Rigorous direct and inverse design of photonic-plasmonic nanostructures

Designing photonic-plasmonic nanostructures with desirable electromagnetic properties is a central problem in modern photonics engineering. As limited by available materials, engineering geometry of optical materials at both element and array levels becomes the key to solve this problem. In this thesis, I present my work on the development of novel methods and design strategies for photonic-plasmonic structures and metamaterials, including novel Green’s matrix-based spectral methods for predicting the optical properties of large-scale nanostructures of arbitrary geometry. From engineering elements to arrays, I begin my thesis addressing toroidal electrodynamics as an emerging approach to enhance light absorption in designed nanodisks by geometrically creating anapole configurations using high-index dielectric materials. This work demonstrates enhanced absorption rates driven by multipolar decomposition of current distributions involving toroidal multipole moments for the first time. I also present my work on designing helical nano-antennas using the rigorous Surface Integral Equations method. The helical nano-antennas feature unprecedented beam-forming and polarization tunability controlled by their geometrical parameters, and can be understood from the array perspective. In these projects, optimization of optical performances are translated into systematic study of identifiable geometric parameters. However, while array-geometry engineering presents multiple advantages, including physical intuition, versatility in design, and ease of fabrication, there is currently no rigorous and efficient solution for designing complex resonances in large-scale systems from an available set of geometrical parameters. In order to achieve this important goal, I developed an efficient numerical code based on the Green’s matrix method for modeling scattering by arbitrary arrays of coupled electric and magnetic dipoles, and show its relevance to the design of light localization and scattering resonances in deterministic aperiodic geometries. I will show how universal properties driven by the aperiodic geometries of the scattering arrays can be obtained by studying the spectral statistics of the corresponding Green’s matrices and how this approach leads to novel metamaterials for the visible and near-infrared spectral ranges. Within the thesis, I also present my collaborative works as examples of direct and inverse designs of nanostructures for photonics applications, including plasmonic sensing, optical antennas, and radiation shaping

Fisher Information and entanglement of non-Gaussian spin states

In this thesis, we study a novel method to extract the Fisher information of quantum states from direct measurements without the need for state reconstruction. Our method characterizes the distinguishability of experimental probability distributions of the collective spin. The Fisher information is obtained via the observed rate of change of their statistical distance as a function of an experimental control parameter, which constitutes a phase transformation of the quantum state. The employed experimental system is a binary Bose-Einstein condensate of several hundred atoms. We use a combination of coherent collisional interaction and linear Rabi coupling of the two atomic states to generate collective non-classical spin states via quantum dynamics close to an unstable fixed point of the corresponding classical system. The fast redistribution of quantum uncertainty results in Gaussian spin-squeezed states for short evolution times which turn into non-Gaussian states on an experimentally feasible time scale. For the generated non-Gaussian states we observe a Fisher information larger than the number of atoms in the detected ensemble, which is a signature of particle entanglement, in a regime where no spin-squeezing is present. We confirm the implied resource for quantumenhanced measurements with the implementation of a model-free Bayesian protocol which obtains a sensitivity beyond the standard quantum limit in accordance with the extracted Fisher information

