Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics. / Vita. / Includes bibliographical references. / by Steven E. Koonin. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by Jens Hoppe. / Ph.D.

When nature is observed at the nanoscale, quantum physics is typically the most accurate model to describe and predict its behavior. Furthermore, quantum effects are increasingly at the core of the operation of new advanced electronic and photonic devices, which, in some cases, are designed on the basis of controlling quantum systems. This thesis focuses on two such systems, united by the methods used to realize them. These methods represent the cutting-edge of nanofabrication, which is the structuring of matter at ultra-small dimensions with a degree of precision and control that has not been previously attained. Pushing these methods to their limits enables the emergence of unique phenomena in the quantum systems explored here. The first system involves the realization of artificial graphene in an AlGaAs/GaAs quantum heterostructure. The appearance of massless charge carriers in graphene, which are described by the relativistic Dirac equation, originates from the linear energy-momentum dispersion of the electronic states in proximity to the K and K’ points of the hexagonal Brillouin zone. This unique quantum behavior is a direct result of the honeycomb symmetry of the graphene lattice. The prospect of reproducing this physics in an adjustable, artificial honeycomb lattice, known as artificial graphene, offers a platform for the exploration of novel quantum regimes of massless Dirac fermions beyond the limits imposed by the inability to manipulate the lattice of the natural material. The electronic properties of a two-dimensional electron gas whose density is modulated by a periodic potential with honeycomb symmetry have been predicted to generate massless Dirac-fermions with tunable Fermi velocity. This thesis reports the observation of a graphene-like band structure in a modulation-doped AlGaAs/GaAs quantum well engineered with a honeycomb lateral surface superlattice. This was accomplished by reactive ion etching of the surface to within a few tens of nanometers from the quantum well. A metal hard-mask, patterned by electron beam lithography combined with metal deposition and lift-off, was used to form a honeycomb artificial lattice with a variable lattice period, down to 40 nm. This is a three-fold reduction with respect to the smallest reported to date in pertinent literature. The BCl3-based shallow etching produces cylindrical pillars below which the two-dimensional electron gas is expected to form quantum dots, where the electron density is higher than in the surrounding etched regions. Low-temperature resonant inelastic light scattering measurements reveal new electronic transitions. An accurate interpretation of these can be found in the joint density of states derived from the calculated graphene-like linearly-dispersed energy bands, induced by the honeycomb potential modulation. The second system comprises the nanoscale engineering of individual electron spin qubits in diamond. Spin systems in solid-state have been intensively investigated as an outstanding pathway towards quantum information processing. One of the advantages of solid-state spintronics is the possibility of applying nanofabrication techniques commonly used by the semiconductor industry to produce and integrate spin qubits. The negatively charged nitrogen-vacancy (NV-) center in diamond stands out because of its optically addressable spin, which shows long coherence time and viable spin initiation, manipulation and read-out. A central challenge has been the positioning of NV- centers with nanometer scale control, that would allow for efficient and consistent dipolar coupling and the integration within an optoelectronic device. I demonstrate a method for chip-scale fabrication of arrays of closely-spaced NV- centers with record spatial localization of approximately 10 nm in all three dimensions and controllable inter-NV spacing as small as 40 nm. This is the highest spatial resolution realized to date in positioning NV- centers at the nanoscale with high throughput, and approaches the length scale of strong dipolar coupling. This method used masked implantation of nitrogen in an ultra-pure CVD-grown diamond substrate through nano-apertures in a thin gold film, patterned via electron-beam lithography and dry etching. The high-density and high-atomic weight of gold results in a mask which is significantly thinner than polymer films used in other works, whilst still successfully impeding ion penetration, with a mask contrast of more than 40 dB. This process allows for the creation of apertures with lower aspect ratio which are therefore easier to pattern in close proximity to one another, i.e., within the dipolar coupling range. The position and spin coherence properties of the resulting near-surface NVs were measured through wide-field super-resolution optically detected magnetic resonance imaging, Hahn echo and CPMG pulsed microwave spectroscopy. The patterning methodology demonstrated here is optimally suited to functional integration with plasmonic nanostructures, which can enhance our ability to control single-photon emission with the prospect of creating near-surface nanoscale sensors of electric or magnetic fields and quantum optoelectronic devices.

No description available.

