Quantum optics provides powerful means to probe quantum mechanics. In this thesis, we study various aspects of quantum phenomena arising in quantum optical systems. Part I studies broadband quantum teleportation. After presenting three different methods of analyzing the standard teleportation protocol, we study the interplay between various bandwidths in determining the fidelity of a broadband quantum field teleportation. Explicit formulae for the degrees of first- and secondorder coherence for the teleportation of resonance fluorescence are derived for this purpose. Part II studies entanglement arising in cascaded open quantum (optical) systems. First, a detailed laser model is produced within quantum trajectory theory to study the total decoherence rate of a laser-driven qubit. Second, using this model, we address the issue of laser quantum state, viewed in connection with separability of the laser-driven-qubit system. Third, a measure of entanglement within quantum trajectory theory called ‘Contextual Entanglement’ is calculated for a few simple systems and compared with the ‘Entanglement of Formation’. Lastly, we introduce a method to quantify entanglement (based on the contextual entanglement) between a source and the field it emits, which we call the ‘Entanglement Spectrum’. It is applied to study the entanglement between a laser-driven qubit and the field the qubit scatters.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Supervisor: William C. Schieve. Vita. Includes bibliographical references. Available also from UMI Company.

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Quantum optics provides powerful means to probe quantum mechanics. In this thesis, we study various aspects of quantum phenomena arising in quantum optical systems. Part I studies broadband quantum teleportation. After presenting three different methods of analyzing the standard teleportation protocol, we study the interplay between various bandwidths in determining the fidelity of a broadband quantum field teleportation. Explicit formulae for the degrees of first- and secondorder coherence for the teleportation of resonance fluorescence are derived for this purpose. Part II studies entanglement arising in cascaded open quantum (optical) systems. First, a detailed laser model is produced within quantum trajectory theory to study the total decoherence rate of a laser-driven qubit. Second, using this model, we address the issue of laser quantum state, viewed in connection with separability of the laser-driven-qubit system. Third, a measure of entanglement within quantum trajectory theory called ‘Contextual Entanglement’ is calculated for a few simple systems and compared with the ‘Entanglement of Formation’. Lastly, we introduce a method to quantify entanglement (based on the contextual entanglement) between a source and the field it emits, which we call the ‘Entanglement Spectrum’. It is applied to study the entanglement between a laser-driven qubit and the field the qubit scatters.

Quantum optics provides powerful means to probe quantum mechanics. In this thesis, we study various aspects of quantum phenomena arising in quantum optical systems. Part I studies broadband quantum teleportation. After presenting three different methods of analyzing the standard teleportation protocol, we study the interplay between various bandwidths in determining the fidelity of a broadband quantum field teleportation. Explicit formulae for the degrees of first- and secondorder coherence for the teleportation of resonance fluorescence are derived for this purpose. Part II studies entanglement arising in cascaded open quantum (optical) systems. First, a detailed laser model is produced within quantum trajectory theory to study the total decoherence rate of a laser-driven qubit. Second, using this model, we address the issue of laser quantum state, viewed in connection with separability of the laser-driven-qubit system. Third, a measure of entanglement within quantum trajectory theory called ‘Contextual Entanglement’ is calculated for a few simple systems and compared with the ‘Entanglement of Formation’. Lastly, we introduce a method to quantify entanglement (based on the contextual entanglement) between a source and the field it emits, which we call the ‘Entanglement Spectrum’. It is applied to study the entanglement between a laser-driven qubit and the field the qubit scatters.

Quantum optics provides powerful means to probe quantum mechanics. In this thesis, we study various aspects of quantum phenomena arising in quantum optical systems. Part I studies broadband quantum teleportation. After presenting three different methods of analyzing the standard teleportation protocol, we study the interplay between various bandwidths in determining the fidelity of a broadband quantum field teleportation. Explicit formulae for the degrees of first- and secondorder coherence for the teleportation of resonance fluorescence are derived for this purpose. Part II studies entanglement arising in cascaded open quantum (optical) systems. First, a detailed laser model is produced within quantum trajectory theory to study the total decoherence rate of a laser-driven qubit. Second, using this model, we address the issue of laser quantum state, viewed in connection with separability of the laser-driven-qubit system. Third, a measure of entanglement within quantum trajectory theory called ‘Contextual Entanglement’ is calculated for a few simple systems and compared with the ‘Entanglement of Formation’. Lastly, we introduce a method to quantify entanglement (based on the contextual entanglement) between a source and the field it emits, which we call the ‘Entanglement Spectrum’. It is applied to study the entanglement between a laser-driven qubit and the field the qubit scatters.

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.