Quantum and Classical Optics of Plasmonic Systems: 3d/2d Materials and Photonic Topological Insulators

At the interface of two different media such as metal and vacuum, light can couple to the electrons of the metal to form a wave that is bound to the interface. This wave is called a surface plasmon-plariton (SPP), generally characterized by intense fields that decay quickly away from the interface. Due to their unique properties, SPPs have found a broad range of applications in various areas of science, including light harvesting, medical science, energy transfer and imaging. In addition to the widely studied classical plasmonics, quantum plasmonics is also attracting considerable interest in the electromagnetics and quantum optics communities. In this thesis several new areas of investigation into quantum plasmonics is presented, focusing on entanglement mediated by SPPs in several different environments: 3D waveguides, 2D surfaces and on photonic topological insulators. Entanglement is an experimentally verified property of nature where pairs of quantum systems are connected in some manner such that the quantum state of each system cannot be described independently. Generating, preserving, and controlling entanglement is necessary for many quantum computer implementations. It is highly desirable to control entanglement between two multi-level emitters such as quantum dots via a macroscopic, easily-adjusted external parameter. SPPs guided by the medium, as a coupling agent between quantum dots, are highly tunable and offer a promising way to achieve having control over a SPP mediated entanglement. We first consider two quantum dots placed above 3D finite length waveguides. We have restricted our consideration to two waveguides types, i.e. a metal nanowire and a groove waveguide. Our main results in this work are to show that realistic finite-length nanowire and groove waveguides, with their associated discontinuities, play a crucial role in the engineering of highly entangled states. It is demonstrated that proper positioning of the emitters with respect to the waveguide edges can lead to a significant increase in entanglement compared to the case of the emitter coupled to an infinite plasmonic waveguide. Moreover, even for the infinite-length case, discontinuities in the waveguides do not always play a detrimental role, to be more specific, an increase in entanglement compared to the unperturbed waveguides can be achieved by introducing coupling slots (engineered perturbations) into the structure. In addition to 3D environments, two dimensional (2D) materials are of intense interest due to their extraordinary capabilities to manipulate reflection and transmission characteristics, and beam-forming. Some notable examples of 2D layered crystals include graphene, black phosphorus (BP) and boron nitride. Graphene in particular has received considerable attention as a promising 2D surface for many applications relating to its integrability and electronic tune-ability. Black phosphorus is also a layered material that has recently been exfoliated into its multilayers, showing good electrical transport properties and promising optical charactristics. Most of the previous studies of the electromagnetic response of 2D surfaces and metallic surface plasmons have considered isotropic structures with omnidirectional plasmonic surface wave propagation on the plane of these materials. Such an omnidirectional surface wave propagation does not allow for launching energy from electromagnetic source to a specific target on the surface, which is a desirable characteristic. However, an appropriate structured anisotropic surface can provide such a capability, such as an array of graphene strips. In addition, by tuning of the graphene doping it is possible to have a hyperbolic surface response. Working in this regime of surface conductivity, it is possible to launch SPPs along a specific direction, which is tunable via doping of the graphene. In this work, the electromagnetic response of anisotropic 2D surfaces has been investigated based on the analysis of the Green’s function for the surface plasmonic wave contribution of the Sommerfeld integral. The Sommerfeld integral form of the Green’s function can be time-consuming to evaluate, and here, it has been shown that for the surface waves, this integral can be evaluated efficiently as a mixture of continuous and discrete spectrums associated to the radiation of the source into the ambient space and energy coupled to the SPPs. Graphene strip arrays provide directive surface waves in the low THz regime, and unperturbed black phosphorus provides a similar response for higher frequency ranges. All plasmonic devices are impacted by SPP diffraction at surface defects and discontinuities. In particular, for reciprocal materials a surface defect/discontinuity can both scatter a forward mode into a backward mode (and vice versa) and cause significant radiation/diffraction of the SPP. The presence of a backward state comes from time reversal (TR) symmetry; when broken, a backward state may be absent, and reflection at a discontinuity can be suppressed. As a result, surface energy becomes unidirectional and follows the contour of the interface. This type of system can be broadly classified as a photonic topological insulators (PTIs). The properties of PTIs are quantified by the Berry phase, Berry connection, and an invariant known as the Chern number. Also the physical meaning of the Berry phase, connection, and curvature, how these quantities arise in electromagnetic problems, and the significance of Chern numbers for unidirectional, scattering-immune surface wave propagation are discussed. The Chern numbers for the electromagnetic modes supported by a biased plasma have been calculated. It has been demonstrated that the modes supported by biased plasmas indeed possess non-trivial Chern numbers, which leads to the propagation of a topologically protected and unidirectional surface modes (energy) at the interface between the biased plasma and topologically trivial material. The ability to guide the energy from one quantum dot to another one is a great advantage to achieve highly entangled states. Here, in this thesis for the first time, we investigated the unidirectional surface wave assisted entanglement in PTIs. We have investigated spontaneous and pumped entanglement of two level systems (quantum dots) in the vicinity of a photonic topological insulator interface, which supports a unidirectional SPP in the common bandgap of the bulk materials. We also have derived a master equation for quantum dots interactions in a general three-dimensional, nonreciprocal, inhomogeneous and lossy environment. The resulting entanglement is shown to be extremely robust to defects occurring in the material system

