Measuring High-Order Phonon Correlations in an Optomechanical Resonator

We use single photon detectors to probe the motional state of a superfluid ^{4}He resonator of mass ∼1  ng. The arrival times of Stokes and anti-Stokes photons (scattered by the resonator's acoustic mode) are used to measure the resonator's phonon coherences up to the fourth order. By postselecting on photon detection events, we also measure coherences in the resonator when ≤3 phonons have been added or subtracted. These measurements are found to be consistent with predictions that assume the acoustic mode to be in thermal equilibrium with a bath through a Markovian coupling.