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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.

Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.

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.

Kwok Chun Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [389]-393). / Text in English; abstracts in English and Chinese. / Kwok Chun Ming. / Abstract --- p.i / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Objective and Methodology --- p.3 / Chapter Chapter 2. --- Theory of the Jaynes-Cummings model --- p.5 / Chapter 2.1 --- Formulation of the Jaynes-Cummings model --- p.5 / Chapter 2.1.1 --- Quantization of the Electromagnetic Field --- p.6 / Chapter 2.1.2 --- Quantization of the Matter Field --- p.11 / Chapter 2.1.3 --- The Interaction between the Radiation and the Matter --- p.13 / Chapter 2.1.4 --- Formulation of the One-quantum JCM --- p.15 / Chapter 2.2 --- Energy Eigenstates and Eigenenergy Spectrum --- p.18 / Chapter 2.3 --- Initial States and Observables --- p.20 / Chapter 2.3.1 --- Initial States --- p.20 / Chapter 2.3.2 --- Field Observables --- p.24 / Chapter 2.3.3 --- Atomic Observables --- p.25 / Chapter 2.4 --- Conclusion --- p.27 / Chapter Chapter 3. --- "Generalized SU(1,1) JCM" --- p.28 / Chapter 3.1 --- "Diagonalization of the SU(1,1) JCM" --- p.28 / Chapter 3.2 --- "SU(1,1) Coherent States and Observables" --- p.32 / Chapter 3.2.1 --- "Realizations of the SU(1,1) JCM" --- p.33 / Chapter 3.2.2 --- "SU(1,1) Coherent States" --- p.33 / Chapter 3.2.3 --- Field Observables --- p.35 / Chapter 3.3 --- Conclusion --- p.36 / Chapter Chapter 4. --- "One-mode, Intensity-dependent JCM" --- p.37 / Chapter 4.1 --- "Properties of the One-mode, Intensity-dependent JCM" --- p.37 / Chapter 4.2 --- Squeezing Effect --- p.40 / Chapter 4.2.1 --- Ordinary Amplitude Squeezing --- p.41 / Chapter 4.2.2 --- "SU(1,1) Squeezing" --- p.44 / Chapter 4.2.3 --- SU(2) Squeezing --- p.47 / Chapter 4.3 --- Atomic Inversion --- p.49 / Chapter 4.4 --- Q-function --- p.52 / Chapter 4.4.1 --- Ordinary Q-function --- p.53 / Chapter 4.4.2 --- "SU(1,1) Q-function" --- p.59 / Chapter 4.5 --- Purity Function --- p.65 / Chapter 4.5.1 --- Field Purity Function --- p.65 / Chapter 4.5.2 --- Atomic Purity Function --- p.68 / Chapter 4.6 --- Asymptotic Behavior of Field Squeezing --- p.70 / Chapter 4.7 --- Conclusion --- p.75 / Chapter Chapter 5. --- "One-mode, Two-quantum JCM" --- p.191 / Chapter 5.1 --- "Properties of the One-mode, Two-quantum