The ability to address and manipulate individual information carriers in a deterministic, coherent, and scalable manner is a central theme in quantum information processing. Neutral atoms trapped by laser light are amongst the most promising candidates for storing and processing information in a quantum computer or simulator, so a scalable and flexible scheme for their control and manipulation is paramount. This thesis demonstrates a fast and versatile method to address and dynamically control the position (the motional degrees of freedom) of neutral atoms trapped in optical tweezers. The tweezers are generated by using the direct image of a Spatial Light Modulator (SLM) which can control and shape a large number of optical dipole-force traps. Trapped atoms adapt to any change in the potential landscape, such that one can re-arrange and randomly access individual sites within atom-trap arrays. A diffraction limited imaging system is used to map the intensity distribution of the SLM onto a cloud of cold atoms captured and cooled using a Magneto Optical Surface Trap (MOST).

Entangled photons are ideally suited to the transmission of photonic quantum information. Mitigating the effects of decoherence is fundamental to distributing photonic entanglement across large distances. One such proposal is entanglement distillation, in which operations on a large ensemble of weakly entangled states generate a smaller ensemble of more strongly entangled states. In this thesis, we experimentally and theoretically analyse various tools required for demonstrating continuous-variable (CV) entanglement distillation, following the proposal by Browne et al., [Phys. Rev. A <b>67</b>, 062320 (2003)]. Specifically, we propose figures of merit to account for the practical limitations of non-deterministic non-Gaussian operations, and analyse the experimental parameters necessary to optimise them. We develop a source of pulsed two-mode squeezed states, which are the initial states of our entanglement distillation protocol. We use weak-field homodyne detection as a phase-dependent photon counting detector, and demonstrate its utility in conditional state generation. Using these states, we demonstrate sub-binomial light as a tool for benchmarking quantum states. Finally, we applied two-mode weak-field homodyne detection to two entangled states and demonstrate correlations in the photon counting statistics which depend on a joint phase from two independent local oscillators. This setup is sufficient to apply an entanglement witness developed by Puentes et al. [New J. Phys. <b>12</b>, 033042 (2010)]. Despite encouraging simulations, we do not witness entanglement with this scheme, which we attribute to a noise source unaccounted for in the simulations. Although we do not demonstrate entanglement distillation outright, the tools we develop to do so represent a general, hybrid approach to CV quantum optics. Developing tools such as phase-resolved projective measurement on two-mode states allows us to probe both the wave and particle nature of entangled light at the single-photon level. Using and expanding these techniques to probe larger quantum systems may prove useful in studies of fundamental physics and quantum enhanced technologies.

An important aspect of third-order optical nonlinearity is the intensity-dependent refractive index, where the intensity of the light itself affects the refractive index. This nonlinear effect is known as Kerr nonlinearity. In this work, a theory of amplification based on Kerr nonlinearity is developed. Kerr nonlinearity is well known to exhibit instability. Our amplification theory is based on seeding this instability. The full theory is developed to obtain the vectorial wave equations of the instability. It is shown that for materials of interest, vectorial effects are negligible across the instability regime and the scalar theory gives an accurate account of Kerr instability amplification. It is also shown that this instability analysis is a spatiotemporal generalization to four-wave mixing, modulation instability, and filamentation instability. It fact, it can be considered a seeded conical emission process. Subsequently, the theory of plane wave Kerr instability is explored. Quantitatively, the importance of pump wavelength, linear dispersive properties, and non-collinear angles for optimal amplification are demonstrated. Next, the seed beam is generalized to a finite Gaussian pulse in both time and space; the effect of a finite seed beam is quantitatively analyzed. Our analysis of Kerr instability in bulk dielectric crystals demonstrates the potential to amplify pulses in the wavelength range of ~1-14 μm. Whereas plane wave amplification is shown to extend to 40 μm in the example materials shown, material damage limits finite pulse Kerr instability amplification to about 14μm. There, seed pulse output energies in the 50 μJ range appear feasible with a ratio of pump to seed pulse energy in the range 400-500. Three key aspects of Kerr amplification are the capacity for single cycle pulse amplification, that it is intrinsically phase-matched, and its simplicity and versatility. As the Kerr instability gain profile is of Bessel-Gaussian nature in the transverse space domain, it lends itself naturally to the amplification of Bessel-Gauss beams. It is shown that pump-to-seed energy amplification that is more effcient than the Gaussian case by a factor of about 5-7. Whereas in the Gaussian case, the efficiency is on the order of about 0.15-0.2%, in the Bessel-Gaussian case it is on the order of about 1%. It is also demonstrated that Bessel-Gaussian seed beams centered at longer wavelengths than ordinary Gaussian beams may be amplified. Lastly, Bessel-Gauss beams are known to have favourable properties, such as being diffraction-free over a certain propagation range. Finally, a quantum optical theory of Kerr instability is developed. In particular, we explore a theory of the generation of ultrashort photon pairs (biphotons) from vacuum with Kerr instability.