Quantum metrology using tailored non-classical states

Squeezed states of light play a significant role in various technologies ranging from high-precision metrology such as gravitational wave detection to quantum information.These quantum states are prepared to carry particular characteristics depending on their application. For instance, some applications require squeezing in one, others only in the combination of two distinct optical modes. Furthermore, squeezing can appear constant for all frequencies or frequency-dependently. In this thesis, novel quantum optical methods employing different, tailored non-classical light sources, are developed and described. The individual squeezed states are controlled and characterised, each tailored for a particular application. In high-precision spectroscopy, the measurement sensitivity is often limited by technical noise at low frequencies. The first publication shows that small phase signals at low-frequency are resolvable without increasing the laser power. We use a phase-modulated field, shifting the signal to high frequencies where technical noise is circumvented. In addition, the field is squeezed by 6 dB at high frequencies to reduce shot noise arising from quantum fluctuations. Our approach resolves sub-shot-noise signals at 100 Hz and 20 kHz on a reduced noise floor. In opto-mechanical sensors such as gravitational wave detectors, the fundamental measurement limitation arises from the combination of shot noise and quantum back-action noise induced by quantum radiation pressure noise. A conventional fixed-quadrature squeezed state generated by a resonant optical parametric oscillator (OPO) can only fight one of these two contributions simultaneously. To cancel both quantum noise contributions, a particularly frequency-dependent squeezed state is required. Our second publication shows that a detuned OPO generates frequency-dependent squeezing. It can be used as an approximate effective-negative mass oscillator in an all-optical coherent quantum noise cancellation scheme and is suitable to coherently cancel quantum noise. Our generated state, which is reconstructed by quantum tomography, rotating over megahertz frequencies, exhibits a rotation angle of 39° and a maximal squeezing degree of 5.5 dB. Two-mode squeezed quantum states are resources required in modern applications such as quantum information processing. In the third publication, we address the challenge of determining the ten independent entries of a two-mode squeezed state’s covariance matrix to fully characterise the quantum state. We demonstrate a full reconstruction of a 7 dB two-mode squeezed state using only a single polarisation-sensitive homodyne detector, which avoids additional optics and potential loss channels. The findings of this thesis are relevant for experiments in high-precision quantum metrology, e.g. in spectroscopy or gravitational wave detectors operating at the standard quantum limit. The insights gained on the generating and handling non-classical states enable advances in quantum information technology.Gequetschtes Licht spielt eine wichtige Rolle für Gravitationswellendetektoren oder Anwendungen in der Quanteninformationstechnologie. Diese Quantenzustände werden je nach Anwendung speziell präpariert. Für einige Anwendungen ist beispielsweise die Quetschung in einer, für andere nur in der Kombination zweier verschiedener optischer Moden erforderlich. Außerdem kann die Quetschung für alle Frequenzen konstant oder frequenzabhängig auftreten. Im Rahmen dieser Arbeit werden neuartige quantenoptische Methoden entwickelt, die unterschiedlich angepasste nicht-klassische Lichtquellen verwenden. Die einzelnen gequetschten Zustände werden anwendungsbezogen erzeugt, stabilisiert und charakterisiert. In der Spektroskopie ist die Messempfindlichkeit oft durch technisches Rauschen bei niedrigen Frequenzen limitiert. Die erste Publikation zeigt die Messung von kleinen, niederfrequenten Phasensignalen, ohne die Leistung des Lasers zu erhöhen. Unser phasenmoduliertes Lichtfeld verschiebt das Signal zu hohen Messfrequenzen und umgeht daher technisches Rauschen. Weil wir zusätzlich mit gequetschtem Licht arbeiten, kann dort auch Quantenrauschen um 6 dB verringert werden. Unsere Messmethode zeigt die Detektion von Signalen, die bei 100 Hz und 20 kHz oszillieren. Die Messgenauigkeit von optomechanischen Sensoren wie zum Gravitationswellendetektoren ist fundamental begrenzt durch eine Kombination aus quantenmechanischem Schrot- und Strahlungsdruckrauschen. Ein Zustand mit konstanter Quetschquadratur, der von einem resonanten optisch parametrischen Oszillator (OPO) erzeugt wird, wirkt nur gegen einen dieser beiden Rauschbeiträge. Um beide Beiträge zu unterdrücken, ist ein besonderer frequenzabhängiger gequetschter Zustand erforderlich. Unsere zweite Publikation zeigt, dass ein von der Resonanzfrequenz verstimmter OPO frequenzabhängiges gequetschtes Licht erzeugt. Er kann annähernd als effektiver negativer Massen-Oszillator verwendet werden, um Quantenrauschen kohärent zu unterdrücken. Der von uns erzeugte Zustand, der durch Quantentomographie rekonstruiert wird und über Megahertz-Frequenzen rotiert, weist einen Rotationswinkel von 39° und eine maximale Quetschung von 5.5 dB auf. Gequetschte Quantenzustände mit zwei Moden werden für moderne Anwendungen wie die Quanteninformationstechnologie benötigt. In der dritten Publikation befassen wir uns mit der Aufgabe, die zehn unabhängigen Einträge der Kovarianzmatrix eines um 7 dB gequetschten Zweimodenzustands zu bestimmen. Damit ist der Quantenzustand vollständig charakterisiert. Wir zeigen eine vollständige Rekonstruktion eines zweimodigen gequetschten Zustands unter Verwendung eines einzigen olarisationsempfindlichen Homodyn-Detektors, der zusätzliche Optiken und potenzielle Verlustkanäle vermeidet. Die Erkenntnisse dieser Arbeit sind relevant für Experimente in der Quantenmetrologie, z.B. in der Spektroskopie oder bei Gravitationswellendetektoren, die mit Sensitivitäten am Standardquantenlimit arbeiten. Die gewonnenen Erkenntnisse über die Erzeugung und Handhabung nicht-klassischer Zustände ermöglichen Fortschritte in der uanteninformationstechnologie

