Stabilization of the transmission Schrodinger equation with boundary time-varying delay

We consider a system of transmission of the Schrodinger equation with Neumann feedback control that contains a time-varying delay term and that acts on the exterior boundary. Using a suitable energy function and a suitable Lyapunov functionnal, we prove under appropriate assumptions that the solutions decay exponentially. Keywords: Schrodinger equation, transmission problem, time-varying delay, exponential stability, boundary stabilization. ¨ MSC: 35Q93, 93D15 REFERENCES [1] Allag, I., & Rebiai, S. (2014). Well-posedness, regularity and exact controllability for the problem of transmission of the Schrödinger equation. Quarterly of Applied Mathematics, 72(1), 93-108.‏. Search in Google Scholar   Digital Object Identifier MathSciNet [2] Bayili, G., Aissa, A. B., & Nicaise, S. (2020). Same decay rate of second order evolution equations with or without delay. Systems & Control Letters, 141, 104700.‏. Search in Google Scholar   Digital Object Identifier [3] Cavalcanti, M. M., Corrêa, W. 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Roadmap on optical rogue waves and extreme events

The pioneering paper 'Optical rogue waves' by Solli et al (2007 Nature 450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of 'optical rogue waves'. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as 'an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses'. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1-4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms 'optical rogue waves' and 'extreme events' do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From this point of view, a number of the scientists who work in this area of research have come together to present their research in a single review article that will greatly benefit all interested parties of this research direction. Whether the authors of this 'roadmap' have similar views or different from the original concept, the potential reader of the review will enrich their knowledge by encountering most of the existing views on the subject. Previously, a special issue on optical rogue waves (2013 J. Opt. 15 060201) was successful in achieving this goal but over two years have passed and more material has been published in this quickly emerging subject. Thus, it is time for a roadmap that may stimulate and encourage further research.Peer ReviewedPostprint (author's final draft

Boundary vibration control of a floating wind turbine system with mooring lines

In this paper, we investigate dynamic modeling, active boundary control design, and stability analysis for a coupled floating wind turbine (FWT) system, which is connected with two flexible mooring lines. It is a coupled beam-strings structure, and we design two boundary controllers to restrain the vibrations of this flexible system caused by external disturbances based on the coupled partial differential equations and ordinary differential equations (PDEs–ODEs) model. Meanwhile, significant performance of designed boundary controllers and system’s stability are theoretically analyzed, and a set of simulation results are provided to show efficacy of the proposed approach

Three-wave Mixing in Superconducting Circuits: Stabilizing Cats with SNAILs

Three-wave mixing, by which a photon splits into two correlated photons and vice versa, is a powerful quantum process with many applications in fundamental quantum mechanics experiments and quantum information processing. However, in superconducting circuits, the predominant form of nonlinearity provided by a Josephson junction is only of even order, and thus symmetry forbids three-wave mixing. This Kerr nonlinearity is useful in its own right for engineering quantum operations, but it is accompanied by unavoidable frequency shifts that become especially problematic as the number of interacting electromagnetic modes, and therefore frequency crowding, increases. How then can we endow superconducting devices with the necessary nonlinearity to perform three-wave mixing? In this thesis, we introduce a simple and compact way to add three-wave-mixing capabilities to a superconducting circuit: the superconducting nonlinear inductive element (SNAIL). Additionally, we optimize these devices for quantum-coherent three-wave mixing applications. The many orders of magnitude over which circuit nonlinearities may be designed allow a rich space for different behaviors. We focus on three-wave mixing for single-mode squeezing in two distinct contexts: quantum-noise-limited parametric amplification, and protection of quantum information in a Schrödinger cat qubit. The former showcases the capability to design three-wave-mixing processes free of residual Kerr nonlinearity; the latter explicitly includes Kerr nonlinearity to protect quantum information from decoherence and quickly manipulate it. Both applications indicate the importance of three-wave mixing in quantum information contexts and for the exploration of fundamental quantum effects

Theoretical and Experimental Studies of XUV Multielectron (Auto-)Ionization Dynamics in Helium and Molecular Hydrogen

This work consists of two parts: theoretical studies of laser-intensity dependent ionization processes in the helium atom and experimental attosecond transient-absorption spectroscopy studies of the (auto-)ionization dynamics of the Qn resonances of molecular hydrogen. In an experiment, motivating the simulations of ionization processes in helium, abrupt ionization of doubly excited states above a certain critical NIR-laser intensity was observed. Numerically solving the quantum-mechanical one-dimensional time-dependent Schrödinger equation for two electrons, the time-dependent population of relevant atomic states during the laser-pulse interaction is directly accessed. With respect to the theoretical results, an ionization mechanism for the doubly excited states is suggested, where non-sequential double ionization, arising due to electron– electron interaction, plays an important role. The investigations of the (auto-)ionization processes of doubly excited states in the hydrogen molecule concentrated on measuring timeand energy-dependent XUV absorption signals to separate the autoionization effects from the overall continuum absorption of H2. First results of (auto-)ionization effects in the hydrogen molecule were obtained in a technically challenging absorption spectroscopy study