As a subset of quantum optics, single photons are one of the competing physical resources for quantum information processing. When used as carriers of quantum information, they have no equal. For the processing of quantum information, single photons have proven difficult to scale beyond the order of ⇠ 10 photons. The lack of single-photon-level interaction has led to creative approaches which rely on postselection to filter the possible measured outcomes to those which appear as though interaction occurred. This approach of post-selection leans heavily on the ability to not only generate but also detect scores of single photons simultaneously and with near perfect efficiency. Our work relaxes the emphasis which has been placed on single photons for quantum information processing to that of states with, in principle, an arbitrary number of photons. Central moment expectations on two-mode squeezed states are shown to exhibit post-selection behavior which reflects the single-photon counterpart. These measures are proven to be robust to loss and return entangled state statistics on average. With naive estimation of the central moment, states with ~ 20 modes are within reach with current technology, closing the gap between quantum states which can and cannot be classically simulated. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

Nesse trabalho utilizamos um modelo analítico para avaliar o desempenho de estruturas semicondutoras contendo pontos quânticos que servem de base para a fabricação de fotodetectores que operam na faixa do infravermelho. O desempenho desses dispositivos foram avaliados através da corrente no escuro e da detectividade. Os trabalhos existentes na literatura, baseados neste modelo, não consideram a de­ pendência da estrutura eletrônica do ponto quântico com suas dimensões. Desta forma, neste trabalho, analisamos o comportamento da corrente no escuro e da de­tectividade em função de vários parâmetros que definem a estrutura da amostra, levando em consideração as dimensões dos QDs. Nossos resultados mostraram quais parâmetros devemos ajustar para fazer fotodetectores: (1) que contenham a maior densidade de QDs com dimensões compatíveis com a energia de ionização desejada; (2) que maximizam o desempenho do dispositivo e (3) minimizam o ruído do mesmo. / In this work we used an analytical model to calculate the dark current and the detectivity of infrared photodetectors based on InAs quantum dots semiconductor heterostructures. The existing works reported in the literature based on this analytical model do not take into account the electronic structure of the QD in the calculations. In this way, in the present work, we took into account the QD dimensions when we analized the dependence of the dark current and the detectivity on the parameters which define the sample structure. Our findings show which parameters must be adjusted in order to obtain photodetectors with: (1) the larger density of QDs with dimensions compatible with the wanted ionization energy; (2) that maximize the performance; (3) and that minimize the noise of the devices.

Fazendo uso da equivalência entre um potencial não-local e um potencial dependente da velocidade, mostramos como construir um potencial não-local capaz de gerar estados comprimidos. No contexto do modelo de Jaynes-Cummings que descreve a interação quântica de um único átomo de dois níveis com um único modo do campo eletromagnético quantizado, mostrando uma nova característica no comportamento dinâmico da inversão atômica, quando o campo é preparado em um estado coerente comprimido par. Usando o modelo de Jaynes-Cummings propomos um método para estudar o estado quântico e a variância do operador de fase, através da medida da distribuição de momento de átomos espalhados, proveniente da interação de um feixe atômico com um único modo do campo eletromagnético via interação de dois fótons. / Exploring the equivalence between a non-local and a velocity-dependent potential we show how to construct a non-local potential, which is able to generate squeezed states. In the context of the Jaynes-Cummings model we describe the quantum interaction of a single two-level atom with a single mode of a quantum electromagnetic field, showing a new feature in the dynamical behavior of atomic inversion when the electromagnetic field is prepared in an even squeezed coherent state. By using the Jaynes-Cummings model, a method to study quantum state and variance of the phase operator is proposed. The method consists in measuring the momentum distribution of atoms resulting from the interaction of a prepared atomic beam with a single mode electromagnetic field via two-photon interaction.