가우시안 상태를 이용한 양자 계측과 효율적인 베이지안 오류 검정

학위논문(박사)--서울대학교 대학원 :자연과학대학 물리·천문학부(물리학전공),2020. 2. 정현석.Precise measurement of physical quantities plays a crucial role in the development of science and technology. The main purpose of the dissertation is two-fold: to investigate the ultimate precision for estimation of physical quantities using Gaussian states and to propose an efficient method for certification of Bayesian error region in general quantum parameter estimation. In the first part, we begin with analyzing sensitivity for estimating a phase difference in an optical interferometer. Optical interferometry is widely used in science and industry for measuring small displacements. Recently, a large-scale optical interferometer so-called the Laser interferometer Gravitational-Wave Observatory (LIGO) has succeeded in detecting a gravitational wave, the signal of which is extremely small. On the other hand, it has been shown that a non-classical feature of quantum states can improve the sensitivity of estimation, such as in optical interferometer, including the LIGO. From a practical point of view, we inspect the practically achievable precision using non-classical Gaussian states in Mach-Zehnder interferometer with feasible measurements and realistic photon loss. We then investigate the precision of single-mode phase estimation using Gaussian measurement, which can be realized by using homodyne detection, and show that non-Gaussian measurement is necessary to utilize the power of Gaussian input probes optimally. Finally, we find the optimal measurement for general Gaussian quantum metrology and identify three distinct optimal measurements corresponding to different circumstances. In the second part, we study the Bayesian error region, which is a crucial concept for a general estimation process. When estimating a physical quantity, one has to supply the error interval (single-parameter) or error region (multi-parameter) as well as the estimate. However, it has been shown that as the dimension of quantum systems of interest grows, it becomes intractable to calculate the size and credibility of Bayesian error regions. As an alternative, we derive an analytical expression for the properties, the size and credibility, of Bayesian error regions, in an asymptotic regime. We then propose an efficient numerical method to calculate them for high-dimensional quantum systems even in a non-asymptotic regime.물리적인 양의 정확한 측정은 과학 기술에서 핵심적이다. 본 학위 논문의 주제는 가우시안 상태를 이용한 양자 계측과 양자 계측에 있어서 효율적인 베이지안 오류 검정 방식을 제안하는 것이다. 먼저 우리는 광학적 간섭계에서 위상 차이를 계측하는 것을 분석한다. 광학적 간섭계는 매우 작은 변위를 측정하고자 할 때 과학 및 기술에 있어서 광범위하게 사용되는 도구이다. 최근에는 레이저 간섭계 중력파 관측소라고 불리는 곳에 있는 큰 규모의 광학적 간섭계를 이용하여 매우 작은 신호의 중력파를 관측해내는데 성공하였다. 한편, 비고전적인 양자 상태를 사용할 경우, 광학적 간섭계 등에서 높은 정확도를 같게 된다는 것이 알려졌다. 우리는 먼저 비고전적인 가우시안 상태와 실험적으로 구현 가능한 측정을 사용하였을 때, 마흐-젠더 간섭계에서 얻을 수 있는 정확도에 대해서 분석한다. 그리 고 단일 모드 위상 추정에서 호모다인 측정만을 이용하여 구현 가능한 가우시안 측정을 사용하였을 때 최적의 정확도를 도달할 수 있는지 알아보고, 결론적으로 비가우시안 측정이 반드시 필요하다는 것을 밝혀내었다. 마지막으로 일반적인 가우시안 양자 계측에 있어서 최적의 측정을 찾고, 단일 모드의 경우에는 상황에 따라 세 가지 서로 다른 최적의 측정 장치가 존재한다는 것을 규명하였다. 두 번째로 우리는 양자 계측에서 핵심적인 역할을 하는 베이지안 오류 영역에 대 해서 알아본다. 어떤 물리적인 값을 추정함에 있어서 우리는 추정값 뿐만 아니라 그에 대응하는 오류 영역을 반드시 제공하여야 한다. 하지만 양자 계측에 있어서 다루고자 하는 계의 차원이 커짐에 따라 오류 영역의 크기와 신용도를 계산하는 것이 기하급수적으로 오래걸린다는 것이 밝혀졌다. 우리는 이러한 문제를 해결하기 위해 점근적인 영역에서 오류 영역의 크기와 신용도의 근사적 표현을 유도 하였다. 또한, 비점근적인 영역에서도 적용할 수 있는 효율적인 수치적 방법을 제시하였다.I. Introduction 1 II. Preliminary 5 2.1 Continuous variable system 5 2.2 Gaussian states 10 2.3 Quantum estimation theory 12 III. Quantum Metrology using Gaussian states 17 3.1 Introduction 17 3.2 Advanced Mach-Zehnder Interferometer 19 3.2.1 Comparison between Coherent & Squeezed vacuum state and two-mode squeezed vacuum state 24 3.2.2 Remarks 32 3.3 Gaussian measurements for single-mode phase estimation with Gaussian states 33 3.3.1 Optimal Sensitivity 34 3.3.2 Optimal Gaussian measurement 36 3.3.3 Optimal measurement 41 3.3.4 Remarks 42 3.4 Optimal measurements for Quantum fidelity and Quantum Fisher information of Gaussian states 44 3.4.1 Optimal measurement for Gaussian quantum fidelity 45 3.4.2 Optimal measurements for single-mode Gaussian states 49 3.5 Conclusion 58 3.6 Appendix 59 IV. Bayesian Error Certification 77 4.1 Introduction 77 4.2 Bayesian Error Region 78 4.3 Analytical approximation 82 4.3.1 Case 1: Interior-point theory for a full likelihood 83 4.3.2 Case 2: Interior-point theory for a truncated likelihood 85 4.3.3 Case 3: Boundary-point theory 88 4.3.4 Remarks on logarithmic divergence and V_{R_0} 91 4.3.5 Examples in quantum-state tomography 92 4.3.6 Remarks 99 4.4 Efficient Monte-Carlo Method 100 4.4.1 In-region sampling 101 4.4.2 Region capacity 103 4.4.3 Numerical Complexity estimation of hit-and-run algorithm 108 4.4.4 Remarks 112 4.5 Conclusion 113 4.6 Appendix 114 V. Conclusion 127 Bibliography 131 Abstract in Korean 143Docto