Roadmap on structured waves

Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compared to a single plane wave. Complex wavefields with inhomogeneities in the amplitude, phase, and polarization, including topological structures and singularities, underpin modern nanooptics and photonics, yet they are equally important, e.g., for quantum matter waves, acoustics, water waves, etc. Structured waves are crucial in optical and electron microscopy, wave propagation and scattering, imaging, communications, quantum optics, topological and non-Hermitian wave systems, quantum condensed-matter systems, optomechanics, plasmonics and metamaterials, optical and acoustic manipulation, and so forth. This Roadmap is written collectively by prominent researchers and aims to survey the role of structured waves in various areas of wave physics. Providing background, current research, and anticipating future developments, it will be of interest to a wide cross-disciplinary audience.Comment: 110 pages, many figure

Strong coupling regime of semiconductor quantum dot embedded in the nano-cavity

Photonic lattices represent suitable systems for investigation of wave propagation in periodic structures [1]. However, different unavoidable defects may arise either during their process of fabrication or as result of misusage, accidental damage, etc. Although undesirable in the first place, these imperfections enable the existence of different types of stable, localized defect modes [2]. In this paper, we investigate light propagation through composite photonic lattice composed of two identical linear and lossless lattices. The interface between them represents a geometric defect, while each lattice contains a single nonlinear defect that is placed symmetrically with respect to the interface. Depending on the input light beam parameters (its position, width and transverse tilt), the width of geometric defect, strength and position of the nonlinear defects, different dynamical regimes have been identified. These dynamical regimes are caused by the balance of photonic lattice potentials’ contributions originating from the presence of the geometric and two nonlinear defects. We have found numerically conditions under which dynamically stable bounded modes can exist in the area between nonlinear defects or between a nonlinear and a geometric defect. Various types of localized modes such as: two-hump, multi-hump, one- and multicomponent moving breathers localized at a certain area among defects have been observed. The parameters can be adjusted to capture light and to prevent light launched inside the area among defects to leave it, i.e. this corresponds to the appearance of the modes trapped inside this area. Since the configuration of the lattice prevents transmission of the light through the area confined by defects, these modes can formally be related to Fano resonances and Fano- blockade [3, 4]. When light is launched outside the area among defects, different dynamical regimes have been distinguished: total reflection, single and double partial reflection and full transmission through the area among defects. These numerical findings may lead to interesting applications such as blocking, filtering and transporting light beams through the optical medium. Photonic devices based on resonant tunneling such as waveguides interacting through the area between defects, may be applied as add-drop filters.V International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 and the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices" : PHOTONICA2015 : book of abstracts; August 24-28, 2015; Belgrad

Light, the universe and everything – 12 Herculean tasks for quantum cowboys and black diamond skiers

The Winter Colloquium on the Physics of Quantum Electronics (PQE) has been a seminal force in quantum optics and related areas since 1971. It is rather mind-boggling to recognize how the concepts presented at these conferences have transformed scientific understanding and human society. In January 2017, the participants of PQE were asked to consider the equally important prospects for the future, and to formulate a set of questions representing some of the greatest aspirations in this broad field. The result is this multi-authored paper, in which many of the world’s leading experts address the following fundamental questions: (1) What is the future of gravitational wave astronomy? (2) Are there new quantum phases of matter away from equilibrium that can be found and exploited – such as the time crystal? (3) Quantum theory in uncharted territory: What can we learn? (4) What are the ultimate limits for laser photon energies? (5) What are the ultimate limits to temporal, spatial and optical resolution? (6) What novel roles will atoms play in technology? (7) What applications lie ahead for nitrogen-vacancy centres in diamond? (8) What is the future of quantum coherence, squeezing and entanglement for enhanced super-resolution and sensing? (9) How can we solve (some of) humanity’s biggest problems through new quantum technologies? (10) What new understanding of materials and biological molecules will result from their dynamical characterization with free-electron lasers? (11) What new technologies and fundamental discoveries might quantum optics achieve by the end of this century? (12) What novel topological structures can be created and employed in quantum optics

Computational Explorations of Enhanced Nonlinearities and Quantum Optical Effects in Photonic Nanostructures

