Analyzing spin states of a Bose-Einstein condensate with number-resolved counting

A tomography of many-body quantum states of indistinguishable particles is generally performed by engineering couplings between the involved states and a subsequent counting of the occupation numbers. While precise couplings belong to the standard experimental toolbox, an accurate number counting presents a considerable challenge for both photonic and atomic quantum states. Here we present an application of a number-resolving atom counting [New J. Phys. 23, 113046 (2021)] for the state reconstruction of an atomic coherent spin state. We generate the coherent spin state by driving a Rabi frequency between two hyperfine states of an ultracold Rubidium ensemble.The result is analyzed by a number-resolving fluoresence detection setup. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. The results offer an exciting perspective for a high-fidelity tomography of entangled states and can be applied for the future demonstration of Heisenberg-limited atom interferometry.