  The existence of ideal quantum measurements is one of the fundamental
predictions of quantum mechanics. In theory the measurement projects onto the
eigenbasis of the measurement observable while preserving all coherences of
degenerate eigenstates. The question arises whether there are dynamical
processes in nature that correspond to such ideal quantum measurements. Here we
address this question and present experimental results monitoring the dynamics
of a naturally occurring measurement process: the coupling of a trapped ion
qutrit to the photon environment. By taking tomographic snapshots during the
detection process, we show with an average fidelity of $94\%$ that the process
develops in agreement with the model of an ideal quantum measurement.
