No description available.

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.

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.

Over the past 15 years ion traps have demonstrated all the building blocks required of a quantum computer. Despite this success, trapping ions remains a challenging task, with the requirement for extensive laser systems and vacuum systems to perform operations on only a handful of qubits. To scale these proof of principle experiments into something that can outperform a classical computer requires an advancement in the trap technologies that will allow multiple trapping zones, junctions and utilize scalable fabrication technologies. I will discuss the construction of an ion trapping experiment, focussing on my work towards the laser stabilization and ion trap design but also covering the experimental setup as a whole. The vacuum system that I designed allows the mounting and testing of a variety of ion trap chips, with versatile optical access and a fast turn around time. I will also present the design and fabrication of a microfabricated Y junction and a 2- dimensional ion trap lattice. I achieve a suppression of barrier height and small variation of secular frequency through the Y junction, aiding to the junctions applicability to adiabatic shuttling operations. I also report the design and fabrication of a 2-D ion trap lattice. Such structures have been proposed as a means to implement quantum simulators and to my knowledge is the first microfabricated lattice trap. Electrical testing of the trap structures was undertaken to investigate the breakdown voltage of microfabricated structures with both static and radio frequency voltages. The results from these tests negate the concern over reduced rf voltage breakdown and in fact demonstrates breakdown voltages significantly above that typically required for ion trapping. This may allow ion traps to be designed to operate with higher voltages and greater ion-electrode separations, reducing anomalous heating. Lastly I present my work towards the implementation of magnetic fields gradients and microwaves on chip. This may allow coupling of the ions internal state to its motion using microwaves, thus reducing the requirements for the use of laser systems.

It is well known that quantisation of gravity within the conventional framework of quantum field theory faces challenges. An intriguing novel prospect was put forward by S. Weinberg in 1979 who suggested that the metric degrees of freedom of gravity could be quantised nonpertubatively provided that the theory becomes asymptotically safe (AS) at high energies. In this thesis we put forward a systematic search strategy to test the AS conjecture in four dimensional quantum gravity. Using modern renormalisation group (RG) methods and heat kernel techniques we derive the RG equations for gravitational actions that are formed from powers of the Ricci scalar and powers of the Ricci tensor. The non-linear fixed point equations are solved iteratively and exactly. We develop a sophisticated algorithm to express the fixed point iteratively, and to high order, in terms of its lower order couplings. We also evaluate universal scaling exponents and find that the relevancy of invariants at an asymptotically safe fixed point is governed by their classical mass dimension, providing structural support for the asymptotic safety conjecture. We also apply our findings to the physics of higher dimensional black holes. Most notably, we find that the seminal ultra-spinning Myers-Perry black holes cease to exist as soon as asymptotically safe RG corrections are taken into account. Further results and implications of our findings are discussed.

Microfabricated ion traps are an important tool in the development of scalable quantum systems. Tremendous advancements towards an ion quantum computer were made in the past decade and most requirements for a quantum computer have been fulfilled in individual experiments. Incorporating all essential capabilities in a fully scalable system will require the further advancement of established quantum information technologies and development of new trap fabrication techniques. In my thesis I will discuss the theoretical background and experimental setup required for the operation of ion traps. Measurement of the important ion trap heating rate was performed in the setup and I will discuss the results in more detail. I will give a review of microfabrication processes used for the fabrication of traps, outlining advantages, disadvantages and issues inherent to the processes. Following the review I will present my work on a concept for a scalable ion trap quantum system based on microwave quantum gates and shuttling through X-junctions. Many of the required building blocks, including ion trap structures with current-carrying wires intended to create strong magnetic field gradients for microwave gates were investigated further. A novel fabrication process was developed to combine current-carrying wires with advanced multilayered ion trap structures. Several trap designs intended for proof of principle experiments of high fidelity microwave gates, advanced detection techniques and shuttling between electrically disconnected ion traps will be presented. Also the electrode geometry of an optimized X-junction design with strongly suppressed rf barrier height will be presented. Further, I developed several modifications for the experimental setup to extend the existing capabilities. A plasma source capable of performing in-situ cleans of the trap electrode surfaces, which has been demonstrated to dramatically reduce the heating rate in ion traps, was incorporated. I will also present a vacuum system modification designed to cool ion traps with current-carrying wires and transport the generated heat out of the vacuum system. In addition a novel low-noise, high-speed, multichannel voltage control system was developed by me. The device can be used in future experiments to precisely shuttle ions from one trapping zone to another and also to shuttle ions through ion trap junctions. Lastly I will outline the process optimization and microfabrication of my ion trap designs. A novel fabrication process which makes use of the extremely high thermal conductivity of diamond substrates and combines it with thick copper tracks embedded in the substrate was developed. Large currents will be passed through the wires creating a strong and controllable magnetic field gradient. Ion trap designs with isolated electrodes connected via buried wires can be placed on top of the current-carrying wires, allowing the most advanced electrode designs to be fabricated with current-carrying wires.