Entanglement is a key resource in many quantum information schemes and in the last years the research on multi-qubit entanglement has drawn lots of attention. In this thesis the experimental generation and characterisation of multi-qubit entanglement is presented. Specifically we have prepared entangled states of up to six qubits. The qubits were implemented in the polarisation degree of freedom of single photons. We emphasise that one type of states that we produce are rotationally invariant states, remaining unchanged under simultaneous identical unitary transformations of all their individual constituents. Such states can be applied to e.g. decoherence-free encoding, quantum communication without sharing a common reference frame, quantum telecloning, secret sharing and remote state preparation schemes. They also have properties which are interesting in studies of foundations of quantum mechanics. In the experimental implementation we use a single source of entangled photon pairs, based on parametric down-conversion, and extract the first, second and third order events. Our experimental setup is completely free from interferometric overlaps, making it robust and contributing to a high fidelity of the generated states. To our knowledge, the achieved fidelity is the highest that has been observed for six-qubit entangled states and our measurement results are in very good agreement with predictions of quantum theory. We have also performed another novel test of the foundations of quantum mechanics. It is based on an inequality that is fulfilled by any non-contextual hidden variable theory, but can be violated by quantum mechanics. This test is similar to Bell inequality tests, which rule out local hidden variable theories as possible completions of quantum mechanics. Here, however, we show that non-contextual hidden variable theories cannot explain certain experimental results, which are consistent with quantum mechanics. Hence, neither of these theories can be used to make quantum mechanics complete.

Nonlinearities in quantum cascade lasers (QCL¡¯s) have wide applications in wavelength tunability and ultra-short pulse generation. In this thesis, optical nonlinearities in InGaAs/AlInAs-based mid-infrared (MIR) QCL¡¯s with quadruple resonant levels are investigated. Design optimization for the second-harmonic generation (SHG) of the device is presented. Performance characteristics associated with the third-order nonlinearities are also analyzed. The design optimization for SHG efficiency is obtained utilizing techniques from supersymmetric quantum mechanics (SUSYQM) with both material-dependent effective mass and band nonparabolicity. Current flow and power output of the structure are analyzed by self-consistently solving rate equations for the carriers and photons. Nonunity pumping efficiency from one period of the QCL to the next is taken into account by including all relevant electron-electron (e-e) and longitudinal (LO) phonon scattering mechanisms between the injector/collector and active regions. Two-photon absorption processes are analyzed for the resonant cascading triple levels designed for enhancing SHG. Both sequential and simultaneous two-photon absorption processes are included in the rate-equation model. The current output characteristics for both the original and optimized structures are analyzed and compared. Stronger resonant tunneling in the optimized structure is manifested by enhanced negative differential resistance. Current-dependent linear optical output power is derived based on the steady-state photon populations in the active region. The second-harmonic (SH) power is derived from the Maxwell equations with the phase mismatch included. Due to stronger coupling between lasing levels, the optimized structure has both higher linear and nonlinear output powers. Phase mismatch effects are significant for both structures leading to a substantial reduction of the linear-to-nonlinear conversion efficiency. The optimized structure can be fabricated through digitally grading the submonolayer alloys by molecular beam epitaxy (MBE). In addition to the second-order nonlinearity, performance characteristics brought by the third-order nonlinearities are also discussed, which include third-harmonic generation (THG) and intensity dependent (Kerr) refractive index. Linear to third-harmonic (TH) conversion efficiency is evaluated based on the phase-mismatched condition. The enhanced self-mode-locking (SML) effect over a typical three-level laser is predicted, which will stimulate further investigations of pulse duration shortening by structures with multiple harmonic levels.

Cations are essential for ribonucleic acids (RNA), as they neutralize the negatively charged phosphate backbone. Divalent metals play important roles in the folding and function of RNA. The relationship between RNA and divalent cations magnesium (Mg(II)) and iron (Fe(II)) has been investigated. Mg(II) is involved in tertiary interactions of many large RNAs, and necessary for ribozyme activity. The influence of Mg(II) on RNA secondary and tertiary structure is investigated experimentally. Mg(II) binding to A-form RNA is accompanied by changes in CD spectra, indicating that Mg-RNA interactions influence the helical structure of RNA duplexes and helical regions of unfolded RNAs. Quantum mechanics calculations are used to probe the energetics of Mg(II)-chelation with phosphate oxygen atoms of nucleic acids. We identify the specific forces that contribute to stability of Mg(II)-chelation complexes in RNA. Fe(II) can serve as a substitute for Mg(II) in RNA folding and function. Fe(II) was abundant on early earth, it is plausible that RNA folding and function was mediated by Fe(II) instead of, or in combination with, Mg(II) in the anoxic environment of early earth. We have investigated oxidoreductase catalytic activity observed in RNA when in combination with Fe(II). This activity, only observed in the presence of Fe(II) and absence of Mg(II)appears to be a resurrection of ancient RNA capabilities that were extinguished upon the depletion of Fe(II) from the environment during the rise of oxygen after the great oxidation event. Finally, metal-ion based cleavage of RNA is used to identify the binding sites of Mg(II) and Fe(II). We observe that both metals cleave RNA in similar positions, providing further support for Fe(II) as a substitute for Mg(II) in RNA.