JCM" --- p.191 / Chapter 5.2 --- Squeezing --- p.196 / Chapter 5.2.1 --- Ordinary Amplitude Squeezing --- p.197 / Chapter 5.2.2 --- "SU(1,1) squeezing" --- p.202 / Chapter 5.2.3 --- SU(2) squeezing --- p.205 / Chapter 5.3 --- Atomic Inversion --- p.206 / Chapter 5.4 --- Q-function --- p.210 / Chapter 5.4.1 --- Ordinary Q-function --- p.210 / Chapter 5.4.2 --- "SU(1,1) Q-function" --- p.215 / Chapter 5.5 --- Purity Function --- p.217 / Chapter 5.5.1 --- Field Purity Function --- p.217 / Chapter 5.5.2 --- Atomic Purity Function --- p.222 / Chapter 5.6 --- Conclusion --- p.225 / Chapter Chapter 6. --- "Two-mode, Two-quantum JCM" --- p.254 / Chapter 6.1 --- "Properties of the Two-mode, Two-quantum JCM" --- p.254 / Chapter 6.2 --- Squeezing --- p.260 / Chapter 6.2.1 --- Ordinary Amplitude Squeezing --- p.260 / Chapter 6.2.2 --- "SU(1,1) Squeezing" --- p.264 / Chapter 6.2.3 --- SU(2) Squeezing --- p.267 / Chapter 6.3 --- Atomic Inversion --- p.269 / Chapter 6.4 --- Q-function --- p.271 / Chapter 6.4.1 --- "SU(1,1) Q-function" --- p.271 / Chapter 6.5 --- Purity Function --- p.273 / Chapter 6.5.1 --- Field Purity Function --- p.273 / Chapter 6.5.2 --- Atomic Purity Function --- p.275 / Chapter 6.6 --- Conclusion --- p.277 / Chapter Chapter 7. --- "Generalized One-mode, Intensity-dependent JCM" --- p.300 / Chapter 7.1 --- "Diagonalization of the Generalizated One-mode, Intensity-dependent JCM" --- p.301 / Chapter 7.2 --- Energy Eigenstates and Eigenenergy Spectrum --- p.307 / Chapter 7.2.1 --- Energy Eigenstates --- p.307 / Chapter 7.2.2 --- Eigenergy Spectrum --- p.309 / Chapter 7.3 --- Conclusion --- p.310 / Chapter Chapter 8. --- Single Trapped and Laser-irradiated JCM --- p.311 / Chapter 8.1 --- Properties of the One-quantum STLI JCM --- p.311 / Chapter 8.2 --- Squeezing Effect --- p.315 / Chapter 8.2.1 --- Ordinary Amplitude Squeezing --- p.315 / Chapter 8.2.2 --- "SU(1,1) Squeezing" --- p.320 / Chapter 8.2.3 --- SU(2) Squeezing --- p.323 / Chapter 8.3 --- Atomic Inversion --- p.326 / Chapter 8.4 --- Q-function --- p.329 / Chapter 8.4.1 --- Ordinary Q-function --- p.329 / Chapter 8.4.2 --- "SU(1,1) Q-function" --- p.332 / Chapter 8.5 --- Purity Function --- p.334 / Chapter 8.5.1 --- Field Purity Function --- p.335 / Chapter 8.5.2 --- Atomic Purity function --- p.338 / Chapter 8.6 --- Non-classical Effects of the Two-quantum STLI JCM --- p.341 / Chapter 8.7 --- Conclusion --- p.342 / Chapter Chapter 9. --- Conclusion --- p.386 / Bibliography --- p.389

