arXiv subjects

Daniel Leykam

Publications and source records attributed to Daniel Leykam.

At least 37 records · Page 2Linked to original sources

arXiv2023

Landscape approximation of low energy solutions to binary optimization problems

We show how the localization landscape, originally introduced to bound low energy eigenstates of disordered wave media and many-body quantum systems, can form the basis for hardware-efficient quantum algorithms for solving binary optimization problems. Many binary optimization problems can be cast as finding low-energy eigenstates of Ising Hamiltonians. First, we apply specific perturbations to the Ising Hamiltonian such that the low energy modes are bounded by the localization landscape. Next, we demonstrate how a variational method can be used to prepare and sample from the peaks of the localization landscape. Numerical simulations of problems of up to $10$ binary variables show that the localization landscape-based sampling can outperform QAOA circuits of similar depth, as measured in terms of the probability of sampling the exact ground state.

quant-ph↗

arXiv2023

Photonic Flatband Resonances in Multiple Light Scattering

We introduce the concept of photonic flatband resonances for the example of an array of high index dielectric particles. We employ the multiple Mie scattering theory and reveal that both short range and long range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both nearfield and far field characteristics, we uncover how the flatbands emerge due to fine tuning of resonators radiation fields, and predict that hybridization of a flatband resonance with an electric hotspot can lead to giant values of the Purcell factor for the electric dipolar emitters.

physics.optics↗

arXiv2023

Self-steepening-induced stabilization of nonlinear edge waves at photonic valley-Hall interfaces

Localized nonlinear modes at valley-Hall interfaces in staggered photonic graphene can be described in the long-wavelength limit by a nonlinear Dirac-like model including spatial dispersion terms. It leads to a modified nonlinear Schrödinger equation for the wave field amplitude that remarkably incorporates a nonlinear velocity term. We show that this nonlinear velocity correction results in a counter-intuitive stabilization effect for relatively high-amplitude plane-wave-like edge states, which we confirm by calculation of complex-valued small-amplitude perturbation spectra and direct numerical simulation of propagation dynamics in staggered honeycomb waveguide lattices with on-site Kerr nonlinearity. Our findings are relevant to a variety of nonlinear photonic systems described by Dirac-like Hamiltonians.

physics.optics↗

arXiv2023

Pseudospin-2 in photonic chiral borophene

Pseudospin is an angular momentum degree of freedom introduced in analogy to the real electron spin in the effective massless Dirac-like equation used to describe wave evolution at conical intersections such as the Dirac cones of graphene. Here, we study a photonic implementation of a chiral borophene allotrope hosting a pseudospin-2 conical intersection in its energy-momentum spectrum. The presence of this fivefold spectral degeneracy gives rise to quasiparticles with pseudospin up to $\pm2$. We report on conical diffraction and pseudospin-orbit interaction of light in photonic chiral borophene, which, as a result of topological charge conversion, leads to the generation of highly charged optical phase vortices.

physics.optics↗

arXiv2022

Unravelling quantum chaos using persistent homology

Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a topology-preserving embedding method that allows reconstructing dynamical attractors, the topologies of which can be used to identify chaotic behaviour. Open quantum systems can similarly exhibit non-trivial dynamics, but the existing toolkit for classification and quantification are still limited, particularly for experimental applications. In this work, we present a topological pipeline for characterizing quantum dynamics, which draws inspiration from the classical approach by using single quantum trajectory unravelings of the master equation to construct analogue 'quantum attractors' and extracting their topology using persistent homology. We apply the method to a periodically modulated Kerr-nonlinear cavity to discriminate parameter regimes of regular and chaotic phase using limited measurements of the system.

quant-ph↗

arXiv2022

Boosting Topological Zero Modes Using Elastomer Waveguide Arrays

We employ the Su-Schrieffer-Heeger model in elastic polymer waveguide arrays to design and realize travelling topologically protected modes. The observed delocalization of the optical field for superluminal defect velocities agrees well with theoretical descriptions. We apply mechanical strain to modulate the lattices' coupling coefficient. This work demonstrates a novel platform for rapid prototyping of topological photonic devices and establishes strain-tuning as a viable design parameter for topological waveguide arrays.

