Control and tomography of phonons in cavity optomechanical nanostructures

Phonons are the quanta of mechanical motion. One possible toolbox for manipulating phonons is provided by the field of cavity-optomechanics, in which light and motion interact via radiation pressure. Of particular importance to applications are cavity-optomechanical nanostructures, whose properties are entirely engineered and which can be integrated on the surface of a chip. In such platforms, new possibilities for the control of phonons emerge. Two key questions arise in these systems where phonons carry information: How can we control the propagation of phonons, and how can we use light to prepare and verify quantum states of mechanical systems? In this thesis, I present three main results using cavity optomechanical nanostructures. First, I will show that phonons confined to a resonator can be made to deterministically couple to an external channel. We propose, and demonstrate via cryogenic measurements, that a particularly simple symmetry-breaking perturbation in nanopatterned silicon allows for the efficient transduction of localized phonons into de-localized phonons. Second, we design and experimentally demonstrate a single-mode phononic wire. Our design incorporates a patterned silicon film with a complete two-dimensional acoustic bandgap. We show through optical measurements that only a single propagating mode is supported for GHz frequency phonons within the bandgap. Low-loss propagation over millimeter length scales is observed. In addition, methods to generate optically induced non-linearities for phonons are discussed. Finally, I describe recent results from our experiment combining photon counting and continuous measurement of mechanical position to perform quantum state tomography. By heralding our measurement on the detection of a single inelastically scattered photon, a single phonon is added to a nanomechanical oscillator. Despite the large thermal occupancy of the oscillator at room temperature, the addition, or subtraction, of a single phonon produces a distinctly non-Gaussian state of motion. The results open up new possibilities for preparing and verifying macroscopic quantum mechanical states using light