The Einstein field equations lie at the heart of gravitational physics. Unfortunately, these equations are difficult to solve. Only a few analytic solutions have been found in the century since the equations were first introduced. Luckily, the rapid development of computing in the last 50 years has opened the door to a wide range of problems. Using advanced algorithms and high-powered supercomputers, the Einstein field equations can be solved numerically for strong-field, high-energy systems. This is the bread and butter of our research.
Solitons are localized waves that propagate with a constant shape and a constant speed. They are found in many areas of physics and generally behave like a moving particle or a "ball of matter". In field theory and cosmology, Q-balls are a type of soliton that carry a conserved charge Q. They arise in supersymmetric extensions of the Standard Model and in some cosmological models for baryogenesis (the origin of matter in the early universe). They have also been proposed as candidates for the dark matter content of the universe.
Mathematically, Q-balls are solitonic solutions of a complex scalar field theory with a non-linear attractive potential. Although their basic stability and existence properties are well-known, the high-energy scattering of Q-balls is a difficult problem due to the complicated nature of the equations. Advanced numerical methods must be used to study these scattering scenarios in detail.
I am presently interested in the relativistic scattering of Q-balls in flat spacetime: head-on collisions, collisions with stationary obstructions and scattering with non-zero impact parameter. I'm also interested in Q-ball dynamics when coupled to the electromagnetic field.
The theory of special relativity tells us that an object can never travel faster than the speed of light. Although this "universal speed limit" holds true in flat space, it has been proposed that distortions in spacetime could permit apparent faster-than-light travel. Within the context of general relativity, the Alcubierre metric (AM) provides a mathematical description of a spacetime that would allow an object to traverse a vast distance in an arbitrarily small time period. To an observer at rest in flat space, it looks as if the object has a speed V > c. This idea is reminiscent of the "warp drive" of science fiction and has led to the AM being coined the "Alcubierre warp drive".
Our research investigates the propagation of electromagnetic waves in the AM. The wave equation for the AM is difficult to solve analytically. As a consequence, most studies of null geodesics (light ray trajectories) have been limited to numerical methods or ray-tracing techniques. We find an analytic method for describing how an arbitrary wave packet will transform as it propagates in this spacetime.
In recent years, laser cooling and trapping techniques have progressed to the point where atoms and molecules can be cooled to near-zero temperatures. At extremely low temperatures, these atoms and molecules can exhibit some unique quantum effects. One of the main ways of gathering data from these systems is through optical imaging. In general, these imaging systems need to achieve high-resolutions in order to resolve features that are typically on the order of micrometers.
In this project, I was responsible for designing, assembling and characterizing a high-performance imaging system that is capable of imaging with a spatial resolution of 1-2 micrometers. This apparatus will be used in experiments with ultra-cold lithium and rubidium at UBC's QDG Lab.
Raman scattering is a useful process for identifying and investigating organic molecules. The prospect of combining surface-enhanced Raman scattering with in-line digital holography is appealing because it could have a wide range of medical and biophysical applications. In particular, this new molecular imaging method, called 'holographic Raman imaging', would serve as a powerful microscopy technique that could act as an alternative to CT scans and MRIs.
In this project, we provided theoretical support for an experiment performed at Dr. Kevin Hewitt's research lab at Dalhousie University. I developed a Mathematica program that uses coherence functions to achieve holographic reconstructions of molecular interference patterns.