In recent years, the availability of intense positron beams allowed for an increase in the number of ionization experiments. The first experiments, which studied noble gases, were followed by measurements of the ionization cross sections for other atoms and molecules and for triple differential cross section measurements. Our work uses various theoretical models to reproduce the existing experimental cross sections. For the calculation of the total ionization cross sections of atoms and molecules, we have explored the use of distorted-wave models, containing a realistic description of the final state of the system and including distortion and polarization effects. Recently, we expanded our work to the study of the electron-capture-in-the-continuum (ECC) phenomenon in positron impact ionization of helium and molecular hydrogen. We employed a 3C theoretical model in representing the final state of the ionization system, which allowed us to obtain good agreement with the existing "triple differential cross section" experiments.

My current research is concerned with the development and application of variational (i.e non-perturbative) methods in quantum field theory. I am particularly interested in using the variational method to derive (and solve) relativistic few-body wave equations from the underlying quantum field theory. I investigate model quantum field theories, such as the Yukawa model, as well as QED and various sectors of the standard model. In addition, I am interested in positron interactions with simple molecules and atoms, particularly ionization and annihilation, as well as bounded variational methods in quantum scattering theory.

I have engaged in research into anti-hydrogen atoms with the aim of testing the symmetry of the antimatter and matter worlds, having spent a lot of time at CERN in Geneva in the process. Research has continued through studies of the more conventional helium atom to see if it can provide a platform to precisely evaluate physics theory. I am also interested in the field of curriculum development for undergraduate physics programs, and I particularly like to design modern, relevant and fun experiments for laboratory courses.

My professional research goals centre around the investigation and solution of mathematical and computational problems of scientific and engineering relevance. During the last few years, I have worked on a variety of highly applied and very challenging problems in electromagnetics, hydrodynamics, and combinations of both. For example, I have researched wire antenna problems, numerical methods for optical gratings, enhanced radar backscatter from the ocean surface, hydrodynamic stability problems, blood flow in compressed vessels, and the hydrodynamics of expanding universes. Certainly, computational science lies at the core of my research interests.

The main goal of computational electromagnetics, for example, is the design and implementation of numerical methods that can be used to efficiently simulate electromagnetic wave interactions with complex material structures. This field has shown an impressive growth in recent years, as improved numerical algorithms enable accurate simulation of the ever more complex phenomena arising in an ever growing number of applications. The numerical methods used in this area draw from the classical approaches, such as the method of moments and finite-element based algorithms into the efficient high-order/accelerated algorithms that have arisen over the last two decades. Applications are found in communications (transmission through optical fiber or wireless communication), remote sensing and surveillance (radar and sonar systems), geophysical prospecting, materials science, and biomedical imaging (optical coherence tomography), to name but a few.

Significant challenges arise in the design of reliable numerical algorithms for engineering and industrial applications such as those mentioned above. These challenges are largely due to the necessity of numerical methods to resolve wave oscillations and interactions of these with geometrically and/or compositionally complex structures, which lead to very high (often prohibitive) computational costs for many problems of interest. The focus of my work has been and will continue to be the development and implementation of efficient, fast and accurate numerical algorithms to enable treatment of challenging engineering and scientific applications.

I employ lasers to make high-precision measurements of atomic properties to test the predictions of Quantum Electrodynamics and the Standard Model of particle physics. Currently, I am studying atomic hydrogen to make a new measurement of the radius of the proton to try to understand the deviant value recently obtained from muonic hydrogen. If the discrepancy is real, it may herald the discovery of a new boson or even gravity in higher dimensions. Also, I am part of a collaboration whose goal is to hold antihydrogen atoms (antimatter versions of the element hydrogen) in a magnetic trap and use them to conduct precise spectroscopic tests of the symmetries and physics of antimatter. Additionally, I am involved in measuring the energies and orbits of helium atoms to provide the most accurate measurement of the "fine structure constant,” the fundamental constant of nature that determines the strength of the electric and magnetic forces between charged objects. The fine structure constant is not only relevant to magnets and electricity, but to how atoms, chemicals, and solid objects are held together.

