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.
