Continuous quantum measurements for many-body systems

The dynamics of quantum many-body systems is hard to predict due to the enormous computational complexity. In recent years, quantum simulators made from ultracold atoms have emerged as a highly controlled platform to investigate quantum dynamics in different regimes. In QuOntM we will develop new technologies for extracting information from quantum simulators. Our developments will be based on the possibility to verify the emergence of a certain model when performing the quantum simulation. For this we will establish methods for learning the effective Hamiltonians for continuous systems. Translating methods for microscopic theories to the realm of quantum field theory we will be able to infer the realized effective Hamiltonian by measurements of the quantum simulator. Our experimental studies are based on the well-established platform of ATOMCHIP where Rubidium atoms are trapped magnetically in a one-dimensional trapping geometry. We will use oscillatory radio- frequency magnetic fields to couple out a controllable number of atoms from the system; these outcoupled atoms will act as a quantum probe of the properties of the system. Detecting the atoms with a single-atom sensitive fluorescence imaging system will enable us to perform weak, repeated probing while maintaining the quantumness of the system. Finally, these methods will allow us to study unequal-time correlation function which will give us new insights into the dynamics far from equilibrium. Ultimately, we want to push the probing in the regime of continuous probing. We aim at enriching the accessible physical phenomena by opening the systems to an environment while at the same time recording all information that is lost from the system. This will give access to so far unexplored quantum phenomena.

This project developed and demonstrated new ways to measure, control, and verify complex quantum many-body systems, combining theory, experiment, and advanced data-driven techniques. Understanding quantum many-body systems-collections of many interacting quantum particles-is one of the central challenges in modern physics. Potential insights underly future quantum technologies, yet their complexity makes them extremely difficult to probe and verify using conventional measurement tools. The goal of our project was to overcome these limitations by developing new strategies for extracting information from quantum many-body systems while respecting the fundamental constraints imposed by quantum mechanics. We investigated novel approaches to measuring quantum systems and succeeded in both theoretically developing and experimentally implementing new measurement and information-extraction schemes. A key achievement was the proposal of Hamiltonian learning as a practical tool for verifying quantum field simulators. Instead of assuming that a simulator behaves as intended, Hamiltonian learning allows one to infer the underlying physical laws directly from measurement data, providing a powerful and scalable method for validation and benchmarking. In parallel, we realized a quantum-limited measurement of non-commuting observables. Because quantum mechanics forbids simultaneous precise measurements of such observables, accessing their information requires carefully designed measurement protocols. Our work demonstrated how to extract maximal information while reaching fundamental quantum limits, opening new possibilities for probing dynamics and correlations in many-body systems. To further expand the accessible regimes of our quantum simulator, we integrated machine-learning techniques and optimal control methods. These tools enabled the preparation of quantum states that are difficult or impossible to reach using traditional approaches. By efficiently navigating complex control landscapes, we were able to stabilize new operating regimes and enhance the performance and flexibility of the simulator. Finally, we developed a novel cavity design that functions as an ultrasensitive quantum microscope. This cavity architecture dramatically enhances the interaction between light and matter, enabling precision measurements of collective quantum properties. Beyond sensing, the cavity also provides new avenues for controlling many-body systems, for example by mediating long-range interactions or enabling measurement-based feedback. Finally, an experimental upgrade resulting from this project will allow local, continuous measurements of a tunnel-coupled Bose gas. This capability represents a major step forward, as it enables real-time observation of spatially resolved quantum dynamics without destroying the system. Together, these advances establish a versatile platform for exploring quantum many-body physics and lay the groundwork for future quantum technologies based on precise measurement, verification, and control.