Based on a multi-mode multi-level Jaynes-Cummings model and multi-photon resonance theory, a set of universal two-qubit and three-qubit gates has been realized where dual-rail qubits are encoded in cavities. In this way, the information has been stored in cavities and the off-resonant levels have been eliminated by the theory of an effective two-level Hamiltonian. A further model, namely the spin-J model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multilevel multi-photon models have been performed. The combination of the two models has been employed to address two-level, three-level, four-level, and even five-level configurations. Considering the present cavity-QED experiments, several numerical simulations have been designed in order to check the robustness of the logic gates to variations in experimentally important parameters including the coupling constants and the detunings. Finally, based on Liouville's equation, and the wave-function treatments, the impact of decoherence processes on the fidelity of the qubit states in the iSWAP and the Fredkin gates has been studied. This thesis may have applications to quantum information processing, involving logic with simple quantum bits, with the possible application to the building of a quantum computer.

This thesis studies three aspects of gravity in quantum field theory. First quantum gravity effects are investigated using effective field theory techniques. In particular, we consider quantum gravity effects in grand unified theory and study their effects on the unification of the masses in such models. We find that the fermion masses unification conditions receive a sizeable correction from the quantum gravitational effects and one thus cannot predict the high energy unification only by the extrapolation from low energy physics without the understanding of gravitational effect in high energy. Secondly we study quantum field theory in curved spacetime in order to understand further about some of the properties of gravity. Keeping gravity as background field we discuss modified gravity theories in different set of parameters called frames; they are the Jordan frame and the Einstein frame respectively. We show how to map gravitational theories at the quantum field theoretical level. The key observation is that there is a non-trivial Jacobian. It can be interpreted as boundary term. Finally we investigate a new canonical quantisation paradigm. In that framework, quantum gravity is power counting renormalisable. Furthermore, the theory is unitary and the problem of time is solved. We use this framework to calculate the solution for the quantum wave function and the semiclassical Hamilton-Jacob function. We study the Hawking-Bekenstein entropy in the spherical symmetric mini-superspace for Schwarzschild black hole, and find that it can be produced naturally from first principles. Importantly it is accompanied naturally by non-thermal quantum correction terms which is generally believed to restore the information loss.

In this thesis we study several topics within the subject of extra dimensions and composite Higgs models. We first look at a scenario with a warped extra dimension known as the Randall-Sundrum (RS) model, and put all Standard Model fields in the bulk. We investigate various aspects of the model and argue that the presence of higher dimensional operators in the 5D bulk has a non-negligible effect on the electroweak precision observables, meaning that current electroweak constraints on non-custodial warped models could be weaker than previously thought. Then, using holographic techniques, we study correlations between the top partner masses and the Higgs potential in composite Higgs models. It is known that a light Higgs (~ 125 GeV) generally requires light top partners at around 700-800 GeV. However in these calculations the 5D volume is always fixed such that the 5D cutoff is around ~ MPl. The effect of lowering this 5D cutoff has been studied previously in bulk RS models as a way of reducing constraints from some flavour and electroweak precision observables, these models were dubbed "Little Randall-Sundrum models". Here we consider a similar setup in the context of holographic composite Higgs models and show that reducing the 5D cutoff leads to a lighter Higgs without a lowering of the top partner masses or an increase in fine-tuning. We find that the model is perfectly consistent with a 125 GeV Higgs and top partners above 1 TeV. This reduced 5D cutoff implies an intermediate scale between the electroweak scale and the Planck scale. Lastly we consider a similar warped model with a low 5D cutoff, except this time our goal is to study diphoton signals from Kaluza-Klein gravitons in a warped extra dimension. With a KK graviton of mass 750 GeV and spin-1 states at ~ 2:5 TeV, we show that having a low 5D cutoff increases the diphoton signal and the decay to gluons. With this model we show that we can explain the recently observed diphoton excess in terms of a Kaluza-Klein graviton from a holographic composite Higgs model, while keeping other decay channels within the relevant experimental bounds.

