  Quantum optomechanics uses optical means to generate and manipulate quantum
states of motion of mechanical resonators. This provides an intriguing platform
for the study of fundamental physics and the development of novel quantum
devices. Yet, the challenge of reconstructing and verifying the quantum state
of mechanical systems has remained a major roadblock in the field. Here, we
present a novel approach that allows for tomographic reconstruction of the
quantum state of a mechanical system without the need for extremely high
quality optical cavities. We show that, without relying on the usual state
transfer presumption between light an mechanics, the full optomechanical
Hamiltonian can be exploited to imprint mechanical tomograms on a strong
optical coherent pulse, which can then be read out using well-established
techniques. Furthermore, with only a small number of measurements, our method
can be used to witness nonclassical features of mechanical systems without
requiring full tomography. By relaxing the experimental requirements, our
technique thus opens a feasible route towards verifying the quantum state of
mechanical resonators and their nonclassical behaviour in a wide range of
optomechanical systems.