I study interactions of atoms and simple molecules in collisions with ions or in exposure to strong laser fields by theoretical and computational methods. My particular interests are in the areas of multiple ionization and capture of electrons in collisions of highly charged ions. Also, I am interested in quantum optics, especially in measurements of the radius of the proton and the line shape problem for high-precision spectroscopy, as well as the problem of electron-positron pair creation in ultra-strong fields. My emphasis is on developing new computational methods and testing time-dependent density functional theory.

My research is concerned with the question of how atomic and molecular few-body systems respond to perturbations exerted on them by impinging particles and external fields. Quantum dynamics induced by collisions or laser fields have implications for a variety of topics and applications ranging from plasma diagnostics to radiation biology. What is more, they constitute a problem of fundamental importance: How do the building blocks of matter interact and evolve in space and time? The better this question is answered, the more is learned about a further issue that receives considerable attention: Can few-body quantum dynamics be manipulated purposefully and controlled actively?

I have participated in a number of projects and activities to elucidate these topics by theoretical analysis and computations. Methods based on density functional theory deal with the many-electron problem, and both nonperturbative and perturbative quantum methods describe the dynamics of the systems. Currently, we are working on a method to describe ionization and fragmentation of multi-center molecules. First applications are concerned with ion-induced fragmentation of water, which is a relevant process in the radiation damage of biological tissue. In the long run we hope to study even more complex systems, thereby exploring the transition from correlated to collective dynamics. Our central goal is to contribute to a microscopic understanding of time-resolved quantum dynamics, and to investigate applicability and limitations of density functional theory by practical calculations.

My research involves studies of coherent transient phenomena in atomic samples such as laser-cooled atoms. Some of this work involves precision measurements using atom interferometry. Applications of this work are related to the development of portable instrumentation. As examples, my students and I have engaged in precision measurements of the atomic recoil frequency, atom interferometric measurements of gravitational acceleration, precise measurements of atomic g factor ratios, numerical simulations of matter wave interference, studies of superfluorescence, measurements of atomic lifetimes and natural line widths, and the development of auto-locked single mode lasers.

My work is in theoretical atomic physics. I am particularly interested in electron and positron scattering, both elastic and inelastic, and I endeavour to calculate cross sections for a wide range of targets. Such cross sections are essential to understanding how matter behaves in a wide range of environments, be they natural (e.g., the Earth’s atmosphere, or astrophysical plasmas) or constructs of humans (e.g., fission or fusion reactors).

I carry out theoretical research on the scattering of electrons and positrons from atoms and simple molecules. I am particularly interested in scattering from heavy atoms, and use the relativistic Dirac equations as the basis for computation of scattering parameters. Collaborating with graduate students and international co-workers, we perform large scale numerical computations of these processes and develop theoretical and numerical methods to carry them out. For example, we have developed the very successful Relativistic Distorted-Wave Method for evaluating the scattering cross sections as well as the spin polarization parameters for the scattered electrons and the Stokes parameters for the light emitted from atoms excited during the scattering interactions. I am also involved in projects which make use of the atomic data we generate. Much of our work is of use in plasma physics, particularly in the modeling of low pressure plasmas. One example is a large-scale Monte Carlo simulation of gas-filled X-ray detectors. I maintain close contact with various experimental groups and often publish joint papers with these groups where theory and experiment can be directly compared.

I conduct antimatter research with the aim of producing and trapping large numbers of antihydrogen atoms. Comparing the atomic structure of antihydrogen and hydrogen provides a direct comparison between matter and antimatter atoms and a strong test of fundamental symmetries in nature. I am also comparing measurements of positronium, an electron bound to an antielectron, to test the predictions of quantum electrodynamics theory.

My research interests include a variety of topics in pure and applied physics, such as laser isotope separation, laser cooling, atom trapping, environmental pollutant monitoring, and electromagnetically-induced transparency for use in optical switching. My group has developed a novel way to use acousto/electro-optic modulators to precisely measure frequency shifts. This has been exploited to measure hyperfine splittings, Stark shifts, and polarizabilities of atoms and thereby precisely test predictions of quantum electrodynamics.  We were the first in Canada to create a Bose-Einstein condensate in the lab. Work is progressing to study so-called optical lattices of condensates.  An array of microtraps to be fabricated using lithography is also being designed. It is of interest for exploring and controlling the interactions between ultracold atoms, such as the transition between a superfluid and a Mott insulator state, and for developing schemes to implement quantum computing.