by Chong, Cheung-Yu = 開放球腔中波動之二分量理論 / 莊翔宇. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 84-87). / Text in English; abstracts in English and Chinese. / by Chong, Cheung-Yu = Kai fang qiu qiang zhong bo dong zhi er fen liang li lun / Zhuang Xiangyu. / Abstract --- p.i / Acknowledgments --- p.iii / Contents --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Open Cavities and Quasinormal Modes --- p.1 / Chapter 1.2 --- Completeness of Quasinormal Modes --- p.3 / Chapter 1.3 --- Objective and Outline of this Thesis --- p.5 / Chapter 2 --- Waves in One-Dimensional Open Cavities I: Completeness --- p.6 / Chapter 2.1 --- Quasinormal Modes of One-Dimensional Open Cavities --- p.6 / Chapter 2.2 --- Green's Function Formalism --- p.7 / Chapter 2.2.1 --- Construction of the Green's Function --- p.8 / Chapter 2.2.2 --- Conditions for Completeness --- p.9 / Chapter 2.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.10 / Chapter 2.3 --- Two-Component Formalism --- p.11 / Chapter 2.3.1 --- Overcompleteness --- p.11 / Chapter 2.3.2 --- Two-Component Expansion --- p.11 / Chapter 2.3.3 --- Linear Space Structure --- p.13 / Chapter 3 --- Waves in One-Dimensional Open Cavities II: Time-Independent Problems --- p.16 / Chapter 3.1 --- Perturbation Theory --- p.16 / Chapter 3.1.1 --- Formalism I: Green's Function Formalism --- p.17 / Chapter 3.1.2 --- Formalism II: Two-Component Formalism --- p.20 / Chapter 3.2 --- Diagonalization Method --- p.23 / Chapter 3.2.1 --- Formalism I: One-Component Expansion --- p.24 / Chapter 3.2.2 --- Formalism II: Green's Function Formalism --- p.25 / Chapter 3.2.3 --- Formalism III: Two-Component Formalism --- p.28 / Chapter 3.2.4 --- Numerical Example --- p.29 / Chapter 4 --- Waves in Open Spherical Cavities I: Completeness --- p.34 / Chapter 4.1 --- Quasinormal Modes of Open Spherical Cavities --- p.34 / Chapter 4.2 --- Green's Function Formalism --- p.36 / Chapter 4.2.1 --- Construction of the Green's Function --- p.37 / Chapter 4.2.2 --- Conditions for Completeness --- p.37 / Chapter 4.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.38 / Chapter 4.3 --- Two-Component Formalism --- p.39 / Chapter 4.3.1 --- Evolution Formula --- p.40 / Chapter 4.3.2 --- Two-Component Expansion --- p.48 / Chapter 4.3.3 --- Outgoing-Wave Boundary Condition --- p.49 / Chapter 4.3.4 --- Numerical Example --- p.51 / Chapter 4.3.5 --- Linear Space Structure --- p.52 / Chapter 5 --- Waves in Open Spherical Cavities II: Time-Independent Prob- lems --- p.57 / Chapter 5.1 --- Perturbation Theory --- p.57 / Chapter 5.1.1 --- Formalism I: Green's Function Formalism --- p.57 / Chapter 5.1.2 --- Formalism II: Two-Component Formalism --- p.60 / Chapter 5.2 --- Diagonalization Method --- p.61 / Chapter 5.2.1 --- Formalism I: One-Component Expansion --- p.61 / Chapter 5.2.2 --- Formalism II: Green's Function Formalism --- p.63 / Chapter 5.2.3 --- Formalism III: Two-Component Formalism --- p.64 / Chapter 5.2.4 --- Numerical Example --- p.65 / Chapter 6 --- Numerical Evolution of Outgoing Waves in Open Spherical Cav- ities --- p.73 / Chapter 6.1 --- Formulation of the Problem --- p.74 / Chapter 6.2 --- Derivation of the Boundary Condition --- p.75 / Chapter 6.3 --- Boundary Condition without High Derivatives --- p.76 / Chapter 6.4 --- Numerical results --- p.78 / Chapter 6.5 --- Discussion --- p.79 / Chapter 7 --- Conclusion --- p.82 / Chapter 7.1 --- Summary of Our Work --- p.82 / Chapter 7.2 --- Future Developments --- p.83 / Bibliography --- p.84

