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In this thesis is presented the realisation of 'The Geonium Chip', a novel planar Penning trap. The chip is designed with the goal of building a truly scalable planar Penning trap, while retaining the accuracy of 3D traps. Manufactured with conventional metalon- silicon microfabrication techniques, the chip takes the 5 electrodes of the compensated cylindrical trap and projects them onto a ground-plane surface, thus forming the basis for its layout by reducing the electrode shape to an array of at rectangular surfaces. In this thesis I describe the conception, design and construction of a full cryogenic set-up, including the magnetics, for trapping and observing a single electron in the Geonium Chip Penning trap. The cyclotron mode of the trapped electron lies in the microwave regime, and thus the Geonium Chip has the potential to become a powerful building block for quantum microwave circuits, with coherent coupling to the cyclotron degree of freedom. This will also allow non-destructive measurement and interaction with the spin state of the electron. The development of the experimental process is detailed from scratch including the design, fabrication, and testing of the Geonium Chip, as well as the design, fabrication and testing of the experimental apparatus. The original solutions and space saving designs developed as part of the construction process are detailed, such as the custom on-chip cryogenic vacuum chamber, planar magnetic field source, and the LED-based electron loading system. The vacuum chamber and control systems are also described, and the in-house manufacturing capabilities of the Geonium group are detailed at length, with an emphasis on rapid prototyping high-accuracy components suitable for experimental use. The apparatus built within this PhD is within a few weeks of performing the first loading of electrons into the chip trap.

Quantum electrodynamics is the spectacularly successful theory of the interaction of light and matter. Its consequences are well-understood, and have been experimentally verified to extreme precision. What is not generally known is how these predictions change when the theory is considered in anything other than free space - near a surface, for example. A material boundary causes vacuum fluctuations of the electromagnetic field to be different from their counterparts in free space, causing the electromagnetic environment of a microscopic system sitting near the boundary to differ from that if the surface were not present. This causes a variety of surface-dependent shifts in the properties of the microscopic system - this work investigates these shifts for a free electron. First using explicit normal mode expansion and analytic continuation of the wave-vector in the complex plane, and then using a semi-phenomenological `noise current' approach, the work presents derivations of formulae for the shifts in the mass and magnetic moment of an electron near a dispersive and absorbing surface. The formalism is also extended to the case where the electron is subject to a harmonic potential. It is noted that results for different models of the surface do not agree in the expected limiting cases due to their differing behaviour at low frequency, which leads to the conclusion that one must be very careful to use an appropriate model of a particular surface when considering quantum electrodynamic surface effects. Analysis of the results shows that use of a realistic model of the surface can make these shifts orders of magnitude larger than previous calculations had suggested, since they all relied on the somewhat unrealistic assumption that the surface is perfectly reflecting. This is shown to be particularly relevant to experiments which aim to measure the anomalous magnetic moment of an electron.

In this work, I detail the reconstruction and upgrades performed on the axial cavity ion trap in the ITCM group at the university of Sussex, and the measurement of the coupling of multiple ions to the cavity mode. This enables the optimal coupling between the ions and the cavity by adjusting the ions position in the radial and axial positions. This covers new ground in extending the optimal coupling beyond two ions which is of great importance for experiments with several ions in an optical cavity. The thesis outlines the background theory of light-matter interaction and cavity QED, before describing the physical ion trap hardware and its assembly. A description of the laser and cavity systems is provided, including techniques for locking both to stable references. A number of novel measurement techniques for measuring and maximising the stability of the ions and cavities are presented, including micromotion minimisation, spectroscopy, magnetic field compensation using the ground state Hanle effect, and Raman spectroscopy. These techniques enable the measurement of crucial parameters of the atomic transitions and the cavity. The work culminates in a description of the optimisation of the coupling between ion strings and the cavity first by adjusting the radial trap position by means of variable capacitors attached to RF electrodes, and then axially by means of adjusting the endcap potentials and therefore the spacing between ions to obtain the greatest localisation while still positioning the ions close to the antinodes of the cavity field.