Informational limits in optical polarimetry and vectorial imaging

Light has provided the means to learn and gather information about the physical world throughout history. In a world where science moves to smaller scales and more specialised problems however, the boundaries of current technology are continually challenged, motivating the search for more sophisticated systems providing greater information content, sensitivity and increased dimensionality. Utilising the vectorial nature of light presents a promising avenue by which to meet these growing requirements. Polarisation can, for example, be used to transmit information, or alternatively, changes in polarisation induced by an object allow study of previously neglected material properties, such as birefringence and diattenuation. Central to this thesis is thus the characterisation and exploitation of the opportunities afforded by the electromagnetic (i.e. vectorial) nature of light. To this end the work follows three running themes: quantification of polarisation information; formulation of simple propagation tools for electromagnetic waves; and development of specific polarisation based optical systems. Characterising the informational limits inherent to polarisation based systems reduces to considering the uncertainty present in any observations. Uncertainty can, for example, arise from stochastic variation in the polarisation state being measured, or from random noise perturbations upon detection. Both factors are considered and quantified here. Development of vectorial optical systems does, however, pose significant difficulties in modelling, due to mathematical complexity and computational requirements. A number of new tools are hence developed, as prove applicable to a wide variety of applications. Examples are naturally given. To illustrate the potential of polarisation based systems, specific current topics are discussed; namely the growing demand for data storage, and single molecule studies. It will be shown that polarisation, can not only be used to multiplex information in data pits on optical media, but also to allow full 3D study of single molecules. Factors pertinent to such studies are studied in detail

