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

拓扑缺陷是物理学中几个不同领域的重要对象。它们以涡旋的形式出现在超流液氦、超导体和液晶中。它们在基本粒子物理学中以弦和单极的形式出现。在早期宇宙理论中，在不同真空区之间的磁区墙上终止的宇宙弦预计会随着宇宙的冷却而出现。在过去的十年里，人们已经有可能创造出玻色-爱因斯坦凝聚，在这种凝聚中，原子保持其量子力学自旋。这导致了更广泛的拓扑缺陷，其中由原子自旋形成的结构起着至关重要的作用。特别是，这种自旋玻色-爱因斯坦凝聚体中的拓扑缺陷与宇宙学和基本粒子物理学中的宇宙弦和其他拓扑缺陷有重要的数学类比。我们的研究将使用广泛的计算机模拟来研究如何利用最近的实验进展来研究所谓的玻色-爱因斯坦凝聚体中的拓扑缺陷的物理，这种凝聚体在当今的实验技术下是高度可控和可观察的。我们的考虑延续到了最近在实验中创造的一种新型量子气体：由短寿命轻物质杂化粒子组成的玻色-爱因斯坦凝聚体。缺陷的结构和稳定性受到原子自旋的大小以及原子相互作用和外场的性质的影响。有可能产生携带不止一个自旋单位的原子凝聚体。这导致可能的缺陷构型的范围大大扩大--包括非常有趣的非阿贝尔涡--我们将确定其结构和稳定性，以便预测实验上可观察到的状态。当考虑到长程相互作用时，这种影响可能已经在具有一个自旋单位的原子中显现出来了。人工创建的将自转和空间运动结合在一起的规范场有可能稳定下来，并使原本不稳定的结构变得可见。我们的研究将使用并扩展经典的Gross-Pitaevskii模型来解释这些效应并预测实验上可观察到的状态。例如，将旋量凝聚体放置在由激光创建的光学晶格中，可以增强量子涨落的作用，使得量子力学效应可以在宏观尺度上观察到。在这项研究中，我们将发展描述强起伏区域中旋量凝聚的理论，并描述可观察到的量子效应，如涡旋的动力学不稳定性。类似的理论发展可用于描述激子-极化子气体中的凝聚转变，激子-极化子是存在于夹在镜面之间的半导体结构中的短暂的光-物质混合“准粒子”。短暂的寿命意味着天然气必须不断补充，凝析油处于泵送和衰减之间的动态平衡，而不是热平衡。光子成分的偏振导致有效自旋为1/2。我们将与实验密切合作，在专门研究凝聚过程的新实验中预测自旋结构和抽运动力学中出现的拓扑缺陷。我们的研究将突出量子气体如何为场论缺陷和织构的稳定性提供新的介质，在实验室研究宇宙现象的类似物具有有趣的前景。这项研究将在南安普顿大学进行，该大学拥有相当多的量子气体专业知识，并将在激子-极化凝聚体方面进行领先的实验和理论研究。与实验的密切合作构成了这项研究的组成部分。这项研究将广泛利用IRIDIS的超级计算能力。

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.