Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 132-138). Available also in a digital version from Dissertation Abstracts.

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Single spins confined in semiconductor quantum dots - artificial atoms in the solid-state - are attractive candidates for quantum mechanical bits, the fundamental units and building blocks of a quantum computer. The ability to address quantum dot spins optically allows us to initialise and manipulate the state of the quantum bit. Gaining information on the qubit, for example by reading out its state, not only requires state-selective optical excitation, but also access to the single photons scattered in response by the quantum dot. Further, for a distributed computer architecture where nodes of few quantum bits are interlinked via optical communication channels photonic quantum bits are required to faithfully transmit the quantum information. In this thesis we advocate resonant excitation of quantum dot transitions and collection of the resonance fluorescence to address two outstanding challenges: generating dephasing-free single photons for use as flying quantum bits and single-shot spin readout. To this end we investigate the spectral and first-order coherence properties of quantum dot resonance fluorescence. In particular, we directly observe highly coherent scattering in the low Rabi frequency limit which has remained unexplored for solid-state single photon emitters so far. At the same time, interactions with the semiconductor environment are revealed and quantified through their optical signatures: exciton-phonon coupling, nuclear spin dynamics and local electric field fluctuations signal a departure from the ideal atom-like behaviour. Taking advantage of the laser-like coherence of single phase-locked quantum dot photons in the Heitler regime, we demonstrate near-ideal two-photon quantum interference. This benchmark measurement is a precursor for the photonic entanglement of distant quantum dot spins in a quantum optical network, and the results here predict a high fidelity operation. Finally, moving to tunnel-coupled quantum dot molecules we show that the overlap of carrier wave functions in two closely spaced quantum dots forms new spin-selective optical transitions not available in single quantum dots. Then, the presence or absence of scattered photons reveals the electron spin. Intermittency in the quantum dot resonance fluorescence allowed us, for the first time, to observe spin quantum jumps in real-time. Both achievements - highly coherent photons and spin readout - provide the missing link to attempt creation of a small-scale quantum network now.

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This dissertation examines aspects of the interaction of multiple coherent light fields for the two-photon two-level model. In this model the interacting energy levels are not connected by an atomic dipole and a two-photon transition between them is necessary. We employ the density matrix formalism allowing easy comparison between the one- and two-photon two-level models. Significant differences are found due to dynamic Stark shifts and conjugate scattering off the pump-induced two-photon coherence. Averages over Doppler broadening are performed and the new upper-level relaxation mechanisms of decay to an intermediate nonresonant level and ionization from the upper state are included. The new relaxation mechanisms, introduced to the theory to better model experiments, are similar except that ionization is intensity dependent. They cause the resulting probe absorption spectra to become more complex and in general asymmetric. Doppler broadening is also important in experiments using gases. We analytically average over a Lorentzian velocity distribution for both co- and counterpropagating pump and probe beams. For copropagating fields the results are similar to those for the one-photon case averaged over inhomogeneous broadening, whereas counterpropagating pump and probe fields yield the so-called Doppler-free configuration that is normally only modelled to third order in the pump amplitude. We consider the pump field amplitude to all orders and find that as long as the width of the Doppler velocity distribution is significantly larger than the two-photon Rabi frequency the results are Doppler-free. The final part of the dissertation treats the question of two-photon squeezed states. This requires quantized sidemodes. Squeezed states are minimum uncertainty states with unequal variances in the two quadratures of the electromagnetic field amplitude. One way to generate these states is via multiwave mixing and we present here the first calculation for nondegenerate two-photon multiwave mixing as it applies to squeezed states. We find that in general two-photon squeezed states require lower intensities and detuning than those predicted by the one-photon model.

Current proposals for the design of quantum computer architectures include combining different quantum systems with designated tasks to build a device that can efficiently store, process, and transfer quantum information. Electron spins in solid-state quantum systems are a viable platform for storing information in these multi-quantum frameworks. While extensive research has been performed to couple solid-state systems to photons and microwaves, an alternative line of research focuses on coupling these systems to phonons, or mechanical motion. The use of phonons in solid-state devices opens up a new approach to interface different quantum systems. This dissertation presents experimental progress in developing and controlling a spin-mechanical system, specifically the interaction between the electron spin of a nitrogen vacancy (NV) center in diamond and mechanical vibrations on the surface of the diamond, and discusses theoretical methods for limiting decoherence in the system. To investigate the strain properties of the NV center, we couple acoustic waves to the NV spin via an optical excitation. We transfer population between the spin ground states by driving phonon-assisted optical transitions and demonstrate the formation of a non-radiative state, which can be used to adiabatically transfer population between two states, through the same mechanism. To mitigate the effects of the nuclear spin bath on the NV center, we study and show preliminary results on the semiclassical dressed states, or quantum states of the NV interacting with optical fields. The dressed states can be insensitive to magnetic fluctuations, thus preserving the quantum state of the system. Finally, we consider a transitionless quantum driving technique that decouples the NV center from a radiative state, preventing decoherence through spontaneous emission. These developments are essential in advancing our understanding of phonon-based interfaces between quantum systems. This dissertation includes previously published and unpublished co-authored material.

This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.