Theoretical investigation of the dynamics of adiabatic quantum mechanics in two different, highly polar systems has been made. The systems were chosen for their fundamental scientific interest, as they represent atoms and molecules with exaggerated properties, as well as ease of experimental study as such highly polar systems are easier to manipulate using readily-available electric fields. A model two-level system is used to derive one approach for maximizing the probability of adiabatic passage through an avoided crossing and this is compared with the classic Landau-Zener result, and the commonly encountered spin-flip problem of a particle with spin located in a rotating magnetic field. This approach is applied to the avoided crossing between the n = 13, n1 − n2 = 11 (dipole moment of 532 D) and the n = 14, n1 − n2 = −12 (dipole moment of -657 D) highly polar Stark states of the lithium atom at 447 kV/m. Ion-pair formation from two neutral lithium atoms, one in the 2s ground state and the other in an excited state, is also investigated. The cross section σ(v) for free ion-pairs is calculated for the initial colliding pairs of atomic states located below the ion-pair threshold. Li(2s) + Li(3d) is seen to possess the largest cross section (σ(v0) = 569.2 a.u.) at its threshold velocity. The implications of this for bound ion-pair, i.e. heavy Rydberg system, production are briefly discussed. Furthermore, experimental progress towards the production of these atomic and molecular systems from a beam of lithium is presented. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-12-09 16:49:41.184

Ab initio molecular orbital theory has been successful in predicting the stabilities of many weak complexes; typical of these are the complexes formed between water and various small molecules. To account for the correlation effect, Moller-Plesset perturbation theory truncated at the second order level was employed. In order to account for the hydrogen bonding, the 6-3lG** basis set was used. The geometry optimisations of the complexes were carried out using the Gaussian-92 suite of programs installed on a Hewlett-Packard 720 computer operating under UNIX. The interaction energies of the complexes were subjected to further analysis by applying the Morokuma decomposition scheme. The electrostatic interaction component accounts for over 40% of the total stabilisation energy in all the typical hydrogen bonded complexes. Gas phase enthalpies were computed and compared with the experimental values of similar systems. For the systems studied here, the prediction is that all complexes are stable at 25° C. A second program, Vibra, was used for carrying out a normal coordinate analysis. A third computer program for the graphical representation of molecular and crystallographic models, Schakal-92, was employed to illustrate the predicted equilibrium geometries and the fundamental vibrational modes. The predicted geometries, interaction energies, charge redistributions, vibrational wave numbers, infrared intensities and force constants are listed and compared with those in the literature, where applicable. Correlations between the various predicted properties show some interesting chemistry. / Thesis (Ph.D.)-University of Natal, Durban, 1996.

The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Submitted. Paper 5: Submitted. Paper 6: Submitted.</p>

The work presented in this thesis revolves around spectral inequalities and their applications in quantum mechanics. In Paper A, the ground state energy of an atom confined to two dimensions is analyzed in the limit when the charge of the nucleus Z becomes very large. The main result is a two-term asymptotic expansion of the ground state energy in terms of Z. Paper B deals with Hardy inequalities for the kinetic energy of a particle in the presence of an external magnetic field. If the magnetic field has a non-trivial radial component, we show that Hardy’s classical lower bound can be improved by an extra term depending on the magnetic field. In Paper C we study interacting Bose gases and prove Lieb-Thirring type estimates for several types of interaction potentials, such as the hard-sphere interaction in three dimensions, the hard-disk interaction in two dimensions as well as homogeneous potentials. / <p>QC 20140520</p>

Superconducting Quantum Interference Devices (SQUIDs) are currently being used as flux qubits and read-out detectors in a variety of solid-state quantum computer architectures. The main limitation of SQUID qubits is that they have a coherence time of the order of 10 us, due to the presence of intrinsic flux noise that is not yet fully understood. The origin of flux noise is currently believed to be related to spin impurities present in the materials and interfaces that form the device. Here we present a novel numerical method that enables calculations of the flux produced by spin impurities even when they are located quite close to the SQUID wire. We show that the SQUID will be particularly sensitive to spins located at its wire edges, generating flux shifts of up to 4 nano flux quanta, much higher than previous calculations based on the software package FastHenry. This shows that spin impurities in a particular region along the wire's surface play a much more important role in producing flux noise than other spin impurities located elsewhere in the device. / Graduate / 0611 / 0607 / 0753 / laforest@uvic.ca

In Introduction, we review integrable and topological solitons. In Numerical Methods, we describe how to minimize functionals, time-integrate configurations and solve eigenvalue problems. We also present the Simulated Annealing scheme for minimisation in solitonic systems. In Classical Aspects, we analyse the effect of the potential term on the structure of minimal- energy solutions for any topological charge n. The simplest holomorphic baby Skyrme model has no known stable minimal-energy solution for n > 1. The one-vacuum baby Skyrme model possesses non-radially symmetric multi-skyrmions that look like 'skyrmion lattices' formed by skyrmions with n = 2. The two-vacua baby Skyrme model has radially symmetric multi- skyrmions. We implement Simulated Annealing and it works well for higher order terms. We find that the spatial part of the six-derivative term is zero. In Quantum Aspects, we find the first order quantum mass correction for the Ф(^4) kink using the semi-classical expansion. We derive a trace formula which gives the mass correction by using the eigenmodes and values of the soliton and vacuum perturbations. We show that the zero mode is the most important contribution. We compute the mass correction of Ф(^4) kink and Sine-Gordon numerically by solving the eigenvalue equations and substituting into the trace formula.

abstract: The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle. / Dissertation/Thesis / Ph.D. Mathematics 2011