In this thesis, we present a comprehensive theoretical analysis and computataional study of optical nonlinearities in the graphene-based and silicon-based metamaterials. The novel numerical methods and corresponding results described in this work give a significant impact on our understanding of surface plasmon resonance in artificial optical materials, which facilitates the design and fabrication of new photonic devices with enhanced nonlinear optical functionalities. // Two generic nonlinear metasurfaces are elaborated in this dissertation, namely, graphene-based metasurfaces and silicon-based metasurfaces. Employing a novel homogenization technique, the effective second-order susceptibility of graphene metasurfaces is calculated, which can be enhanced by more than two orders of magnitude as compared to the intrinsic value of graphene sheet. There is excellent agreement between the predictions of the homogenization method and those based on rigorous numerical solutions of Maxwell equations. Moreover, we also illustrate that the effective Raman susceptibilities of silicon-based metasurfaces can be enhanced by 3 to 4 orders of magnitude as compared to the intrinsic value of silicon. Even though the homogenization method for silicon-based metasurfaces is not as accurate as graphene-based, this result still gives a qualitative analysis on the effective Raman susceptibility of silicon-based metasurfaces. // Additionally, the optical nonlinearity is utilized to design a two-mode quantum waveguide made of coupled silicon photonic crystal nanocavities in the last part of the thesis. Finally, we also explore the implications of our work to the development of new active photonic nano devices with new or improved functionalities

Interfacing single photons and single quantum dots with photonic nanostructures

Photonic nanostructures provide means of tailoring the interaction between light and matter and the past decade has witnessed a tremendous experimental and theoretical progress in this subject. In particular, the combination with semiconductor quantum dots has proven successful. This manuscript reviews quantum optics with excitons in single quantum dots embedded in photonic nanostructures. The ability to engineer the light-matter interaction strength in integrated photonic nanostructures enables a range of fundamental quantum-electrodynamics experiments on, e.g., spontaneous-emission control, modified Lamb shifts, and enhanced dipole-dipole interaction. Furthermore, highly efficient single-photon sources and giant photon nonlinearities may be implemented with immediate applications for photonic quantum-information processing. The review summarizes the general theoretical framework of photon emission including the role of dephasing processes, and applies it to photonic nanostructures of current interest, such as photonic-crystal cavities and waveguides, dielectric nanowires, and plasmonic waveguides. The introduced concepts are generally applicable in quantum nanophotonics and apply to a large extent also to other quantum emitters, such as molecules, nitrogen vacancy ceters, or atoms. Finally, the progress and future prospects of applications in quantum-information processing are considered.Comment: Updated version resubmitted to Reviews of Modern Physic

Strong coupling regime of semiconductor quantum dot embedded in the nano-cavity

Self-assembled quantum dots on semiconductor substrate have found many applications in optoelectronic devices such as single photon emitters, qubits for quantum computers, etc [1,2]. In this work, we study the interaction of the electron in nano-dot embedded in the nano-cavity with photons of a incident beam. Theoretical framework of our study is the semi-classical model Hamiltonian, which describes nano-dot interacting with the electromagnetic field. For the practical calculations we have employed rotating wave approximation. The influence of both, decay rates of cavities and quantity of coupling constant to level shift of electrons in a quantum dot have been analyzed. The boundary between strong coupling and weak-coupling regimes has been presented.V International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 and the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices" : PHOTONICA2015 : book of abstracts; August 24-28, 2015; Belgrad

Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor

In this paper, we use a powerful mathematical concept based on Fisher information (FI) to estimate the cross-sensitivity of multi-parameter sensors. FI has been used in various branches of natural and social sciences [1], in both classical and quantum systems [2]. Lately, it has been used for estimation of interferometer sensitivity in quantum optics [3], as well as in classical optical interferometers [4]. Here, we expand its application to fibre grating sensors that are sensitive to several environmental (temperature, humidity) and mechanical (strain, pressure, curvature) parameters simultaneously [5]. FI is a local probability measure of obtaining an unknown parameter θ from the data measured at the sensor output, X. In the theory of measurement, FI directly enters the relation which determines the lower bound of the measurement uncertainty known as Cramer-Rao bound (CRB = 1/ FI (θ ) ). The sensor sensitivity is optimized by maximization of the corresponding FI. In the case of a multi-parameter sensor, FI assumes a matrix form defined via the probability distribution function f(X| θ) of the measured variable X conditioned by θ, where both X and θ are vector quantities. ( ) ( ) i n j n f X FI E i j i j ; 1,2,... ; 1,2,..., 2 ln , = = ∂ ∂ ∂ = − θ θ θ θ . Here, we develop a comprehensive model of the spectral response of fibre gratings to changes in multiple parameters and apply Fisher's formalism to optimize their sensitivity in the realistic parameter space. We start from a 1-parameter model of a long-period grating sensor of curvature and corroborate our approach by comparison with the conventional sensitivity models and the experimental data. We then expand the model to describe a 2-parameter long-period grating sensor of curvature and temperature. Based on this analysis, we recommend the multi-parameter interrogation scheme (estimator) and optimize grating parameters to render the highest sensitivity.V International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 and the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices" : PHOTONICA2015 : book of abstracts; August 24-28, 2015; Belgrad