  We present a single-shot method to measure motional states in the number
basis. The technique can be applied to systems with at least three
non-degenerate energy levels which can be coupled to a linear quantum harmonic
oscillator, such as in trapped ion experiments. The method relies on probing an
Autler-Townes splitting that arises when two levels are strongly coupled via a
phonon-number changing transition. We demonstrate the method using a single
trapped ion and show that it may be used in a non-demolition fashion to prepare
phonon number states. We also show how the Autler-Townes splitting can be used
to measure phonon number distributions.
