This dissertation presents theories of multiwave mixing in two- and three-level media. The first part of the dissertation treats the semiclassical theories in two-level media. Chapter 2 gives the simple semiclassical theory of four-wave mixing when the two pump frequences differ by more than the reciprocal of the population-difference lifetime. This difference washes out the pump spatial holes as well as one of the two reflection gratings. We compare the results to the degenerate treatment of Abrams and Lind and find significant differences in the reflection coefficient spectra. Chapter 3 presents the semiclassical theory of multiwave in a squeezed vacuum characterized by unequal in-phase and in-quadrature dipole decay times. For a highly squeezed vacuum, we find sharp resonances in both probe absorption and reflection coefficients, which provide sensitive ways to measure the amount of squeezing in the vacuum. The second part of the dissertation treats the quantum theories in two- and three-level media. Chapter 4 develops the fourth-order quantum theory of multiwave mixing to describe the effects of sidemode saturation in two-level media. We derive explicit formulas for the fourth-order quantum coefficients and show that the fourth-order quantum theory reproduces the third-order semiclassical coefficient obtained by truncating a continued fraction. We apply the results to cavity problems and find significant differences in the sideband spectra given by the second- and fourth-order treatments, particularly as the sidemode approaches the laser threshold. The final chapter presents a quantum theory of multiwave mixing in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong pump intensities and good broad-band squeezing for low pump intensities.

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Since information has been regarded as a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, "nanostructures," through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of quantum dots technology is described. In so doing, the theoretical background and the practicalities required for this thesis are introduced. A discussion of the current quantum hardware used for quantum information processing is given. In particular, the solid-state proposals to date are emphasised. A detailed prescription is given, using an optically-driven coupled quantum dot system, to reliably prepare and manipulate exciton maximally entangled Bell and Greenberger-Horne-Zeilinger (GHZ) states. Manipulation of the strength and duration of selective light-pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state based quantum information. The all-optical generation of states of the so-called Bell basis for a system of two quantum dots (QDs) is exploited for performing the quantum teleportation of the excitonic state of a dot in an array of three coupled QDs. Theoretical predictions suggest that several hundred single quantum bit rotations and controlled-NOT gates could be performed before decoherence of the excitonic states takes place. In addition, the exciton coherent dynamics of a coupled QD system confined within a semiconductor single mode microcavity is reported. It is shown that this system enables the control of exciton entanglement by varying the coupling strength between the optically-driven dot system and the microcavity. The exciton entanglement shows collapses and revivals for suitable amplitudes of the incident radiation field and dot-cavity coupling strengths. The results given here could offer a new approach for the control of decoherence mechanisms arising from entangled "artificial molecules." In addition to these ultrafast coherent optical control proposals, an approach for reliable implementation of quantum logic gates and long decoherence times in a QD system based on nuclear magnetic resonance (NMR) is given, where the nuclear resonance is controlled by the ground state "magic number" transitions of few-electron QDs in an external magnetic field. The dynamical evolution of quantum registers of arbitrary length in the presence of environmentally-induced decoherence effects is studied in detail. The cases of quantum bits (qubits) coupling individually to different environments ("independent decoherence"), and qubits interacting collectively with the same reservoir ("collective decoherence") are analysed in order to find explicit decoherence functions for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A non-trivial behaviour - "recoherence" - is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. The results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not become entangled with the environment, making them ideal elements for the engineering of "noiseless" quantum codes. The relations between decoherence of the quantum register and computational complexity based on the new dynamical results obtained for the register density matrix are also discussed. This thesis concludes by summarising and pointing out future directions, and in particular, by discussing some biological resonant energy transfer processes that may be useful for the processing of information at a quantum level.