physics.optics↗

arXiv2022

Dark soliton detection using persistent homology

Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and computational resources to train. We show how a topological data analysis technique, persistent homology, can be used to rapidly and reliably identify qualitative features in experimental image data. The identified features can be used as inputs to simple supervised machine learning models such as logistic regression models, which are easier to train. As an example we consider the identification of dark solitons using a dataset of 6257 labelled atomic Bose-Einstein condensate density images.

physics.atom-ph↗

arXiv2022

Persistent homology analysis of a generalized Aubry-André-Harper model

Observing critical phases in lattice models is challenging due to the need to analyze the finite time or size scaling of observables. We study how the computational topology technique of persistent homology can be used to characterize phases of a generalized Aubry-André-Harper model. The persistent entropy and mean squared lifetime of features obtained using persistent homology behave similarly to conventional measures (Shannon entropy and inverse participation ratio) and can distinguish localized, extended, and crticial phases. However, we find that the persistent entropy also clearly distinguishes ordered from disordered regimes of the model. The persistent homology approach can be applied to both the energy eigenstates and the wavepacket propagation dynamics.

cond-mat.dis-nn↗

arXiv2022

Computing Electronic Correlation Energies using Linear Depth Quantum Circuits

Efficient computation of molecular energies is an exciting application of quantum computing for quantum chemistry, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing variational quantum algorithms, which require deep entangling quantum circuit ansatzes to capture correlations, to small molecules. Here we demonstrate a variational NISQ-friendly algorithm that generates a set of mean-field Hartree-Fock (HF) ansatzes using multiple shallow circuits with depth linear in the number of qubits to estimate electronic correlation energies via perturbation theory up to the second order. We tested the algorithm on several small molecules, both with classical simulations including noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. As fidelities of quantum processors continue to improve our algorithm will enable the study of larger molecules compared to other approaches requiring higher-order polynomial circuit depth.

quant-ph↗

arXiv2022

Photonic quantum Hall effects

This article reviews the development of photonic analogues of quantum Hall effects, which have given rise to broad interest in topological phenomena in photonic systems over the past decade. We cover early investigations of geometric phases, analogies between electronic systems and the spectra of periodic photonic media including photonic crystals, efforts to generalize topological band theory to open, dissipative, and nonlinear wave systems, pursuit of useful device applications, and ongoing studies of photonic Hall effects in classical nonlinear optics and the quantum regime of strong photon-photon interactions.

physics.optics↗

arXiv2022

Fock State-enhanced Expressivity of Quantum Machine Learning Models

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.

quant-ph↗

arXiv2021

Nonlinear signatures of Floquet band topology

We study how the nonlinear propagation dynamics of bulk states may be used to distinguish topological phases of slowly-driven Floquet lattices. First, we show how instabilities of nonlinear Bloch waves may be used to populate Floquet bands and measure their Chern number via the emergence of nontrivial polarization textures in a similar manner to static (undriven) lattices. Second, we show how the nonlinear dynamics of non-stationary superposition states may be used to identify dynamical symmetry inversion points in the intra-cycle dynamics, thereby allowing anomalous Floquet phases to be distinguished from the trivial phase. The approaches may be readily implemented using light propagation in nonlinear waveguide arrays.