Hui Ka Ming = 非對稱Hubbard模型之量子蒙地卡羅與精準對角化研究 / 許嘉明. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 85-88). / Text in English; abstracts in English and Chinese. / Hui Ka Ming = Fei dui cheng Hubbard mo xing zhi liang zi Mengdi Kaluo yu jing zhun dui jiao hua yan jiu / Xu Jiaming. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Asymmetric Hubbard Model And Its Physical Background / Chapter 2.1 --- Physical Motivation of the Study --- p.4 / Chapter 2.2 --- Symmetry Properties --- p.5 / Chapter 2.2.1 --- Particle-Hole Transformation --- p.5 / Chapter 2.2.2 --- U(l) Group --- p.5 / Chapter 2.2.3 --- SU(2) Group --- p.6 / Chapter 2.3 --- Relations with Other Models --- p.7 / Chapter 2.3.1 --- Falicov-Kimball Model --- p.7 / Chapter 2.3.2 --- Asymmetric t-J and Heisenberg Model --- p.7 / Chapter 2.3.3 --- Anderson and Kondo Model。 --- p.8 / Chapter 3 --- Exact Diagonalization and Density Matrix Renormalization Group --- p.11 / Chapter 3.1 --- Exact Diagonalization --- p.12 / Chapter 3.1.1 --- Second Quantization Representation --- p.13 / Chapter 3.1.2 --- Binary Representation Of Quantum States --- p.15 / Chapter 3.1.3 --- Two-Table Method --- p.15 / Chapter 3.1.4 --- Generation of Matrix Elements --- p.18 / Chapter 3.1.5 --- Lanczos Method --- p.20 / Chapter 3.1.6 --- Continued Fraction Dynamics At T=0 --- p.22 / Chapter 3.2 --- Density Matrix Renormalization Group --- p.23 / Chapter 3.2.1 --- Infinite system DMRG --- p.24 / Chapter 3.2.2 --- DMRG and Quantum Entanglement --- p.27 / Chapter 4 --- Determinant Quantum Monte Carlo And Finite Temperature Green Function --- p.29 / Chapter 4.1 --- Introduction --- p.29 / Chapter 4.2 --- General Scenario of Fermionic Monte Carol Method --- p.30 / Chapter 4.3 --- Review on Monte Carlo Method for Ising Model --- p.31 / Chapter 4.3.1 --- Ising Model --- p.31 / Chapter 4.3.2 --- Metropolis Algorithm --- p.31 / Chapter 4.3.3 --- Measurement --- p.32 / Chapter 4.3.4 --- Near The Critical Points --- p.33 / Chapter 4.4 --- Determinant Quantum Monte Carlo --- p.33 / Chapter 4.4.1 --- Suzuki-Trotter Decomposition --- p.34 / Chapter 4.4.2 --- Hubbard-St rant onovich Transformation --- p.34 / Chapter 4.5 --- Green Functions in DQMC And Wick's Theorem --- p.37 / Chapter 4.5.1 --- Equal-'Time' Green Functions --- p.37 / Chapter 4.5.2 --- Unequal-'Time' Green Functions --- p.38 / Chapter 4.5.3 --- Wick's Theorem --- p.38 / Chapter 4.6 --- Practical Consideration of DQMC --- p.39 / Chapter 4.6.1 --- Metropolis for DQMC --- p.39 / Chapter 4.6.2 --- Updating the Equal-time Green function --- p.41 / Chapter 4.6.3 --- Matrix Multiplication Stabilization --- p.42 / Chapter 4.6.4 --- A Survey In Negative Sign Problem --- p.43 / Chapter 4.6.5 --- Insight from Feynman --- p.44 / Chapter 4.6.6 --- Sign Problem As A NP-hard problem --- p.45 / Chapter 4.6.7 --- Personal Account on the Problem --- p.46 / Chapter 5 --- Dynamical Mean Field Theory --- p.47 / Chapter 5.1 --- Classical Mean Field Theory . --- p.49 / Chapter 5.2 --- DMFT as an Impurity Problem --- p.52 / Chapter 5.3 --- Scaling of Hopping Integral and Self-consistent Condition --- p.53 / Chapter 5.4 --- A QMC Impurity Solver --- p.55 / Chapter 5.5 --- Further development of DMFT --- p.56 / Chapter 6 --- Results and Discussion --- p.57 / Chapter 6.1 --- Physical Observable --- p.57 / Chapter 6.2 --- Methodology of the Studies --- p.58 / Chapter 6.3 --- Results --- p.59 / Chapter 6.4 --- Discussion and Suggestion --- p.83 / Chapter A --- DMRG of tight-binding model --- p.89 / Chapter B --- Scaling and Density of State of D-dimensional Hubbard Model --- p.94