Wong Sik Lik = 廣義薛定諤貓態之非經典性質 / 王適力. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 120-124). / Text in English; abstracts in English and Chinese. / Wong Sik Lik = Guang yi xue ding e mao tai zhi fei jing dian xing zhi / Wang Shili. / Acknowledgements --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Coherent States and Schrodinger Cats --- p.4 / Chapter 2.1 --- Short review on Quantization of single- mode electromagnetic field --- p.5 / Chapter 2.2 --- Number states as field states --- p.6 / Chapter 2.3 --- Coherent states as field states --- p.7 / Chapter 2.4 --- Features of Coherent states --- p.8 / Chapter 2.4.1 --- Coherent states and Minimum Uncertainty --- p.8 / Chapter 2.4.2 --- Coherent states and Poissonian distribution --- p.10 / Chapter 2.5 --- Non- Classical properties of Schrodinger Cat States --- p.12 / Chapter 2.5.1 --- Quadrature Squeezing of ECS --- p.13 / Chapter 2.5.2 --- Photon Statistics of ECS --- p.14 / Chapter 2.5.3 --- Wigner function of ECS --- p.15 / Chapter 2.5.4 --- Q-function of ECS --- p.23 / Chapter 3 --- Generalized Schodinger Cat States : Perelomov's type GSCS & Barut-Girardello's type GSCS --- p.26 / Chapter 3.1 --- Review on SU(1，1) Lie algebra --- p.26 / Chapter 3.2 --- "SU(1,1) Perelomov's type GCS" --- p.28 / Chapter 3.3 --- "SU(1,1) Perelomov's type GSCS" --- p.30 / Chapter 3.4 --- "SU(1,1) Barut-Girardello's type GCS" --- p.32 / Chapter 3.5 --- "SU(1,1) Barut-Girardello's type GSCS" --- p.33 / Chapter 4 --- Nonclassical properties of Perelomov's type GSCS --- p.36 / Chapter 4.1 --- Nonclassical properties of PGSCS of the single-mode realization --- p.36 / Chapter 4.1.1 --- Quadrature Squeezing of PGSCS --- p.36 / Chapter 4.1.2 --- Photon Statistics of PGSCS --- p.41 / Chapter 4.1.3 --- Q-function of PGSCS --- p.43 / Chapter 4.1.4 --- Wigner function of PGSCS --- p.49 / Chapter 4.2 --- Nonclassical properties of PGSCS of the two-mode realization --- p.49 / Chapter 4.2.1 --- Quadrature Squeezing of PGSCS --- p.49 / Chapter 4.2.2 --- Photon Statistics of PGSCS --- p.52 / Chapter 4.2.3 --- Q´ؤfunction for PGSCS --- p.55 / Chapter 4.2.4 --- Wigner function of PGSCS --- p.58 / Chapter 4.3 --- Nonclassical properties of PGSCS of the Holstein-Primakoff realization --- p.60 / Chapter 4.3.1 --- Quadrature squeezing of PGSCS --- p.60 / Chapter 4.3.2 --- Photon Statistics of PGSCS --- p.62 / Chapter 4.3.3 --- Q-function of PGSCS --- p.62 / Chapter 4.3.4 --- Wigner function of PGSCS --- p.69 / Chapter 5 --- Nonclassical properties of Barut-Girardello's type GSCS --- p.71 / Chapter 5.1 --- Nonclassical properties of BGSCS of the two- mode bosonic realization --- p.71 / Chapter 5.1.1 --- Squeezing properties of BGSCS --- p.71 / Chapter 5.1.2 --- Photon Statistics of BGSCS --- p.74 / Chapter 5.1.3 --- Q- function of BGSCS --- p.77 / Chapter 5.1.4 --- Wigner function of BGSCS --- p.77 / Chapter 5.2 --- Nonclassical properties of BGSCS of the Holstein-Primakoff realization --- p.81 / Chapter 5.2.1 --- Squeezing properties of BGSCS --- p.81 / Chapter 5.2.2 --- Photon statistics of BGSCS --- p.83 / Chapter 5.2.3 --- Q- function of BGSCS --- p.83 / Chapter 5.2.4 --- Wigner function of BGSCS --- p.85 / Chapter 6 --- "SU(1,1) Squeezing and Generalized Q´ؤfunction" --- p.90 / Chapter 6.1 --- "SU(1,1) Squeezing of PGSCS & BGSCS" --- p.90 / Chapter 6.1.1 --- "Reviews on SU(1,1) squeezing" --- p.90 / Chapter 6.1.2 --- "SU(1,1) Squeezing of PGSCS" --- p.92 / Chapter 6.1.3 --- "SU(1,1) Squeezing of BGSCS" --- p.93 / Chapter 6.2 --- "SU(1,1) Generalized Q´ؤfunction" --- p.95 / Chapter 6.2.1 --- GQk- function of PGSCS --- p.97 / Chapter 6.2.2 --- GQk-function of BGSCS --- p.101 / Chapter 6.2.3 --- GQk´ؤfunction of Glauber coherent state and Squeezed vacuum --- p.103 / Chapter 7 --- Discussion and Conclusion --- p.109 / Appendices --- p.111 / Chapter A --- Derivation of Equations 4.1 and 4.2 --- p.112 / Chapter B --- Derivation of Equation 4.16 --- p.115 / Chapter C --- Derivation of < n > and < n2 > on P.75 --- p.117 / Chapter D --- Deriavation of Equation 6.10 --- p.119 / Bibliography --- p.120

Thesis (Ph. D.)--University of Queensland, 2002. / Includes bibliographical references.

Next-generation information technology is expected to rely on discrete two-state quantum systems that can deterministically emit single photons. Quantum dots are mesoscopic (~10,000 atoms large) semiconductor islands grown in a host crystal of larger band-gap that make well-defined two-level quantum systems and are very attractive due to stability, record coherence times, and the possibility of integrating them into larger structures, such as optical microcavities. This work presents experimental progress towards understanding the coherent optical processes that occur in single quantum dots, particularly such phenomena that might be one day utilized for quantum communication applications. High resolution low temperature optical spectroscopy is used in conjunction with first order (amplitude) and second-order (intensity) correlation measurements of the emitted field. A novel technique is introduced that is capable of harvesting the fluorescence of single dots at the same frequency as the laser, previously impossible due to insurmountable scattering. This technique enables the observation, for the first time, of single quantum dot resonance fluorescence, in both the weak and strong excitation regimes, which forms the basis for deterministic generation of single photons. Guided by the rich theoretical description available from quantum optics with atoms we obtain insight into the complex dynamics of this driven system. Quantum dots confined to novel optical microcavities were further investigated using micro photoluminescence. An optical microcavity properly coupled to a two-level system can profoundly modify its emission characteristics via quantum electrodynamical effects, which are highly attractive for single photon sources. The all-epitaxial structures we probe are distinguished by a bulk morphology that overcomes the fragility problems of existing approaches, and provides high quality factors as well as small mode volumes. Lasing is obtained with larger strucutres. Additionally, isolation of individual dots is further realized in smaller cavities and the Purcell effect observed in time-resolved photon counting experiments. / text

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Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 157-164). Also available for download via the World Wide Web; free to University of Oregon users.