Quantum Metrology of Grid Deformations and Squeezed Light: With applications in quantum imaging & quantum information

In this thesis we make progress towards applications of quantum estimation theory to new physical systems. We first consider two commonly visited problems in quantum metrology: source optimisation and source localisation. For the first, we focus on estimating the distances, d, between neighbouring light sources along an array, which undergoes stretching deformations. We evaluate how changing the nature of the sources impacts the estimation precision of d by using the quantum Fisher information (QFI) as a figure of merit. By comparing this quantity for arrays of single photon emitters, coherent, thermal, and entangled sources, we find that the classical coherent and thermal states outperform the single photon emitters. This would be favourable since generating classical states is less resource-expensive to create. However, a quantum enhancement is observed when entanglement is employed. In agreement with separate work, the optimal state is that which entangles the eigenstates corresponding to the maximum and minimum difference eigenvalues of the generator. We demonstrate that not all entangled states can reproduce similar precision enhancements. This insight is reminiscent of previous studies, where entanglement was concluded as a necessary but insufficient resource for quantum metrology. Next, we address the source localisation problem to detect any deformations applied to a grid of sources. Improving this detection depends on our ability to engineer grids that maximise the sensitivity of the QFI matrix. Hence, we derive the generators of local translations of unitary evolutions that describe any general grid deformation, and show that our result is a multi-parameter extension of other results in the literature. We obtain a general result for the quantum Fisher information matrix (QFIM) through these generators for any grid deformation and explore specific spatial maps, including composite stretches, shears, and rotations. Since the QFI matrix depends only on the properties of the probe state and the configuration of the emitters, we explore how we can modify both to enhance our estimation sensitivity to determine the applied grid deformation. Physically motivated, we find the best arrangement of sources that enhances the sensitivity of detection for a set number of sources. Finally, we consider the optimal estimation of a complex squeezing operation in phase space. The use of squeezed light as a quantum resource is ubiquitous in quantum optics, and a complete characterisation of a complex squeezing operation is pivotal for fundamental reasons. This is a true multi-parameter quantum estimation problem of incompatible observables. Specifically, we find that the symmetric logarithmic derivates (SLDs) for amplitude and directional squeezing do not commute. This prohibits simultaneous optimal estimates of both parameters, even in the asymptotic limit. As a result, we focus on finding separable optimal estimates. The Cramér-Rao bound is determined to provide a theoretical benchmark on the bi-variate estimation precision for general single mode Gaussian probes. Using this and the SLDs, we present a practical experimental implementation that can realise the individual fundamental precision bounds

Biomechanical modeling of deglutition

Swallowing is a physiological process whose malfunction a effects the human quality of life, e.g. malnutrition, dehydration or asphyxia, and has been studied using in vivo approaches. However, advances in computational capacity have encouraged the production of more accurate computational models of offering advantages such as flexibility and reduced experimental costs. Hence, this work proposed the numerical solution of a 2D sagittal swallowing model with physiological accurate tongue's dorsum dynamics based on real time magnetic resonance imaging (RT-MRI) of a healthy young adult. The work designed a full factorial set of simulations and with a second order Box Behnken' surface response design, dimensional relationships were established between food bolus' rheology, swallowing speed, output flow rate, force and shear force over the tongue. Moreover, a dimensionless model was also proposed and exponential behaviors of pressure and friction coefficients as a function of Reynolds numbers were found with an exponential relationship. Such results are intended to predict swallowing flow conditions based on bolus' rheology and the speed of the swallowing event, and also serve as a first validation for more complex models that use other representation techniques. As validation approaches, the work addressed three indirect validations.MaestríaMAGISTER EN INGENIERÍA ÉNFASIS EN INGENIERÍA MECÁNIC