In recent years, there have been rapid breakthroughs in quantum technologies that offer new opportunities for advancing the understanding of basic quantum phenomena; realizing novel strongly correlated systems; and enhancing applications in quantum communication, computation, and sensing. Cutting edge quantum technologies simultaneously require high fidelity quantum-limited measurements and control. Large-scale applications of these capabilities hinge on understanding system-reservoir dynamics of many-body quantum systems, whose Hilbert space grows exponentially with system size. Ultracold atoms - our workhorse for quantum simulation, are an ideal platform for understanding the system-reservoir dynamics of many-body systems. In this talk, I will present the characterization of measurement back-action in atomic Bose-Einstein condensates, weakly interacting with a far-from resonant, i.e., dispersively interacting, laser beam. We theoretically describe this process using a quantum trajectories approach where the environment measures the scattered light and I will present our measurement model based on an ideal photodetection mechanism. Next, I will discuss our experimental quantification of the resulting wavefunction change with two observations: the contrast of a Ramsey interferometer and the deposited energy [1, 2]. In this perspective, I will then identify the ensuing systematic effects: stray optical lattices (a technical consequence of weak retro-reflections of the probe beam) and probe-induced photoassociation (an intrinsic atomic process). Not all degrees of freedom are equally impacted by these systematic effects: the reduction in contrast of a Ramsey interferometer is back-action limited whereas the added energy is in excess of what is expected from light scattering alone. I will conclude with a discussion of experimental and theoretical implications, and potential future directions for research.
 E. Altuntaş and I. B. Spielman, arXiv preprint arXiv:2209.04400 (2022).
 E. Altuntaş and I. B. Spielman, arXiv preprint arXiv:2212.03431 (2022).