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The high-fidelity analysis of many-body quantum states of indistinguishableatoms requires the accurate counting of atoms. Here we report the tomographicreconstruction of an atom-number-resolving detector. The tomography isperformed with an ultracold rubidium ensemble that is prepared in a coherentspin state by driving a Rabi coupling between the two hyperfine clock levels.The coupling is followed by counting the occupation number in one level. Wecharacterize the fidelity of our detector and show that a negative-valuedWigner function is associated with it. Our results offer an excitingperspective for the high-fidelity reconstruction of entangled states and can beapplied for a future demonstration of Heisenberg-limited atom interferometry.

Tomography of a number-resolving detector by reconstruction of an atomic many-body quantum state