Precision Measurements with Ultracold Matter-Wave Devices

Ultracold atoms provide a useful platform for quantum sensing, which through matter-wave interferometry enables precision measurements beyond classical limits. In realistic settings, interactions with the environment and intrinsic many-body dynamics play a crucial role in determining interferometric performance. This thesis investigates phase estimation and sensitivity limits in atom interferometers within the framework of open quantum systems. To this end we employ the two-mode model of the Bose–Einstein condensate in a double-well potential together with tools from quantum estimation theory like Fisher information and the Cramér–Rao bound to characterize the interferometric sensitivity. Within a Lindblad formalism, we analyze the impact of both particle-conserving and particle non-conserving noise on interferometric protocols. We identify the emergence of insensitivity points, evolution times at which phase estimation becomes impossible, and show that their location depends on system parameters but is independent of noise strength. While specific measurement strategies may suggest advantages for number- conserving processes, ultimate precision bounds reveal that particle non-conserving noise leads to lower achievable sensitivity. We further examine how the scaling of the system– environment coupling affects precision. By comparing models with and without Kac rescaling, we demonstrate that the commonly expected degradation from Heisenberg- limited to shot-noise-limited sensitivity is not universal. For linear coupling to a harmonic environment, extensivity-restoring rescaling can preserve Heisenberg scaling. Then we explored the modification of the interferometric protocol by substituting the usual unitary Beam-Splitter with a projective measurement induced splitting of the initial populations. Finally, we extend existing Sagnac interferometry schemes based on single atomic clocks to the regime of Bose–Einstein condensates. We analyze implementations relying on fully confined atoms and state-dependent transport, and quantify the impact of Bose-Einstein statistics and finite temperature on the sensitivity of such interferometric platforms.