Topological Defect Structures and Quantum Effects in Spinor Bose-Einstein Condensates

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Topological defects are important objects in several different areas of physics. They appear as vortices in superfluid liquid helium, in superconductors and in liquid crystals. They appear in elementary-particle physics as strings and monopoles. In theories of the early universe, cosmic strings that end on domain walls between regions of different vacua are predicted to arise as the universe cools.In the last decade it has become possible to create Bose-Einstein condensates where the atoms retain their quantum-mechanical spin. This leads to a wider range of topological defects, where structures formed by the spins of the atoms play a crucial role. In particular, the topological defects in such spinor Bose-Einstein condensates have important mathematical analogies with cosmic strings and other topological defects in cosmology and elementary-particle physics. Our research will use extensive computer simulations to investigate how recent experimental advances can be employed to study the physics of so-called topological defects in Bose-Einstein condensates, which are highly controllable and observable with today's experimental technology. Our considerations carry over to a novel type of quantum gas that has recently been created in experiments: Bose-Einstein condensates of short-lived light-matter hybrid particles.The structure and stability of the defects are influenced by the magnitude of the atomic spin as well as by the nature of the atomic interactions and externally imposed fields. It is possible to create condensates of atoms that carry more than one unit of spin. This results in a drastically enlarged range of possible defect configurations - including highly intriguing non-Abelian vortices - whose structure and stability we will determine, in order to predict experimentally observable states. When long-range interactions are taken into account, the effects may be pronounced already in atoms with one unit of spin. Artificially created gauge-fields that couple spin and spatial motion have the potential to stabilise and make observable otherwise unstable structures. Our research will use and expand the classic Gross-Pitaevskii model to account for these effects and predict experimentally observable states.Placing the spinor condensate, for example, in an optical lattice created with laser beams enhances the role of quantum fluctuations, such that quantum-mechanical effects can become observable on a macroscopic scale. In this research we will develop theory for describing the spinor condensate in this strongly fluctuating regime and describe observable quantum effects, such as dynamical instabilities of vortices.A similar theoretical development can be used to describe the condensation transition in gases of exciton-polaritons, which are short-lived light-matter hybrid "quasiparticles" that exist in semiconductor structure sandwiched between mirrors. The short lifetime means that the gas must be constantly replenished, and the condensate exists in a dynamic balance between pumping and decay, rather than in thermal equilibrium. The polarisation of the photon component leads to an effective spin of 1/2. We will collaborate closely with experiment to predict spin structures and topological defects arising in the pumping dynamics in novel experiments specifically designed to study the condensation process.Our research will highlight how quantum gases provide novel media for the stability properties of field-theoretical defects and textures, with the intriguing prospect of studying analogues of cosmological phenomena in the laboratory.The research will be conducted at the University of Southampton, host to considerable expertise in quantum gases, and to leading experimental and theoretical research in exciton-polariton condensates. Close collaboration with experiment forms an integral part of the research. The research will make extensive use of the IRIDIS supercomputing facillity.