Modelling Condensed Matter Systems with Quantum Gases in Optical Cavities

量子模拟器是实验上非常容易接近的系统，其行为类似于复杂的量子系统，否则无法轻松研究。因此，它们有望为凝聚态系统提供新的见解，并可能成为量子计算机的第一个应用。目前对量子模拟器的研究主要集中在生成所谓的无阻挫哈密顿量的基态。在这里，我们计划更进一步。我们的目标是设计和建立一个量子模拟器，研究更复杂的凝聚态系统的行为，即具有强耦合以及高度非局部相互作用和非零耗散的系统。这样的系统可以通过将玻色爱因斯坦凝聚体（BEC）与光学腔相结合的实验来实现。我们计划建立这样一个实验，并在理论上尽可能精确地建立模型。计划中的研究利用了我们在腔QED，非线性动力学，冷原子，量子光学和多体系统方面的共同专长。

Quantum simulators are experimentally very accessible systems whose behaviour resembles that of a complex quantum system which cannot be studied as easily otherwise. They are hence expected to provide new insight into condensed matter systems and may become the first application of quantum computers. Current research on quantum simulators focusses mainly on the generation of the ground states of so-called frustration free Hamiltonians. Here we plan to go a step further. Our aim is to design and to build a quantum simulator which studies the behaviour of even more complex condensed matter systems, i.e. of systems with strong couplings as well as highly non-local interactions and with non-zero dissipation. Such a system can be realised by an experiment which combines a Bose Einstein condensate (BEC) with an optical cavity. We plan to set up such an experiment and to model it theoretically as precisely as possible. The planned research draws on our common expertise in cavity-QED, non-linear dynamics, cold atoms, quantum optics, and many-body systems.