Correlated Phases in Novel Superconductors and Ultracold Atomic Gases

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The treatment of electrons as non-interacting and wave-like has yielded an amazingly successful quantum description of materials like metals and semiconductors, which form the basis of the electronics that we take for granted today. The success of this picture is all the more remarkable when one considers the size of the Coulomb interaction between the negatively-charged electrons - one only has to experience static electricity in order to appreciate the measurable effects that a small imbalance of charge can have. Thus, it is perhaps no surprise that physicists are increasingly discovering strongly-correlated systems where simple, non-interacting theories are no longer valid. A prime example is the superconductor, in which electrons form pairs at low temperatures and then flow without any resistance. Indeed, an electrical current in a superconductor can, in principle, flow forever. While this pairing phenomenon is well understood in many superconducting materials, new classes of superconductors have emerged in recent decades that are generally associated with magnetism and which superconduct at much higher temperatures than predicted by conventional theory. Clearly, developing a proper understanding of these strongly-correlated materials is more than just an esoteric pursuit: the possibility of lossless electrical current at room temperature would have a major impact on energy efficiency. The formidable challenge for the theorist is to develop fresh concepts that go beyond the current weakly-interacting descriptions. One small step in this direction is to first tackle simple versions of strongly-correlated phenomena. Fortunately, physicists now have the technological capacity to manipulate and control cold gases of atoms that have been trapped by light and magnetic fields, and thus these systems provide the ideal environment in which to study simple models. Already, I have been heavily involved in developing theories of strongly-interacting atomic superfluids , which can be regarded as neutral analogues of superconductors. The ultimate advantage of these systems is the ability to address each variable, e.g. interaction strength, one at a time and thus isolate the basic physics underlying strongly-correlated phenomena. Ideally one needs a programme of interdisciplinary theoretical research that considers unconventional superconductors in parallel with models of atomic gases, and this is the nature of the proposed research. As well as exploring model systems of superfluidity and magnetism in cold atomic gases, I aim to investigate the iron-based superconductor, a newly-discovered class of high-temperature superconductor that promises to shed light on other novel superconductors. The key idea is that the study of simple engineered atomic systems can lend insight into the iron-based superconductors, while the puzzles of unconventional superconductors can direct my research on correlated phenomena in atomic gases. This, together with input from the experiments in each highly active field, would hopefully bring us closer to a more complete understanding of interacting systems.