This thesis presents the development of photonic microcells for use as the host for coherent optics phenomena and related applications. A photonic microcell consists of a length of hollow-core photonic crystal fibre (HC-PCF) with a gas-filled core that is spliced to conventional optical fibre at either end to seal the gas within the fibre. Towards the goal of demonstrating and assessing the coherence properties of quantum optical effects in photonic microcells, the fabrication of two types of HC-PCF is presented. The established photonic bandgap HC-PCF offers extremely low transmission loss of ~10 dB/km over kilometre distances. However, the fibre has a limited transmission bandwidth of ~50 THz and exhibits modal coupling unfavourable for many applications. Work is presented on the tailoring of this fibre by control and shaping of the core-surround in order to improve its modal properties. A second type of HC-PCF is based on a large-pitch lattice, whose guidance relies on a new mechanism. This fibre exhibits a much improved bandwidth (>1000 THz) and has a relatively higher but still practical loss of ~1 dB/m. The development of photonic microcells at microbar pressure level and with low optical insertion loss is shown, an important step in the improvement of the technology for coherent optics applications which will take advantage of the extreme gas-laser interaction efficiency achieved in HC-PCF. Finally, quantum optical effects are demonstrated in HC-PCF and photonic microcells loaded with both the molecular gas acetylene and atomic vapour rubidium. The observation of electromagnetically induced transparency (EIT) in acetylene-filled HC-PCF represents the first such observation in a molecular gas, while the use of a photonic microcell allows a comparison of many experimental configurations to explore the coherence properties of coherent optical systems in the core of a HC-PCF. Furthermore, EIT is observed unambiguously in a rubidium loaded HC-PCF for the first time, and the anti-relaxation effects of a polymer coating demonstrated in this configuration.

The quantum description of light offers a unique set of optical effects that has led to promising applications beyond those described by classical physics. Although well-defined quantum states of light do not persist in typical classical environments, phenomena such as entanglement often enhance optical approaches to communication, measurement, and sensing. With the emergence of new tasks in classical and quantum optical technology, new tools are required that must be specifically engineered including the generation of quantum states. This thesis is concerned with three principle tasks in engineering and implementing entangled photonic states. First, the use of frequency anti-correlated and polarization entangled two-photon states generated during spontaneous parametric down conversion (SPDC) to precisely evaluate optical delays with quantum interferometry is demonstrated in a realistic commercially available optical telecommunication device. Second, the study of correlated orbital angular momentum (OAM) states for efficient object identification is presented. Finally, experimental efforts towards the development of sources for entangled weak coherent states are discussed. The generation of broadband entangled states leading to well-defined second order interference patterns is a necessary step for the application of low coherence quantum interferometry as a metrological device. The flexibility of non-uniformly chirped periodically poled nonlinear crystals offers a rich set of tools for precise state engineering. The experimental evaluation of a broadband source of polarization entanglement is presented. In addition, design considerations for applications that require optimized quantum interference features are discussed along with a numerical investigation of the limits of quantum interferometry with even order dispersion cancellation. We present an experimental demonstration of correlated OAM sensing exploiting the two-dimensional and correlated nature of states produced during SPDC projected onto the OAM basis. Efficient object recognition through the identification of azimuthal symmetries of arbitrary objects is achieved by observing the full two-photon joint OAM spectrum and focusing on non-conserved OAM components not found in the natural OAM spectrum of SPDC. Finally, quantum key distribution (QKD) is currently the most successful quantum optical application; however, a limiting trade off between the achievable rates and distances confines the approach to niche applications. The generation of entangled coherent states has been proposed to transition QKD into a new regime that would set aside single photons and two-photon entangled states for higher intensity coherent pulses. The key technical limitation that has prohibited the demonstration of such states is a reliable source of single-photon cross phase modulation. The plausibility and experimental efforts towards creating such an environment in a solid state device is presented.