Number-resolved Analysis of Many-body Quantum States

Quantum sensors have emerged as a revolutionary technology that harnesses quantum phenomena to surpass the resolution of classical sensors. By leveraging the unique property of quantum particles to exist in superposition states, quantum sensors can be employed for interferometry, a highly precise measurement technique. Interferometers utilizing massive particles offer exceptional precision in measuring acceleration, rotation and time, making them highly relevant for navigation, geodesy and fundamental research. To enhance the sensitivity beyond classical limits and approach the fundamental Heisenberg limit, exploiting the quantum mechanical property of entanglement is crucial. Achieving interferometry close to the Heisenberg limit requires carefully engineered entangled quantum states, low-noise interferometer components and a detection on the single-particle level. Since the sensitivity of an interferometer scales with the number of employed particles, a source capable of generating large entangled states is desirable. Due to their high phase-space density and well-defined spatial mode, Bose-Einstein condensates (BECs) present a promising source for atom interferometry. They offer great potential to create large entangled states, making them ideal candidates for quantum-enhanced atom interferometry. However, a considerable challenge lies in pairing sources of entangled states with single-particle-resolving detection. This work addresses this challenge by presenting the creation and number-resolved analysis of many-body quantum states in an apparatus designed for atom interferometry close to the Heisenberg limit. Based on three publications, this thesis contributes to the development of tools for analyzing many-body quantum states. By utilizing a hybrid evaporation approach that combines a magnetic quadrupole trap with a crossed-beam optical dipole trap, BECs containing 2 * 10^5 atoms are rapidly created within 3.3 s. A number-resolving detection based on a magneto-optical trap is presented, its noise sources are analyzed and its potential for preparing mesoscopic atomic ensembles is demonstrated. Building upon these findings, an enhanced version of the number-resolving detection is implemented in the experimental apparatus which maintains single-atom resolution for hundreds of atoms. The detection system is capable of accurately counting subsamples of the BEC prepared through microwave transitions and optical removals. Furthermore, a coherent spin state consisting of 35 atoms is analyzed with number-resolution. The fidelity of the detector is characterized through quantum detector tomography and a state reconstruction is performed. The techniques developed in this work directly enable the number-resolved analysis of entangled states, such as a twin-Fock state, representing the next step towards atom interferometry at the Heisenberg limit