Control strategies for quantum fields

Some of the most intriguing problems in physics, ranging from the early universe to quantum materials, are linked to the dynamics of large ensembles of interacting particles exhibiting genuine quantum behavior. These quantum many-body problems and their description in terms of quantum field theory are often hard or impossible to simulate in their full complexity on even the fastest classical computers. To circumvent this problem, so-called quantum simulators became a very active field of research over the last decade. Similar to analog computers, quantum simulation aims at building highly configurable experiments to reproduce the desired physics behind quantum many-body systems with these model systems. One central aspect when utilizing such model systems as quantum simulators is how to control the model system to perform the desired simulation, i.e., how to prepare the initial states and how to mirror the desired simulation target with the experimentally available model. Thereby, trapped clouds of ultra-cold atoms are ideal model systems that are flexible and sufficiently mature to be routinely generated in labs around the world. The key motivation of this project is to develop control algorithms that enable such operations with sufficient precision for ultra-cold atom experiments. As such we aim at developing tools for two distinct physical situations: First, to control the quantum fields in small thermal machines that can be generated by splitting the atom cloud into several compartments. Such experiments would help to investigate thermodynamic properties of many-body systems in the quantum regime. At the heart of this newly developing field of quantum thermodynamics lies the question on whether or how excitations of an isolated quantum many-body system relax such as classical many-body systems eventually do. These questions ultimately continue the long-standing discussion on the relation between the microscopic and the macroscopic world. Second, we aim at exploring and developing algorithms to optimize the splitting of a single atomic cloud into two. Describing this splitting process in full detail is beyond computational capabilities. Thus, pre-calculated protocols to achieve splitting of the cloud typically yield unsatisfying results. However, we conjecture that the combination of existing simplified models and measurement information is sufficient to iteratively learn and refine control trajectories. This would allow us to prepare desired quantum states of the split cloud that are essential for many quantum field and quantum metrology experiments.

Laser light and magnetic fields can be used to trap clouds of atoms at extremely low temperatures, only a tiny fraction of a degree above absolute zero. In this state, the atoms behave as a single quantum object and can serve as a highly flexible model system for studying complex quantum phenomena that are otherwise far too difficult to calculate on a computer. The aim of this project was to develop new methods for steering such ultracold atom clouds quickly and precisely enough that they can be used as reliable quantum simulators. A central result of the project was the development of learning-based control methods that shape the optical potentials confining the atoms. In simple terms, we taught the experiment how to create tailored "landscapes" of light that can divide the atom cloud into separate compartments or guide it into a desired form. This makes it possible to prepare the starting conditions for quantum experiments much faster and more reliably than before. We also advanced mathematical methods to control realistic models of elongated atom clouds. These tools improve our ability to predict and direct the motion of the atoms under experimental conditions. Building on this foundation, we developed and experimentally validated methods to split a single Bose-Einstein condensate coherently into two parts at almost the fastest possible speed, while keeping the cloud close to its quietest and coldest state. In this way, the splitting acts like a beam splitter for quantum gases: it divides the cloud without strongly disturbing its fragile quantum properties. This fast yet gentle splitting is an important step toward preparing special entangled quantum states that are beneficial for future quantum technologies. Experiments showed that such split systems can exhibit strongly correlated behavior, which is promising for quantum simulation and for measurement methods that go beyond current limits of precision. In the future, the mathematical control toolbox developed in this project can help researchers study how energy and heat flow in small quantum systems, for example in model quantum thermal machines built from several coupled atom clouds. To make these methods accessible to other researchers, we also made important parts of the toolbox openly available on GitHub. Overall, the project brings us closer to the goal of designing and manipulating complex quantum matter in a reliable and practical way.