Ho kai Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 112-114). / Ho Kai Cheung. / Acknowledgements --- p.i / Abstract --- p.ii / Contents --- p.iii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- QNM and Green's function --- p.6 / Chapter 2.1 --- Introduction to QNM --- p.7 / Chapter 2.2 --- QNM and Green's function --- p.9 / Chapter 2.3 --- Modes of the universe and Green's function --- p.11 / Chapter Chapter 3. --- Correlation function and Green's function --- p.16 / Chapter 3.1 --- Equation of motion approach --- p.17 / Chapter 3.2 --- NM approach --- p.20 / Chapter Chapter 4. --- Correlation function : QNM expansion --- p.23 / Chapter 4.1 --- QNM expansion of correlation function --- p.24 / Chapter 4.2 --- Physical Examples --- p.27 / Chapter 4.2.1 --- One dimensional laser cavity --- p.27 / Chapter 4.2.2 --- Dielectric slab --- p.40 / Chapter Chapter 5. --- Quantization of EM field : modes of the universe approach --- p.49 / Chapter 5.1 --- Spherical wave expansion --- p.49 / Chapter 5.2 --- Quantization of EM field --- p.52 / Chapter 5.3 --- Correlation function : NM expansion --- p.56 / Chapter Chapter 6. --- QNM expansion of EM correlation function I --- p.59 / Chapter 6.1 --- TE part result --- p.61 / Chapter 6.2 --- TM part result --- p.65 / Chapter Chapter 7. --- QNM expansion of EM correlation function II --- p.69 / Chapter 7.1 --- Dyadic Green's function --- p.69 / Chapter 7.2 --- Green's function and correlation function : EM case --- p.72 / Chapter 7.3 --- QNM expansion of correlation function --- p.73 / Chapter Chapter 8. --- Sum rules --- p.76 / Chapter 8.1 --- Proof of sum rules --- p.77 / Chapter 8.2 --- Equivalence of two approaches --- p.78 / Chapter 8.3 --- Discussion of the QNM expansion --- p.79 / Chapter Chapter 9. --- EM field fluctuation in dielectric sphere --- p.82 / Chapter 9.1 --- Modes of the universe approach (revision) --- p.83 / Chapter 9.2 --- QNM approach --- p.85 / Chapter 9.3 --- Increase convergence by sum rules --- p.90 / Chapter Chapter 10. --- Conclusion --- p.97 / Appendix A. Scalar Green's function by normalized NM --- p.100 / Appendix B. Modification of existence of QNM on imaginary axis --- p.102 / Appendix C. Tensor Tij --- p.104 / Appendix D. Evaluation of aW+(wn)/aw --- p.106 / Appendix E. Classical dyadic Green's function --- p.107 / Appendix F. QNM expansion of Tij inside a leaky cavity --- p.109 / Appendix G. Symmetric properties of Fij --- p.111 / Bibliography --- p.112

