  Generation of non-Gaussian quantum states of macroscopic mechanical objects
is key to a number of challenges in quantum information science, ranging from
fundamental tests of decoherence to quantum communication and sensing. Heralded
generation of single-phonon states of mechanical motion is an attractive way
towards this goal, as it is, in principle, not limited by the object size. Here
we demonstrate a technique which allows for generation and detection of a
quantum state of motion by phonon counting measurements near the ground state
of a 1.5 MHz micromechanical oscillator. We detect scattered photons from a
membrane-in-the-middle optomechanical system using an ultra-narrowband optical
filter, and perform Raman-ratio thermometry and second-order intensity
interferometry near the motional ground state ($\bar{n}=0.23\pm0.02$ phonons).
With an effective mass in the nanogram range, our system lends itself for
studies of long-lived non-Gaussian motional states with some of the heaviest
objects to date.
