We propose and demonstrate experimentally the discrimination between two spin states of an atom purely on the basis of their angular momentum. The discrimination relies on angular momentum selection rules and does not require magnetic effects such as a magnetic dipole moment of the atom or an applied magnetic field. The central ingredient is to prevent by coherent population trapping an optical pumping process which would otherwise relax the spin state before a detectable signal could be obtained. We detected the presence or absence of a single quantum (1ħ) of angular momentum in a trapped calcium ion in a single observation with success probability 0.86. As a practical technique, the method can be applied to read out some types of quantum ...