The objective of this thesis is to develop the quantum theory of the motional degrees of freedom of a charged particle in a Penning trap. The theory is treated within the formalism of quantum optics, and explores the use of dressed-atom methods by exploiting the threefold SU(N) algebraic structure of the problem. The quantum form of the experimental techniques of sideband coupling and driving to the ultra-elliptical regime are examined in this context, and resulting future applications considered. Interpretation of the quantum dynamics of the separate x and y motions of an electron is discussed, motivated by the desire to modify the trapping potential without changing the basic experimental configuration. A detailed discussion of operator methods which exploit the algebraic structure of the problem is given. This results in a clearer understanding of the physical manifestations of a range of unitary transformations upon a general three-dimensional system, and a novel interpretation of the mapping between canonical angular momentum components of isotropic and anisotropic trapping systems. The results highly promote future use of these methods in Penning trap theory, detailing a robust formulation of unitary operations which can be used to prepare the quantum state of a charged particle. The majority of the results can be applied to any Penning trap, but the theory is based throughout upon the “Geonium Chip" trap at Sussex; the scalability and planar design of this trap promotes it as natural candidate in experimental quantum optics and Gaussian quantum information studies. The work in this thesis aims to provide framework for such future applications.

Tsoi, Tze Shun = 光子和原子在一維波導中的相互作用 / 蔡子淳. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 94-97). / Abstract also in Chinese. / Tsoi, Tze Shun = Guang zi he yuan zi zai yi wei bo dao zhong de xiang hu zuo yong / Cai Zichun. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Basic description of QED in a one-dimensional waveguide --- p.4 / Chapter 2.1 --- EM fields in a waveguide: from classical to quantum --- p.4 / Chapter 2.1.1 --- Classical EM fields in a conducting waveguide --- p.5 / Chapter 2.1.2 --- Quantization of the electromagnetic fields --- p.8 / Chapter 2.2 --- "Atom, dipole interactions and interaction models" --- p.11 / Chapter 2.2.1 --- Atom and dipole interactions --- p.12 / Chapter 2.2.2 --- Two-level atom --- p.12 / Chapter 2.2.3 --- A-atom --- p.14 / Chapter 2.3 --- Comparison: waveguide vs free space --- p.15 / Chapter 2.3.1 --- Electric field intensity of a photon packet --- p.15 / Chapter 2.3.2 --- Spontaneous decay rate --- p.16 / Chapter 3 --- Single-excitation solution for two-level atoms --- p.20 / Chapter 3.1 --- Case of a single atom --- p.20 / Chapter 3.2 --- Case of a chain of N identical atoms --- p.26 / Chapter 3.2.1 --- The Hamiltonian and eigenvectors --- p.27 / Chapter 3.2.2 --- Transmission spectrum of a single photon --- p.31 / Chapter 3.2.3 --- Dynamics of spontaneous emission --- p.34 / Chapter 3.3 --- Dissipative loss to non-waveguide modes --- p.39 / Chapter 3.4 --- Interactions with non-identical atoms --- p.41 / Chapter 3.4.1 --- Vacuum Rabi oscillations using atomic mirrors --- p.42 / Chapter 3.4.2 --- Atoms with non-identical resonant energies --- p.46 / Chapter 4 --- Two-photon transport with a two-level atom --- p.50 / Chapter 4.1 --- The energy eigenstate solution --- p.51 / Chapter 4.1.1 --- Single-photon case --- p.51 / Chapter 4.1.2 --- Two-photon case --- p.53 / Chapter 4.2 --- Laplace transformation method --- p.57 / Chapter 4.2.1 --- Single-photon case --- p.58 / Chapter 4.2.2 --- Two-photon case --- p.61 / Chapter 4.2.3 --- Lorentzian-packet states --- p.64 / Chapter 4.2.4 --- Photon-photon correlations --- p.65 / Chapter 5 --- Interactions with A-atoms --- p.70 / Chapter 5.1 --- Hamiltonian and eigenvectors --- p.71 / Chapter 5.1.1 --- N = 1 case --- p.71 / Chapter 5.1.2 --- N > 1 case --- p.75 / Chapter 5.2 --- Final state properties --- p.80 / Chapter 5.2.1 --- Polarization dependent transmission and reflection --- p.80 / Chapter 5.2.2 --- Collective atomic states --- p.82 / Chapter 5.2.3 --- Scattering with a photon wave packet --- p.83 / Chapter 5.3 --- Decoherence: effects of the coupling with the non-waveguide modes --- p.85 / Chapter 5.4 --- Application: an “NM´ح polarizer made of a few atoms --- p.86 / Chapter 6 --- Conclusion --- p.91 / Bibliography --- p.94 / Chapter A --- Derivation of the one-dimensional spontaneous rate r1d --- p.98 / Chapter B --- Description of a photon packet --- p.101 / Chapter C --- Derivation of the two-photon packet solution --- p.105 / Chapter D --- “Completeness´ح of the two-photon Lorentzian-packet states --- p.108

Coherent effects are studied in a dense atomic vapor driven by laser fields. With optical properties dramatically modified by these effects, the medium can be used to manipulate some of the properties of laser field. Our experiments demonstrate the coherent control over transmission, spatial distribution and noise feature of the laser field interacting with coherent media. The results have potential applications in the field such as precision metrology, precision spectroscopy, optical imaging and lithography. We develop an experiment to investigate the atomic excitation by few-cycle radio frequency (RF) pulses interacting with Zeeman sublevels. The system provides the flexibility to fully control all parameters of RF pulses. Such a flexibility can not be achieved in optical domain. Based on this system, experiments can be conducted to simulate processes in ultra-short laser physics. In particular, we study the carrier-envelope effect of few-cycle pulses and the strong off-resonant excitation by short pulses. We also discuss the selective reflection spectrum on a highly dense atomic vapor in which the dipole-dipole interaction can not be neglected. The spectrum broadening due to dipole-dipole interaction is much broader than the Doppler broadening. Our experiments show that the excitation by a pump laser can reduce the dipole-dipole interaction, thus reduce the broadening and improve the spectral resolution. The excitation dependence is studied at various atomic densities.