by Direct Current Magnetron Sputtering (DCMS) and six Nb/Cu films grown by High Power Impulse Magnetron Sputtering (HiPIMS) with systematic variation of deposition conditions. Five out of the six HiPIMS Nb/Cu films show a strong third harmonic response that is likely coming from RF vortex nucleation due to a low-Tc surface defect with a transition temperature between 6.3 K and 6.8 K, suggesting that this defect is a generic feature of air-exposed HiPIMS Nb/Cu films. A phenomenological model of surface defect grain boundaries hosting a low-Tc impurity phase is introduced and studied with Time-Dependent Ginzburg-Landau (TDGL) simulations of probe/sample interaction to better understand the measured third harmonic response. The simulation results show that the third harmonic response of RF vortex nucleation caused by surface defects exhibits the same general features as the data, including peaks in third harmonic response with temperature, and their shift and broadening with higher microwave amplitude. We find that the parameters of the phenomenological model (the density of surface defects that nucleate RF vortices and the depth an RF vortex travels through these surface defects) vary systematically with film deposition conditions. From the point of view of these two properties, the Nb/Cu film that is most effective at reducing the nucleation of RF vortices associated with surface defects can be identified.

cond-mat.supr-con↗

arXiv2024

Effects of Strong Capacitive Coupling Between Meta-Atoms in rf SQUID Metamaterials

We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency Superconducting Quantum Interference Devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the $N\times N \times 2$ overlapping metamaterial array, where we develop an understanding of the many ($8N^2-8N+3$) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10-30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.

cond-mat.supr-con↗

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↗

arXiv2023

Control of the Scattering Properties of Complex Systems By Means of Tunable Metasurfaces

We demonstrate the ability to control the scattering properties of a two-dimensional wave-chaotic microwave billiard through the use of tunable metasurfaces located on the interior walls of the billiard. The complex reflection coefficient of the metasurfaces can be varied by applying a DC voltage bias to varactor diodes on mushroom-shaped resonant patches, and this proves to be very effective at perturbing the eigenmodes of the cavity. Placing multiple metasurfaces inside the cavity allows us to engineer desired scattering conditions, such as coherent perfect absorption (CPA), by actively manipulating the poles and zeros of the scattering matrix through the application of multiple voltage biases. We demonstrate the ability to create on-demand CPA conditions at a specific frequency, and document the near-null of output power as a function of four independent parameters tuned through the CPA point. A remarkably low output-to-input power ratio of $\frac{P_{out}}{P_{in}} = 3.71 \times 10^{-8}$ is achieved near the CPA point at 8.54 GHz.

cond-mat.mes-hall↗

arXiv2023

Anomalous Loss Reduction Below Two-Level System Saturation in Aluminum Superconducting Resonators

Superconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two-level systems (TLS) which become the dominant source of loss in the few-photon and low temperature regime. In this study, capacitively-coupled aluminum half-wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators was observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters.

cond-mat.supr-con↗

arXiv2023

Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

Working in analogy with topological insulators in condensed matter, photonic topological insulators (PTI) have been experimentally realized, and protected electromagnetic edge-modes have been demonstrated in such systems. Moreover, PTI technology also emulates a synthetic spin-1/2 degree of freedom (DOF) in the reflectionless topological modes. The spin-1/2 DOF is carried by Quantum Valley Hall (QVH) / Quantum Spin Hall (QSH) interface modes created from the bianisotropic meta waveguide (BMW) platform, and realized both in simulation and experiment. We employ the PTI setting to build an ensemble of wave chaotic 1D metric graphs that display statistical properties consistent with Gaussian Symplectic Ensemble (GSE) statistics. The two critical ingredients required to create a physical system in the GSE universality class, the half-integer-spin DOF and preserved time-reversal invariance, are clearly realized in the QVH/QSH interface modes. We identify the anti-unitary T-operator for the PTI Hamiltonian underlying our experimental realization. An ensemble of PTI-edgemode metric graphs are proposed and experimentally demonstrated. We then demonstrate the Kramers degeneracy of eigenmodes of the PTI-graph systems with both numerical and experimental studies. We further conduct spectral statistical studies of the edgemode graphs and find good agreement with the GSE theoretical predictions. The PTI chaotic graph structures present an innovative and easily extendable platform for continued future investigation of GSE systems.

physics.optics↗