Observation of Microcanonical Atom Number Fluctuations in a Bose-Einstein Condensate

Quantum systems are typically characterized by the inherent fluctuation of their physical observables. Despite this fundamental importance, the investigation of the fluctuations in interacting quantum systems at finite temperature continues to pose considerable theoretical and experimental challenges. Here we report the characterization of atom number fluctuations in weakly interacting Bose-Einstein condensates. Technical fluctuations are mitigated through a combination of non-destructive detection and active stabilization of the cooling sequence. We observe fluctuations reduced by \SI{27}{\percent} below the canonical expectation for a non-interacting gas, revealing the microcanonical nature of our system. The peak fluctuations have near linear scaling with atom number $\Delta N_{0,\mathrm{p}}^2 \propto N^{1.134}$ in an experimentally accessible transition region outside the thermodynamic limit. Our experimental results thus set a benchmark for theoretical calculations under typical experimental conditions.