Unconventional Atomic/Molecular Topological States

最近在超冷原子/分子气体和非常规光学晶格方面的实验进展使我们能够将我们对量子世界的探索推向一个新的极限，在这个极限中，量子多粒子系统可以被非常精确地控制和测量。在现代量子物理学中，一个关键的发展是量子系统的几何/拓扑解释，拓扑场论和物质拓扑态的概念由此发展。本研究的主要目的是通过实现，表征和理解超冷原子气体中的拓扑非平凡量子态来提高我们对物质量子拓扑态的认识。这些研究所揭示的物理学原理对固体物理、量子信息和量子计算等其他科学研究领域具有重要意义。此外，该研究计划还包含教育部分，旨在提高人们对新量子态研究的认识，并为公众，特别是下一代，提供有关量子计算未来发展的新知识。该实验室为量子多体系统及其拓扑性质的研究提供了一个理想的平台，该实验室利用量子场论和精确数值方法等现代理论技术进行理论和数值研究。通过确定最适合在原子系统中实现的拓扑状态，该研究将为实验研究提供直接指导。此外，原子气体的独特性质将使我们能够稳定和研究新的拓扑状态，这在其他系统中从未实现过。通过研究这些非传统的拓扑状态，新的物理原理可以出现，并将被研究。

Recent experimental progress in ultra-cold atomic/molecular gases and unconventional optical lattices has allowed us to push our exploration of the quantum world to a new limit, where a quantum many-particle system can be controlled and measured with exceptional precision. In modern quantum physics, one key development is the geometric/topological interpretation of quantum systems, from which topological field theory and the concept of topological states of matter are developed. The main objective of this investigation is to improve our knowledge on quantum topological states of matter by realizing, characterizing and understanding topologically-nontrivial quantum states in ultra-cold atomic gases. The physics principles revealed in this investigation may shed new light on other branches of scientific research including solid state physics, quantum information and quantum computation. In addition, the research plan contains an education component, which promotes awareness towards the research on novel quantum states and provides the general public, especially the next generation, novel knowledge on the future development of quantum computation. This setup offers an ideal platform for the investigation of quantum many-body systems and their topological properties.The investigation contains a combined effort of theoretical and numerical studies utilizing modern theoretical techniques such as quantum field theory and exact numerical methods. By identifying topological states that are most suitable for realization in atomic systems, the study will provide direct guidance for experimental investigations. In addition, the unique properties of atomic gases will allow us to stabilize and to study novel topological states, which have never been realized in other systems. By studying these unconventional topological states, new principles of physics can emerge and will be studied.