Rapid generation and number-resolved detection of spinor Rubidium Bose-Einstein condensates

High data acquisition rates and low-noise detection of ultracold neutral atoms present important challenges for the state tomography and interferometric application of entangled quantum states in Bose-Einstein condensates. In this article, we present a high-flux source of $^{87}$Rb Bose-Einstein condensates combined with a number-resolving detection. We create Bose-Einstein condensates of $2\times10^5$ atoms with no discernible thermal fraction within $3.3$ s using a hybrid evaporation approach in a magnetic/optical trap. For the high-fidelity tomography of many-body quantum states in the spin degree of freedom [arXiv:2207.01270], it is desirable to select a single mode for a number-resolving detection. We demonstrate the low-noise selection of subsamples of up to $16$ atoms and their subsequent detection with a counting noise below $0.2$ atoms. The presented techniques offer an exciting path towards the creation and analysis of mesoscopic quantum states with unprecedented fidelities, and their exploitation for fundamental and metrological applications.