Parametric down-conversion (PDC) is a nonlinear optical process widely used to generate pairs of photons. It occurs when an intense laser traverses an optical parametric amplifier (OPA). When the gain of the amplifier is increased, the number of downconverted photons increases exponentially: this is the high-gain regime of PDC. High-gain PDC is potentially a versatile tool for metrology. It is a source of highly-entangled states and bright squeezed states for applications in quantum information and interferometry. In addition, the high number of photons in high-gain PDC makes it possible to use diodes and cameras directly, instead of single-photon detectors and coincidence-counting apparatus. However, all the quantum-optical experimental methods need to be generalized or adapted for a high-photon flux. Most of the theoretical and experimental techniques used or developed in this thesis aim to address this transition from low to high-photon flux of PDC. I theoretically and experimentally provide strategies to harness the mode structure of PDC, bringing us steps closer to a usable source of bright squeezed vacuum for interferometry and quantum imaging. I present experimental progress in reducing the number of frequency modes of high-gain PDC, which is naturally broadband, and consequently highly multimode. Our theory for high-gain PDC generated in a nonlinear crystal provides a set of modes containing physically meaningful information, i.e. the pairwise quantum correlations between independant modes. In addition, I provide a thorough discussion on the limit of SU(1,1) interferometry in regards to internal loss and gain unbalancing. Finally, I tie the frequency spectrum of high-gain PDC to the properties of vacuum fluctuations, allowing to predict the number of photons from first principles, making it a powerful tool for spectroradiometry. Those developments are a springboard towards usable high-gain PDC for metrology.

In this thesis, we explore the quantum dynamics of light interactions with optically thick collections of atoms. We provide a theoretical description of several recent experiments in which some key operations necessary for the implementation of quantum communication networks are demonstrated. Collective Raman scattering from an atomic ensemble is shown to produce probabilistic entanglement between the polarization of a scattered photon and an associated collective atomic excitation. The predicted correlations agree with experimental observations. We also propose a method to use cascade transitions to produce entanglement between a photon with a frequency in the telecom range (ideal for transmission over optical fibers) and a near infrared photon (ideal for storage in an atomic ensemble), and a description of the experimental demonstration is provided. We also propose and describe the implementation of a deterministic source of single photons. In addition, we generalize the theory of dark-state polaritons in ensembles of three level Lambda atoms to account for the nuclear spin degeneracy of alkali atoms. This generalized theory provides a description of the first demonstration of single photon storage and retrieval from atomic ensembles. Additionally, in the presence of a uniform magnetic field, we predict the occurrence of collapses and revivals of the photon retrieval efficiency as a function of storage time within the ensemble. These predictions are in very good agreement with subsequent experimental observations. We also exploit the ability of photon storage to entangle remote atomic qubits.

This dissertation formulates and applies a theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse variations. The resonance fluorescence spectrum in a high finesse optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Our analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular we determine a quantum limit to the semiclassical theory of FM modulation spectroscopy. Finally, we derive the corresponding theory for the two-photon, two-level medium. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem. We discuss the role of the Stark shifts on the emission spectrum and show how the Rayleigh scattering is markedly different.

Ge Guo Qin. / "April 18, 2001." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 129-143). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Au-Yeung, Kin Chung = 以光學模擬量子自旋和機械鐘擺的相互作用 / 歐陽健聰. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 80-81). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Au-Yeung, Kin Chung = Yi guang xue mo ni liang zi zi xuan he ji xie zhong bai de xiang hu zuo yong / Ouyang Jiancong.