Harnessing optical micro-combs for microwave photonics

In the past decade, optical frequency combs generated by high-Q micro-resonators, or micro-combs, which feature compact device footprints, high energy efficiency, and high-repetition-rates in broad optical bandwidths, have led to a revolution in a wide range of fields including metrology, mode-locked lasers, telecommunications, RF photonics, spectroscopy, sensing, and quantum optics. Among these, an application that has attracted great interest is the use of micro-combs for RF photonics, where they offer enhanced functionalities as well as reduced size and power consumption over other approaches. This article reviews the recent advances in this emerging field. We provide an overview of the main achievements that have been obtained to date, and highlight the strong potential of micro-combs for RF photonics applications. We also discuss some of the open challenges and limitations that need to be met for practical applications.Comment: 32 Pages, 13 Figures, 172 Reference

Topological Phenomena in Time-Multiplexed Resonator Networks

In 2008, the prediction that gyromagnetic photonic crystals could host analogs of the quantum Hall effect sparked a revolution in photonics, as it became apparent that the synergy between photonics and topological physics provides distinct opportunities for fundamental research and technological innovation. Since then, topological photonics has produced experimental realizations of numerous theories from topological condensed matter physics, while the inherent robustness of topological edge states has enabled novel devices like topological lasers and topological quantum sources. Despite this success, practical challenges limit the breadth of topological phenomena accessible to the existing experimental platforms for topological photonics. Therefore, to accelerate the pace of scientific discovery and to inspire the next generation of topological technologies, it is desirable to develop a platform that overcomes the limitations of traditional topological photonic architectures. In this thesis, I propose time-multiplexed resonator networks as a next-generation platform for topological photonics, and I present three experimental projects that demonstrate the diverse capabilities of this platform. In the first project, I use a time-multiplexed resonator network to demonstrate topological dissipation, in which nontrivial topology is encoded in the dissipation spectrum of a resonator array. I show measurements of dissipative topological phenomena in one- and two-dimensions and discuss how topological dissipation can be used to design resonator arrays with topologically robust quality factors. In the second project, I adapt a time-multiplexed resonator network to realize a topological mode-locked laser, and I show that this laser can realize non-Hermitian topological phenomena that had not previously been demonstrated in topological photonics. Finally, I experimentally study the dynamics of cavity solitons in a topological resonator array. This project demonstrates a general technique for realizing cavity solitons in large arrays of coupled resonators, which has become a relevant challenge in the soliton community over the past several years.</p

Experiments on synthetic dimensions in photonics

The first and introductory section of the dissertation presents the working principle of a one- and two-dimensional photonic mesh lattice based on the time-multiplexing technique. The basis of a random walk interrelated to the corresponding light and quantum walk is comprehensively discussed as well. The second part of the dissertation consists of three experiments on a one-dimensional photonic mesh lattice. Firstly, the Kapitza-based guiding light project models the Kapitza potential as a continuous Pauli-Schrödinger-like equation and presents an experimental observation of light localization when the transverse modulation is bell-shaped but with a vanishing average along the propagation direction. Secondly, the optical thermodynamics project experimentally demonstrates for the first time that any given initial modal occupancy reaches thermal equilibrium by following a Rayleigh-Jeans distribution when propagates through a multimodal photonic mesh lattice with weak nonlinearity. Remarkably, the final modal occupancy possesses a unique temperature and chemical potential that have nothing to do with the actual thermal environment. Finally, the quantum interference project discusses an experimental all-optical architecture based on a coupled-fiber loop for generating and processing time-bin entangled single-photon pairs. Besides, it shows coincidence-to-accidental ratio and quantum interference measurements relying on the phase modulation of those time bins. The third part of the dissertation comprises two experiments on a two-dimensional photonic mesh lattice. The first project discusses the experimental realization of a two-dimensional mesh lattice employing short- and long-range interaction. To some extent, the second project presents a nonconservative system based on a two-dimensional photonic mesh lattice exploiting parity-time (PT) symmetry

Numerical and Analytical Methods in Electromagnetics

Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics

The Dipole Response of an Ionization Threshold within Ultrashort and Strong Fields

In this work, the strong-field-modified dipole response at the ionization threshold of helium is studied. The dipole response is induced by an attosecond pulse in the extreme ultraviolet spectral range and is manipulated by an ultrashort and strong femtosecond pulse in the near-infrared. To probe the response, the transient absorption spectrum of helium is recorded for different time delays between both pulses and different intensities of the femtosecond pulse. From the spectra, the dipole response of the ionization threshold is reconstructed, which is linked to the dynamics of excited electrons with energies in the transition region from bound to free. To identify the underlying processes of light-matter interaction leading to the observed structures in the time and spectral domain, different quantum-mechanical model simulations are conducted. As a result, the measured dipole response reveals light-induced energy shifts of the photoelectron’s kinetic energy close to the parent ion, signatures for field-driven recollisions of a photoelectron into the parent ion, and a temporal amplitude and phase gating mechanism. With the latter, the build-up dynamics of complex spectral structures are temporally resolved, which are the time-dependent separation and line-shape modification of the doubly excited Rydberg series as well as the temporal build-up of the ionization threshold