Measurements of High-Order Phonon Correlations in an Optomechanical System via Single-Photon Detection

We have used photon-counting techniques to probe and control the state of an acoustic mode having an effective mass of 6 ng. The acoustic mode resides in a body of superfluid helium which is confined inside a fiber-optic cavity. When a laser excites this cavity, every Stokes- and anti-Stokes sideband photon heralds the production (or annihilation) of an individual phonon from the acoustic mode. We record the arrival times of the sideband photons and use the correlations in this data to measure the phonon coherences up to the fourth order. These measurements agree well with theoretical predictions that assume the acoustic mode is in a thermal state. By post-selecting the data, we also measure the phonon coherences (up to third order) of phonon-subtracted/added thermal states, as well as the dynamics of their mean phonon occupancy. We discuss how such coherences can in principle be used to reconstruct the phonon-added thermal state's Wigner function. Lastly, we will describe how these measurements benefit from this device's design, which offers truly single-mode optomechanical coupling, and removes the need for an in situ alignment.