Lau Kwok-kwong = 量子場在一維耗散性空腔中的特性 / 劉國光. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 82-83). / Text in English; abstracts in English and Chinese. / Lau Kwok-kwong = Liang zi chang zai yi wei hao san xing kong qiang zhong de te xing / Liu Guoguang. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Formalism of QNMs --- p.8 / Chapter 2.1 --- A Review of QNMs --- p.9 / Chapter 2.1.1 --- Projection for QNMs 一 Bilinear mapping --- p.11 / Chapter 2.1.2 --- Incoming field --- p.13 / Chapter 2.2 --- Physical examples of QNMs --- p.15 / Chapter 2.2.1 --- Dielectric rod --- p.15 / Chapter 2.2.2 --- Laser cavity --- p.16 / Chapter 2.3 --- Modes-of-the-universe approach --- p.17 / Chapter 3 --- Field Quantization --- p.21 / Chapter 3.1 --- Field operators and Commutation Relations --- p.22 / Chapter 3.2 --- Thermal Expectation Values --- p.23 / Chapter 3.2.1 --- "Quantum limit, T →0" --- p.25 / Chapter 3.2.2 --- "Classical limit, T→∞" --- p.26 / Chapter 3.3 --- Physical interpretation of QNM operators --- p.27 / Chapter 4 --- Discrete modes and background fields --- p.31 / Chapter 4.1 --- LSL Discrete modes --- p.32 / Chapter 4.2 --- Construction of discrete modes operators based on QNMs --- p.34 / Chapter 4.2.1 --- Commutation relations --- p.38 / Chapter 4.2.2 --- Equations of motion --- p.38 / Chapter 4.2.3 --- Input-Output relation of the discrete modes --- p.39 / Chapter 4.3 --- Properties of the background field --- p.40 / Chapter 4.3.1 --- Classical approach to understand the background field . --- p.41 / Chapter 5 --- Spontaneous Emission in a leaky cavity --- p.53 / Chapter 5.1 --- Spontaneous Emission: one qusaimode calculation --- p.54 / Chapter 5.2 --- Spontaneous Emission with background effect --- p.57 / Chapter 5.3 --- Difference between the rotating wave approximation and the background --- p.61 / Chapter 6 --- The connection between QNMs and System-Bath models --- p.66 / Chapter 6.1 --- Single-mode SBM --- p.68 / Chapter 6.1.1 --- Equation of motion --- p.68 / Chapter 6.1.2 --- Commutation relations --- p.70 / Chapter 6.1.3 --- Input-output relation --- p.72 / Chapter 6.2 --- N-modes SBM --- p.72 / Chapter 6.2.1 --- N = 2 case --- p.74 / Chapter 6.2.2 --- N >2 case --- p.76 / Chapter 7 --- Conclusion --- p.79 / Bibliography --- p.82 / Chapter A --- Correlation Function --- p.84 / Chapter B --- Relation between surface term and imaginary part of the frequency --- p.86 / Chapter C --- Green function approach --- p.88 / Chapter D --- Numerical results of SBM --- p.92

This thesis deals with the implementation of quantum channels using linear optics. We begin with overviews of some important concepts in both quantum information and quantum optics. First, we discuss the quantum bit and describe the evolution of the states via quantum channels. We then discuss both quantum state and process tomography, methods for how to determine which states and operations we are experimentally implementing in the lab. Second, we discuss topics in quantum optics such the generation of single photons, polarization entanglement, and the construction of an entangling gate. The first experiment is the implementation of a quantum damping channel, which intentionally can add a specific type and amount of decohering noise to a photonic qubit. Specifically, we realized a class of quantum channels which contains both the amplitude-damping channel and the bit-flip channel, and did so with a single, static, optical setup. Many quantum channels, and some gates, can only be implemented probabilistically when using linear optics and postselection. Our main result is that the optical setup achieves the optimal success probability for each channel. Using a novel ancilla-assisted tomography, we characterize each case of the channel, and find process fideilities of $0.98 \pm 0.01$ for the amplitude-damping channel and $0.976 \pm 0.009$ for the bit-flip. The second experiment is an implementation of a protocol for quantum computing on encrypted data. The protocol provides the means for a client with very limited quantum power to use a server's quantum computer while maintaining privacy over the data. We perform a quantum process tomography for each gate in a universal set, showing that only when the proper decryption key is used on the output states, which is hidden from the server, then the action of the quantum gate is recovered. Otherwise, the gate acts as the completely depolarizing channel.

Thesis (Ph. D.)--University of Oregon, 2004. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 204-209). Also available for download via the World Wide Web; free to University of Oregon users.

