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.

-- > Introduction The FWF-funded Standalone Grant P32033-N32 "Numerics for Many-Body Physics and Single-Shot Images" has successfully concluded, delivering pioneering advancements in the study of ultracold atoms. This project focused on enhancing our understanding of quantum many-body systems-collections of atoms interacting at extremely low temperatures-and their physical properties seen in observations, so-called single-shot images. -- > Achievements One of the standout accomplishments of this initiative was developing new methods to better understand quantum correlations. These are the intricate relationships between particles that often defy classical physics explanations and that are observable in systems like ultracold atoms. The project's findings are in exceptional agreement with state-of-the-art experiments, shedding light on the dynamics and structures of these correlations. -- > Technological Advancements Central to this project was the creation of advanced tools like UNIQORN and MCTDH-X, software packages designed to simulate and decode complex data from quantum many-body systems across one, two, and three spatial dimensions. UNIQORN, detailed in a Letter published in Physical Review A ( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.L041301 ), and MCTDH-X, featured in Quantum Science and Technology ( https://iopscience.iop.org/article/10.1088/2058-9565/ab788b ) have both been instrumental in advancing our capabilities to analyze quantum dynamics. These tools are freely available, can describe state-of-the-art experiments ( https://journals.aps.org/prx/abstract/10.1103/PhysRevX.9.011052 ) and do foster an ongoing dialogue and development within the scientific community. A Review placing and relating the methodological achievements with MCTDH-X in relation to the wider field of quantum many-body systems and other available methods was published in the reputable Reviews of Modern Physics ( https://doi.org/10.1103/RevModPhys.92.011001 ). -- > Community Impact and Recognition Contributions to high-impact journals and the ongoing use of our open-source software underscore the significant scientific and practical impacts of P32033-N32. The enthusiastic uptake and development of UNIQORN and MCTDH-X by researchers globally highlight the project's success in enriching the scientific toolbox for studying quantum phenomena. -- > Conclusion This project not only elevates the scientific understanding of many-body systems and quantum correlations but also solidifies the FWF's role in supporting cutting-edge research. The insights and tools developed are guiding current and future research, bridging fundamental theory with practical applications. -- > Future Outlook As we move forward, the methodologies and software established through this project ( http://ultracold.org ) are set to unlock new possibilities in quantum physics research, promising exciting advancements and further enrichments of our understanding of the quantum world with applications in quantum information processing and storage, quantum sensing, and many other fields.