Laser systems and a linear radiofrequency (rf) Paul trap with an integrated co-axial cavity have been developed for experiments in cavity QED and probabilistic entanglement. Single 40Ca+ ions and large Coulomb crystals have been trapped routinely and laser cooled with long trapping lifetimes. A technique to achieve precise overlap of the pseudopotential minimum of the rf-field with the cavity mode has been implemented through variable capacitors in the resonant rf-circuit used to drive the trap. Three-dimensional micromotion compensation has been implemented. An 894 nm laser has been frequency stabilised to a Pound-Drever-Hall cavity which is in turn stabilised to atomic Cs using polarisation spectroscopy. The Allan variance of the error signal has been reduced to less than a kilohertz on timescales greater than a second. A novel implementation of the scanning cavity transfer lock has been developed to transfer the stability of the 894 nm laser to the 397 nm ion cooling and 866 nm repumping lasers. The bandwidth of the system has been increased to 380 Hz and the Allan variance of the error signal has been reduced to less than ten kilohertz on timescales of greater than a second. The pseudopotential minimum of the rf field has been overlapped optimally with the optical cavity mode through mapping of the fluorescence from cavity-field repumped ions as a function of their displacement. Coupling to the cavity mode has been confirmed by observation of resonant fluorescence into the cavity mode using the cavity-assisted Raman transition process. The thesis demonstrates that the setup is ready for the controlled production of single photons with pre-determined polarisation states, and progression onto new schemes to entangle multiple ions that are coupled to the optical cavity mode.

In the chapter 3, we study ferromagnetic fluctuations on two types of bilayer triangular lattices by the single-band Hubbard model. We start from the tight-binding model to obtain energy spectrum, the density of sates, and the spin susceptibility. With finite Coulomb interaction turned on, we apply the random phase approximation and use the determinant quantum Monte Carlo method to study spin susceptibility for the two bilayer triangular lattices and make comparisons of their magnetic properties. The effects of the interlayer coupling is also examined in detail. / In the chapter 4, we addresses the issue of the ferromagnetism in graphene-based samples. To study magnetic correlations in graphene, we systematically carry out quantum Monte Carlo simulations of the Hubbard model on a honeycomb lattice. In the filling region below the Van Hove singularity, the system shows a short-range ferromagnetic correlation, which is slightly strengthened by the on-site Coulomb interaction and markedly by the next-nearest-neighbor hopping integral. The ferromagnetic properties depend on the electron filling strongly, which may be manipulated by the electric gate. Due to its resultant high controllability of ferromagnetism, graphene-based samples may facilitate the new development of many applications. / In the chapter 5, we examined theoretically the magnetism of impurity adatoms in graphene by quantum Monte Carlo simulation technique based on Hirsch-Fye algorithm. When tuning the Fermi energy of graphene by gate voltage with available experiments, the values of occupancy and local moment for impurity can be changed. Furthermore, with medium and large hybridizations between impurity and graphene atoms, the local moment can be switched on and off by Kondo effects. We also use maximum entropy method to study the spectral density from Green's function for impurity, and we find very unconventional behaviors which are absolutely different from the cases in the normal metal. These signatures of spectral density enlarge the possibility for controlling the impurity magnetism by gate voltage. / In this research thesis, we mainly study three strongly correlated systems: Hubbard model in bilayer triangular lattice which corresponds to the real material of NaxCoO2 · yH 2O, strong-interaction electrons in graphene system and Anderson impurity in graphene. Our numerical method is determinant quantum Monte Carlo method which will be introduced in the chapter 2. / Hu, Feiming = 阻錯系統的量子門特卡洛研究 / 胡飛鳴. / Adviser: Lin Hai-Qing. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 107-126). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Hu, Feiming = Zu cuo xi tong de liang zi Mente Kaluo yan jiu / Hu Feiming.

Entanglement is an established resource in quantum information processing, and there is a clear imperative to study many-body systems both in quantum technology applications and for probing fundamental physical laws. Ion trap cavity quantum electrodynamics is a highly promising platform for research. Prerequisites are the controlled coupling of many ions to the cavity field along with the ability to initialize the quantum states and drive coherent transitions between them. A coaxial ion trap and high finesse cavity system has been shown to couple strings of up to five ions to the cavity mode with nearly optimal coupling strength thanks to precise control over their positions in the standing wave and their mutual Coulomb interaction. The predictive power of the theoretical model demonstrates that the scheme can be extended to more ions or to higher coupling regimes. In a separate experiment it has been demonstrated that a quantum state can be initialized, before coherently transferring the population to a qubit state through the cavity interaction. The emission of polarized photons in the cavity mode has been measured, taking the system closer to the generation of cluster states for quantum information research and fundamental studies in many-body entanglement. Building on the aforementioned work, an infrastructure has been put in place for the direct observation of vacuum Rabi oscillations between a single ion and the cavity. In this scheme, the contribution to the dynamics from the dominant incoherent channel is minimized through post-selection of the data. As a quantum system coupled to a reservoir with memory, it will provide experimental constraints on theoretical work in the field of non-Markovian dynamics.