Noise-Free Measurement of Harmonic Oscillators with Instantaneous Interactions

We present a method of measuring the quantum state of a harmonic oscillator through instantaneous probe-system selective interactions of the Jaynes-Cummings type. We prove that this scheme is robust to general decoherence mechanisms, allowing the possibility of measuring fast-decaying systems in the weak-coupling regime. This method could be applied to different setups: motional states of trapped ions, microwave fields in cavity or circuit QED, and even intracavity optical fields.