We study the role of correlations with the environment as the source of non-Markovian quantum evolutions. We first focus on the impact that correlations with the environment can have on the dynamical map that evolve the system. We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present. We discuss the implications and limitations of the Markov approximation necessary to derive the Kossakowski-Lindblad master equation. A generalized non-Markovian master equation is derived from the dynamical map of systems correlated with their environment. The physical meaning of not completely positive maps is studied to obtain a consistent theory of non-Markovian quantum dynamics. These are associated to inverse maps necessary to establish correlations and they give rise to a canonical embedding map that is local in time. This master equation goes beyond the Kossakowski-Lindblad master equation. Non-equilibrium quantum thermodynamics can be be studied within this theory. Through out this discussion, the general dynamics of two interacting qubits is used as an example for illustrations. / text

Nowadays, the information society that presides the everyday life is dependent on the communication industry to facilitate unintelligible data transfers between authenticated parties. Human desire to communicate secretly since the beginnings of the civilisation. Methods of secret communication were developed by many ancient societies, including those of Mesopotamia, Egypt, India, China and Japan, but details regarding the origins of cryptology, i.e. the science and art of secure communication, remain unknown. Secure communication as well as the protection of sensitive data against unauthorised eavesdropping are inevitably important. For example, the device, used for communication between military commanders, consisted of a tapered baton around which was wrapped a spiral strip of parchment or leather containing the message. The key is a random sequence of 0’s and 1’s, and therefore the resulting cryptogram, i.e. the plaintext plus the key, is also random and completely scrambled unless one knows the key. Indeed, Shannon proved that if the key is secret, the same length as the message, truly random, and never reused, then the one-time pad is unbreakable. All one-time pads suffer from serious practical drawback, known as the key distribution problem. The key itself must be established between the sender and the receiver by means of a very secure channel for example a very secure telephone line, a private meeting or hand-delivery by a trusted courrier. Even if a secure channel is available, this security can never be truly guaranteed, a fondamental problem remains because any classical private channel can be monitored passively without the sender or receiver knowing that the eavesdropping has taken place. Since all information, including cryptographic keys, is encoded in measurable physical properties of some object or signal, classical theory leaves open the possibility of passive eavesdropping, because in principle it allows the eavesdropper to measure physical properties without disturbing them. This is not the case in quantum theory, which forms the basis for quantum cryptography. Modern cryptographic practice rests on the use of one-way functions which are easy to evaluate in the forward direction but infeasible to compute in the reverse direction without additional information. For example, multiplying large prime numbers can be done in a time that is a polynomial function of their size, but finding the prime factors of the product is believed to require exponential time. Factoring the product of two large prime numbers can be accomplished in polynomial time on a quantum computer. However, the advancement of computing power and the advent of the quantum computer together with the vulnerability of this scheme to mathematical progress have prompted the introduction of quantum cryptography which process through the laws of quantum mechanics, ensures provably secure data transfers. The use of physical mechanisms for cryptography is well known in quantum cryptography, based on the combinations of concept from quantum mechanics and information theory, i.e. the impossibility of cloning quantum information. The Heisenberg’s uncertainty principle is exploited to designe an unconditionally secure quantum communications schemes. Quantum cryptography mades enormous progress in the technology of quantum optics, optical fibers and free space optical communication. It can be used over a classical communications channel providing a physical protection to individual bits of information as well as a hardware implemented solution. The implementation of this theoretical concept requires much practical innovation for transparent deployment into current cryptographic solutions. The theory of quantum cryptography as well as its potential relevance and the application of prototype system at the University of KwaZulu-Natal are described and the phenomenon of single-photon interference is used to perform quantum cryptography over an optical communications link. The method of BB84 (a quantum key distribution protocol that works with qubits which are two-dimensional) is presented to solve the problem of key distribution between two parties. Theoretically, BB84 is secured under certain conditions. The practical of id 3000 Clavis (quantum key distribution system) over installed terrestrial cables of distances 13,08 km at Cato Manor in Durban between Central Application Office and Minicipal original Office buildings and 15.6 km in Pinetown between Pinetown Civic Center and Pinetown Clinic buildings is the proof that the solution to the key distribution problem is given by quantum cryptography. The experiments in this work are the practical real quantum key distribution that produces the key which can be shared between two parties at the distances enunciated above. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2009.