physics.optics↗

arXiv2021

Quantum transient heat transport in the hyper-parametric oscillator

We explore nonequilibrium quantum heat transport in nonlinear bosonic systems in the presence of a non-Kerr-type interaction governed by hyper-parametric oscillation due to two-photon hopping between the two cavities. We estimate the thermodynamic response analytically by constructing the $su(2)$ algebra of the nonlinear Hamiltonian and predict that the system exhibits a negative excitation mode. Consequently, this specific form of interaction enables the cooling of the system by inducing a ground state transition when the number of particles increases, even though the interaction strength is small. We demonstrate a transition of the heat current numerically in the presence of symmetric coupling between the system and bath and show long relaxation times in the cooling phase. We compare with the Kerr-type Bose-Hubbard form of interaction induced via cross-phase modulation, which does not exhibit any such transition. We further compute the nonequilibrium heat current in the presence of two baths at different temperatures and observe that the cooling effect for the non-Kerr-type interaction persists. Our findings may help in the manipulation of quantum states using the system's interactions to induce cooling.

quant-ph↗

arXiv2021

Photonic band structure design using persistent homology

The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical systems such as spin models and multiqubit entangled states. Here we propose persistent homology as a tool for characterizing and optimizing band structures of periodic photonic media. Using the honeycomb photonic lattice Haldane model as an example, we show how persistent homology is able to reliably classify a variety of band structures falling outside the usual paradigms of topological band theory, including "moat band" and multi-valley dispersion relations, and thereby control the properties of quantum emitters embedded in the lattice. The method is promising for the automated design of more complex systems such as photonic crystals and Moire superlattices.

physics.optics↗

arXiv2021

Gradient catastrophe of nonlinear photonic valley-Hall edge pulses

We derive nonlinear wave equations describing the propagation of slowly-varying wavepackets formed by topological valley-Hall edge states. We show that edge pulses break up even in the absence of spatial dispersion due to nonlinear self-steepening. Self-steepening leads to the previously-unattended effect of a gradient catastrophe, which develops in a finite time determined by the ratio between the pulse's nonlinear frequency shift and the size of the topological band gap. Taking the weak spatial dispersion into account results then in the formation of stable edge quasi-solitons. Our findings are generic to systems governed by Dirac-like Hamiltonians and validated by numerical modeling of pulse propagation along a valley-Hall domain wall in staggered honeycomb waveguide lattices with Kerr nonlinearity.

physics.optics↗

arXiv2021

Probing band topology using modulational instability

We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations of the nonlinear Bloch waves are sensitive to topological band inversions. At longer timescales, nonlinear wave mixing induces spreading of energy through the entire band and spontaneous creation of wave polarization singularities determined by the band Chern number. Our analytical and numerical results establish modulational instability as a tool to probe bulk topological invariants and create topologically non-trivial wave fields.

physics.optics↗

arXiv2020

Topological phases in ring resonators: recent progress and future prospects

Topological photonics has emerged as a novel paradigm for the design of electromagnetic systems from microwaves to nanophotonics. Studies to date have largely focused on the demonstration of fundamental concepts, such as non-reciprocity and waveguiding protected against fabrication disorder. Moving forward, there is a pressing need to identify applications where topological designs can lead to useful improvements in device performance. Here we review applications of topological photonics to ring resonator-based systems, including one- and two-dimensional resonator arrays, and dynamically-modulated resonators. We evaluate potential applications such as quantum light generation, disorder-robust delay lines, and optical isolation, as well as future research directions and open problems that need to be addressed.

physics.optics↗

arXiv2020

Edge modes in 2D electromagnetic slab waveguides: analogues of acoustic plasmons

We analyze planar electromagnetic waves confined by a slab waveguide formed by two perfect electrical conductors. Remarkably, 2D Maxwell equations describing transverse electromagnetic modes in such waveguides are exactly mapped onto equations for acoustic waves in fluids or gases. We show that interfaces between two slab waveguides with opposite-sign permeabilities support 1D edge modes, analogous to surface acoustic plasmons at interfaces with opposite-sign mass densities. We analyze this novel type of edge modes for the cases of isotropic media and anisotropic media with tensor permeabilities (including hyperbolic media). We also take into account `non-Hermitian' edge modes with imaginary frequencies or/and propagation constants. Our theoretical predictions are feasible for optical and microwave experiments involving 2D metamaterials.

physics.class-ph↗