Lee, Kwun Yan = 腔量子電動力學模型中光子-原子集體相互作用 / 李冠昕. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 81-86). / Text in English; abstracts in English and Chinese. / Lee, Kwun Yan = Qiang liang zi dian dong li xue mo xing zhong guang zi-yuan zi ji ti xiang hu zuo yong / Li Guanxin. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Basic description of cavity QED systems --- p.4 / Chapter 2.1 --- Mode functions --- p.4 / Chapter 2.2 --- Quantization of electromagnetic fields --- p.7 / Chapter 2.2.1 --- Generalized modes of photons --- p.8 / Chapter 2.2.2 --- Cavity modes and dipole interactions --- p.10 / Chapter 2.3 --- Interaction models --- p.11 / Chapter 2.3.1 --- Jaynes-Cummings model --- p.12 / Chapter 2.3.2 --- Raman model (∧-type atoms) --- p.12 / Chapter 2.3.3 --- Two-model interaction: X-like 4-level atoms --- p.14 / Chapter 3 --- Phot on-atom entanglement generated by AC Stark shift --- p.16 / Chapter 3.1 --- Introduction --- p.16 / Chapter 3.2 --- The model --- p.18 / Chapter 3.3 --- Evolution of states --- p.19 / Chapter 3.4 --- Schmidt analysis of entanglement --- p.21 / Chapter 3.5 --- Break time: Deviation from continuous approximation --- p.26 / Chapter 3.6 --- Fractional revival of entanglement --- p.29 / Chapter 3.7 --- Number-phase correlation --- p.29 / Chapter 3.8 --- Consideration of cavity field leakage: Input-output relation --- p.31 / Chapter 4 --- Dynamical modes in Dicke superradiance --- p.36 / Chapter 4.1 --- Introduction --- p.36 / Chapter 4.2 --- Spontaneous emission from a single atom --- p.38 / Chapter 4.2.1 --- Free space problem --- p.39 / Chapter 4.2.2 --- Leaky cavity problem --- p.40 / Chapter 4.3 --- Spontaneous emission for NA-atoms --- p.43 / Chapter 4.4 --- Dynamical mode formalism --- p.44 / Chapter 4.4.1 --- Motivation --- p.44 / Chapter 4.4.2 --- Optimal dynamic mode functions --- p.46 / Chapter 4.4.3 --- Mode purity function --- p.48 / Chapter 4.4.4 --- Two-time collective dipole correlation function --- p.48 / Chapter 4.5 --- Results --- p.51 / Chapter 4.5.1 --- Two-atom case --- p.52 / Chapter 4.5.2 --- Many atoms case: Fully excited systems --- p.52 / Chapter 4.5.3 --- Many atoms case: Halfly excited systems --- p.56 / Chapter 4.5.4 --- Many atoms case: NA ´ؤ δ excited systems --- p.57 / Chapter 4.6 --- Remarks on three-dimensional systems --- p.58 / Chapter 5 --- Single-mode treatment of Raman interaction inside a cavity --- p.61 / Chapter 5.1 --- Introduction --- p.61 / Chapter 5.2 --- The model and Hamiltonians --- p.63 / Chapter 5.3 --- A dominant dynamic field mode --- p.66 / Chapter 5.3.1 --- Bosonization: Undepleted atom number approximation . --- p.66 / Chapter 5.3.2 --- Bosonization: Inclusion of atom number depletion --- p.70 / Chapter 5.4 --- Single-mode interaction by time-dependent variational principle --- p.72 / Chapter 5.5 --- Photon-atom squeezing --- p.75 / Chapter 6 --- Conclusion --- p.78 / Bibliography --- p.81 / Chapter A --- Dicke states and spin coherent states --- p.87 / Chapter A.1 --- Dicke states --- p.87 / Chapter A.2 --- Spin coherent states --- p.90 / Chapter B --- Adiabatic elimination and AC Stark shift --- p.93 / Chapter B.1 --- 2-level system --- p.93 / Chapter B.2 --- Raman transition --- p.94 / Chapter C --- Derivation of Master equation --- p.98 / Chapter C.1 --- Dissipative quantum systems: The master equation approach --- p.98 / Chapter C.1.1 --- Born and Markov approximation --- p.99 / Chapter C.2 --- Master equation in collective spontaneous emissions --- p.103 / Chapter C.3 --- Analytical solution by Laplace transform --- p.106

We study the Dyson Schwinger Equation for the fermion propagator in the quenched approximation. We construct a non-preservative fermion-boson vertex that ensures the fermion propagator satisfies the Ward-Takahashi identity, is multiplicatively renormalizable, agrees with the lowest order perturbation theory for weak couplings and has a critical coupling for dynamical mass generation that is strictly gauge independent. This is in marked contrast to the rainbow approximation in which the critical coupling changes by 50% just between the Landau and Feynman gauges. We also show how to construct a vertex which not only has the aforementioned properties but also agrees with the results obtained from the CJT effective potential for the critical exponent of the mass function. These vertices are expressed in terms of two functions which satisfy an integral and a derivative condition. By considering the perturbative expansion for the transverse vertex, we have performed numerical evaluation of the first of these functions which will hopefully guide their non-perturbative structure. The use of vertices satisfying these properties should lead to a more believable study of mass generation.

Thesis (Ph. D.)--University of Washington. / Bibliography: l. 121-123.