Quantum Simulations with Quantum Optical Systems

建造量子计算机是一项非常有益的任务。这样的计算机将帮助我们进行某些计算，这些计算是现在或未来的经典计算机无法完成的。中性原子被限制在光学晶格中，由激光操纵，为我们提供了实现量子计算机或进行量子模拟的最有前途的途径之一。然而，要执行有用的量子计算（例如因式分解），需要大约100,000个量子比特，而有趣的量子模拟需要的量子比特数量要少得多，并且在计划的实验设置范围内。该项目的主要目标是从理论上研究模拟量子系统的新途径，以克服迄今为止存在的数值方法。这一目标与物理学的其他分支相关，比如凝聚态物理学，因为它将使我们能够理解迄今为止无法通过理论描述或数值模拟的某些材料的物理性质。一方面，我们将研究如何在光学晶格和其他量子光学系统中使用原子来构建量子模拟器。另一方面，我们将开发数值算法来模拟使用（经典）计算机的多体量子系统。我们还将把这些算法应用于各种量子光学实验装置的研究。除此之外，我们将从量子信息论的角度分析量子多体系统。特别是，我们将研究它们的纠缠特性，以获得这些系统所表现出的有趣现象（例如，量子相变）的新视角。我们还将开发理论工具来识别、分类和量化当前实验中的纠缠。

Building a quantum computer is a very rewarding task. Such computers would help us to perform certain computations which are not possible with present or future classical computers. Neutral atoms confined in optical lattices and manipulated by lasers provide us with one of the most promising avenues to implement a quantum computer or to perform quantum simulations. Whereas to perform a useful quantum computation (e.g. for factorization) one needs approximately 100.000 qubits, interesting quantum simulations require a much smaller number of qubits and are within reach of planned experimental setups.The main goal of this project is to theoretically study new routes towards simulating quantum systems which overcome the numerical methods that exist so far. This goal is relevant for other branches of physics, like condensed matter physics, since it would allow us to understand physical properties of certain materials that so far have eluded a theoretical description or numerical simulations. We will, on the one hand, study how to use atoms in optical lattices and other quantum optical systems to build quantum simulators. On the other hand, we will develop numerical algorithms to simulate many-body quantum systems using (classical) computers. We will also apply those algorithms to the study of various quantum optical experimental setups. Apart from that, we will analyze quantum many-body system from the perspective of Quantum Information Theory. In particular, we will study their entanglement properties in order to obtain a new perspective on interesting phenomena (e.g., quantum phase transitions) exhibited by those systems. We will also develop theoretical tools to identify, classify and quantify entanglement in current experiments.