Generation and Dynamics of Complex Hamiltonians in Coupled Cavity Systems

Quantum systems are much more complex than classical ones. Therefore, they offer on the one hand the possibility to perform computations that classical computers cannot do. On the other hand, if they are large and composed of many particles, their description requires more data than a classical computer can handle. The investigation of large quantum many particle systems is thus very difficult as it is in general not possible to simulate a quantum many body system on a classical computer. To overcome this problem, scientists had to employ a different approach which makes use of the fact that the same physical mechanisms can inNature appear in various contexts. Hence one can use a system which can be well controlled and tuned in the laboratory to mimic other systems which are much more difficult to study. Those well controllable and tunablesystems are called quantum simulators . Due to their high precisioncontrollability and tuneability, quantum simulators are also suitable for creating entanglement, which is a key resource for quantum informationprocessing. If two or more particles are entangled, they share properties which cannot be attributed to one individual particle. These purely quantumcorrelations are responsible for the new possibilities quantum information processing offers compared to its classical counterpart. Several interesting candidates for a quantum simulator respectively entanglement production device have been studied in recent years. A very successful one is a lattice formed by standing waves of light with very cold atoms trapped in it. So far a very high degree of control and tunability has been achieved for global properties, but it still is very difficult to control and measure the individual constituent particles. In the proposed project we will investigate a new way to implement quantum simulators and create entanglement which would allow forexperimental access to properties of individual particles. Our approach makes use of arrays of micro-cavities, very small devices that can trap light for a long time. Atoms are trapped at each micro-cavity and interact with the light stored in it. The experimental realisation of such arrays of micro-cavities has seen some tremendous progress recently and the first arrays mounted on devices to trap the atoms in their vicinity have been realised. Within the proposed project, we will investigate thepossibilities for creation of various types of entangled states andeffective many particle systems in these newly built structures.