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研究对象。它们在超流体液氦、超导体和液晶中以漩涡的形式出现。它们在基本粒子物理学中以弦和单极子的形式出现。在早期宇宙的理论中，宇宙弦在不同真空区域之间的畴壁上结束，预计随着宇宙冷却而出现。在过去的十年中，已经有可能创造出玻色-爱因斯坦凝聚体，其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具有重要的数学相似性。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玻色-爱因斯坦凝聚体中所谓的拓扑缺陷的物理学，这些缺陷在今天的实验技术下是高度可控和可观察的。我们的考虑延续到最近在实验中创造的一种新型量子气体：玻色-爱因斯坦凝聚体的短寿命光-物质混合粒子。缺陷的结构和稳定性受原子自旋的大小以及原子相互作用和外部施加场的性质的影响。有可能创造出携带超过一个单位自旋的原子凝聚物。这导致可能的缺陷配置范围急剧扩大-包括非常有趣的非阿贝尔涡旋-其结构和稳定性我们将确定，以预测实验观察到的状态。当考虑到远距离相互作用时，在具有一个单位自旋的原子中，这种效应可能已经很明显了。人工创造的自旋和空间运动相结合的标准场有可能稳定并观察到原本不稳定的结构。我们的研究将使用并扩展经典的Gross-Pitaevskii模型来解释这些影响并预测实验观察到的状态。例如，将旋量凝聚体放置在由激光束形成的光学晶格中，可以增强量子涨落的作用，这样就可以在宏观尺度上观察到量子力学效应。在这项研究中，我们将发展描述这种强波动状态下旋量凝聚的理论，并描述可观察到的量子效应，如涡旋的动力不稳定性。类似的理论发展可以用来描述激子-极化子气体中的冷凝跃迁，激子-极化子是存在于夹在镜子之间的半导体结构中的短暂的光-物质混合“准粒子”。短的寿命意味着必须不断地补充气体，并且冷凝物存在于泵送和衰变之间的动态平衡中，而不是热平衡中。光子分量的偏振导致有效自旋为1/2。我们将与实验密切合作，在专门研究冷凝过程的新颖实验中预测自旋结构和泵浦动力中产生的拓扑缺陷。我们的研究将强调量子气体如何为场论缺陷和纹理的稳定性提供新的介质，并具有在实验室中研究宇宙现象类似物的有趣前景。这项研究将在南安普顿大学进行，该大学在量子气体方面拥有相当多的专业知识，并在激子-极化子凝聚体方面进行了领先的实验和理论研究。与实验密切合作是研究的重要组成部分。这项研究将广泛使用iris超级计算设备。

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.