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

Chan, Yun San = 光子晶格系統中相干行為的研究 / 陳潤燊. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 109-112). / Abstracts in English and Chinese. / Chan, Yun San = Guang zi jing ge xi tong zhong xiang gan xing wei de yan jiu / Chen Runshen. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgements --- p.V / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Periodic system and photonic crystal --- p.1 / Chapter 1.1.1 --- Properties and Applications --- p.1 / Chapter 1.1.2 --- Coherent Phenomena --- p.2 / Chapter 1.1.3 --- Quantum Optical Analogue --- p.9 / Chapter 1.2 --- Coupled Optical Waveguides --- p.11 / Chapter 1.2.1 --- Coupled-mode Theory --- p.11 / Chapter 1.2.2 --- Field Evolution Analysis (FEA) --- p.14 / Chapter 1.2.3 --- Hamiltonian Optics (HO) --- p.15 / Chapter 1.3 --- Experimental Realization --- p.17 / Chapter 1.4 --- Objectives --- p.17 / Chapter 2 --- Parabolic Optical Waveguide Array --- p.19 / Chapter 2.1 --- Introduction --- p.19 / Chapter 2.1.1 --- Generalized Bloch Oscillation --- p.19 / Chapter 2.1.2 --- DO-BO Transition --- p.20 / Chapter 2.2 --- Model and Formalism --- p.20 / Chapter 2.3 --- Results --- p.25 / Chapter 2.3.1 --- Dipole Oscillation --- p.29 / Chapter 2.3.2 --- Bloch Oscillation --- p.29 / Chapter 2.3.3 --- Right Reflection --- p.31 / Chapter 2.3.4 --- Mechanical Analogue --- p.32 / Chapter 2.3.5 --- Lift-n-Shift Process --- p.33 / Chapter 2.4 --- Summary --- p.39 / Chapter 3 --- Binary POWA --- p.40 / Chapter 3.1 --- Introduction --- p.40 / Chapter 3.2 --- Model and Formalism --- p.41 / Chapter 3.3 --- Results --- p.45 / Chapter 3.3.1 --- Dipole Oscillation --- p.48 / Chapter 3.3.2 --- Bloch-dipole-Zener Oscillation --- p.51 / Chapter 3.3.3 --- Bloch-Zener oscillation --- p.54 / Chapter 3.4 --- Viable Experimental Realization --- p.57 / Chapter 3.5 --- Summary --- p.58 / Chapter 4 --- Parabolically Graded Square Lattice --- p.60 / Chapter 4.1 --- Introduction --- p.60 / Chapter 4.2 --- Model and Formalism --- p.61 / Chapter 4.3 --- Results --- p.65 / Chapter 4.3.1 --- Orthogonal Coupling --- p.65 / Chapter 4.3.2 --- Weak Diagonal Coupling --- p.76 / Chapter 4.4 --- Summary --- p.81 / Chapter 5 --- Elliptical Optical Waveguide Array --- p.82 / Chapter 5.1 --- Introduction --- p.82 / Chapter 5.2 --- Model and Formalism --- p.83 / Chapter 5.2.1 --- Kac Matrix --- p.83 / Chapter 5.2.2 --- Kac Matrix and Spin --- p.85 / Chapter 5.2.3 --- System Configuration --- p.86 / Chapter 5.3 --- Results --- p.91 / Chapter 5.3.1 --- Upper Dipole Oscillation --- p.92 / Chapter 5.3.2 --- Lower Dipole Oscillation --- p.94 / Chapter 5.3.3 --- Bloch Oscillation --- p.95 / Chapter 5.3.4 --- Upper Reflection --- p.96 / Chapter 5.3.5 --- Lower Reflection --- p.98 / Chapter 5.3.6 --- Harmonic Oscillations --- p.98 / Chapter 5.3.7 --- Lift-n-Shift Process --- p.101 / Chapter 5.4 --- Summary --- p.102 / Chapter 6 --- Conclusion --- p.104 / Chapter 6.1 --- Suggestion of Future Works --- p.106 / Chapter 6.1.1 --- POWA --- p.106 / Chapter 6.1.2 --- BPOWA --- p.106 / Chapter 6.1.3 --- PGSL --- p.107 / Chapter 6.1.4 --- EOWA --- p.107 / Chapter A --- List of abbreviations --- p.108 / Bibliography --- p.109

This thesis is concerned with retrodiction and measurement in quantum optics. The latter of these two concepts is studied in particular form with a general optical multiport device, consisting of an arbitrary array of beam-splitters and phase-shifters. I show how such an apparatus generalizes the original projection synthesis technique, introduced as an in principle technique to measure the canonical phase distribution. Just as for the original projection synthesis, it is found that such a generalised device can synthesize any general projection onto a state in a finite dimensional Hilbert space. One of the important findings of this thesis is that, unlike the original projection synthesis technique, the general apparatus described here only requires a classical, that is a coherent, reference field at the input of the device. Such an apparatus lends itself much more readily to practical implementation and would find applications in measurement and predictive state engineering. If we relax the above condition to allow for just a single non-classical reference field, we show that the apparatus is capable of producing a single-shot measure of canonical phase. That is, the apparatus can project onto any one of an arbitrarily large subset of phase eigenstates, with a probability proportional to the overlap of the phase state and the input field. Unlike the original projection synthesis proposal, this proposal requires a binomial reference state as opposed to a reciprocal binomial state. We find that such a reference state can be obtained, to an excellent approximation, from a suitably squeezed state. The analysis of these measurement apparatuses is performed in the less usual, but completely rigorous, retrodictive formalism of quantum mechanics.