Single-Shot Measurements of Phonon Number States Using the Autler-Townes Effect

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 nondegenerate energy levels which can be coupled to a linear quantum harmonic oscillator. The method relies on probing an Autler-Townes splitting that arises when a phonon-number changing transition is strongly coupled. We demonstrate the method using a single trapped ion and show that it may be used in a nondemolition fashion to prepare phonon number states. We also show how the Autler-Townes splitting can be used to measure phonon number distributions.