Numerics for many-body physics and single-shot images

Matter at the quantum level behaves not totally deterministically but rather probabilistically. When many particles are trapped and cooled down to almost absolute zero temperatures they clump up together and may form a Bose-Einstein condensate (BEC). A BEC represents the ultimate quantum state where all external noise is switched off and the quantum-mechanical whisper of nature can be heard. Among all the probabilistic quantum states, this collective state of many particles in a BEC is maximally deterministic, reflecting a maximum of coherence and a minimum of correlations. This means that all particles behave alike; knowing the motion of one translates to knowing the motion of the whole. The exciting experiments at the AtomInstitut Wien performed in the labs of J. Schmiedmayer routinely produce Bose-Einstein condensates and aim at the complete control of the probabilistic nature of ultracold atoms. The scientists are directly taking pictures of the ultracold atoms that they produce; these so-called single-shot images are just like regular photos -- they show the positions of all the particles in the produced sample. Due to the quantum nature of the particles in these pictures, their positions are random. So-called quantum correlations and squeezing are quantified by taking many single-shot images and then analyzing the degree of randomness in these pictures. This is the most simple way to obtain the desired inforamtion from the made observations, but this way of analysis necessitates the availability the single-shot images. The research project Numerical models for many-body physics and single-shot images tackles the fundamental issue of how to extract the content of useful inforamtion about the quantum state in the photos that are taken of ultracold particles in state-of-the-art experiments. For this purpose, a sophisticated numerical method, MCTDH-B/F, is developed and applied by Axel Lode, a PhD student, and a PostDoc to model the ultracold clouds as well as the process of taking pictures from them. In order to optimally harness the information from these single-shot images, statistics and machine learning will be employed. The numerical models and analysis tools will be devised by the project team embedded in the Wolfgang Pauli institute (WPI). In the WPI N. Mauser, an expert for the numerical solution of the Schrödinger equation and other applied mathematicians will support the project. The research will be conducted in direct collaboration with the scientists who perform the experiments, J. Schmiedmayer and T. Schumm, who are themselves also members of the WPI.