  The high-fidelity analysis of many-body quantum states of indistinguishable
atoms requires the accurate counting of atoms. Here we report the tomographic
reconstruction of an atom-number-resolving detector. The tomography is
performed with an ultracold rubidium ensemble that is prepared in a coherent
spin state by driving a Rabi coupling between the two hyperfine clock levels.
The coupling is followed by counting the occupation number in one level. We
characterize the fidelity of our detector and show that a negative-valued
Wigner function is associated with it. Our results offer an exciting
perspective for the high-fidelity reconstruction of entangled states and can be
applied for a future demonstration of Heisenberg-limited atom interferometry.
