Quantum theory and applications

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Quantum mechanics governs essentially all phenomena at microscopic scales and below. I intend to examine several problems in quantum mechanics and its more sophisticated relative, quantum field theory. Four independent projects are included: 1. Decoherence of small quantum systems. The so-called second quantum revolution is unfolding at a rapid pace, giving rise to promising technologies such as quantum communication, computing and cryptology. All of these quantum technologies rely on quantum properties of small systems (entanglement in particular) which are fragile due to interactions between the system and its environment, causing decoherence, a measure of the degradation of ``quantumness". In one project, we are studying decoherence of a qubit attached to a system which might have ``edge states", which are of great theoretical interest. We find that the decoherence of the qubit depends dramatically on the presence of an edge state, so by measuring the decoherence rate one can infer the presence or absence of an edge state. In a second project, we are studying decoherence in states slightly bigger than a qubit (three-state systems, etc), to determine ways to connect the system to its environment which prolong coherence. 2. Lepton number violating processes and CP violation. We are studying (from a theoretical point of view) processes which could take place at large accelerators such as the Large Hadron Collider which combine two interesting yet very rare properties: lepton number violation and CP violation. (Indeed, the first has never been observed, but it is theoretically possible in some promising particle physics models.) 3. Particle trajectory simulation in soft tissue in the presence of magnetic fields. One of the main techniques used in cancer treatment is radiotherapy, bombardment of cancerous tissue with charged particles such as electrons. In order to destroy cancerous tissue while minimizing damage to healthy tissue, it is important to determine dose deposition. Well-developed algorithms permit accurate determination of the path and energy deposition of charged particles in soft tissue. A new technique of imaging radiotherapy involves magnetic resonance imaging. The magnetic fields used in this technique affect particle trajectories and current algorithms are not accurate; we are developing new algorithms that take into account magnetic fields, the goal being to attain accuracies comparable to standard algorithms in the absence of magnetic fields. 4. Gravitation, quantum mechanics and entanglement. Combining quantum mechanics and gravitation is one of the major challenges of theoretical physics. We are studying a much more modest problem: the (classical) gravitational field created by systems which have quantum properties such as quantum superposition and entanglement, which was mentioned above.