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.
"The importance of nonlinear/chaotic dynamics in BEC-cavity interactions was identified. Experiments have demonstrated regimes where e.g. light emission from the cavity varies randomly. This randomness was originally assumed to arise from e.g. detector noise. We have demonstrated that this apparent randomness is a feature of the interaction between light and BECs, and is an example of nonlinear , chaotic behaviour, which appears predictable for small times, but unpredictable for long times. Randomness due to e.g. detectors is not necessary.
We discovered that interaction of a cold atomic gas or ultracold Bose-Einstein Condensate (BEC) with many transverse modes of an optical field can give rise to self-structuring of the optical intensity and atomic density, leading to complex spatial patterns e.g. hexagons honeycombs etc. We developed the theory of this self-structuring instability for both cold atoms and BEC and demonstrated good agreement with experiments."