The fluctuations in thermodynamic and transport properties in many-body systems gain importance as the number of constituent particles is reduced. Ultracold atomic gases provide a clean setting for the study of mesoscopic systems; however, the detection of temporal fluctuations is hindered by the typically destructive detection, precluding repeated precise measurements on the same sample. Here, we overcome this hindrance by utilizing the enhanced light-matter coupling in an optical cavity to perform a minimally invasive continuous measurement and track the time evolution of the atom number in a quasi two-dimensional atomic gas during evaporation from a tilted trapping potential. We demonstrate sufficient measurement precision to detect atom number fluctuations well below the level set by Poissonian statistics. Furthermore, we characterize the nonlinearity of the evaporation process and the inherent fluctuations of the transport of atoms out of the trapping volume through two-time correlations of the atom number. Our results establish coupled atom-cavity systems as a novel testbed for observing thermodynamics and transport phenomena in mesosopic cold atomic gases and, generally, pave the way for measuring multi-time correlation functions of ultracold quantum gases.
Tracking evaporative cooling of a mesoscopic atomic quantum gas in real time