Title: Atom Number Fluctuations in Bose Gases -- Statistical analysis of parameter estimation

Abstract: The investigation of the fluctuations in interacting quantum systems at finite temperatures showcases the ongoing challenges in understanding complex quantum systems. Recently, atom number fluctuations in weakly interacting Bose-Einstein condensates were observed, motivating an investigation of the thermal component of partially condensed Bose gases. Here, we present a combined analysis of both components, revealing the presence of fluctuations in the thermal component. This analysis includes a comprehensive statistical evaluation of uncertainties in the preparation and parameter estimation of partially condensed Bose gases. Using Monte Carlo simulations of optical density profiles, we estimate the noise contributions to the atom number and temperature estimation of the condensed and thermal cloud, which is generally applicable in the field of ultracold atoms. Furthermore, we investigate the specific noise contributions in the analysis of atom number fluctuations and show that preparation noise in the total atom number leads to an important technical noise contribution. Subtracting all known noise contributions from the variance of the atom number in the BEC and thermal component allows us to improve the estimate of the fundamental peak fluctuations.