  Owing to their long-lifetimes at cryogenic temperatures, mechanical
oscillators are recognized as an attractive resource for quantum information
science and as a testbed for fundamental physics. Key to these applications is
the ability to prepare, manipulate and measure quantum states of mechanical
motion. Through an exact formal solution to the Schrodinger equation, we show
how tripartite optomechanical interactions, involving the mutual coupling
between two distinct optical modes and an acoustic resonance enables quantum
states of mechanical oscillators to be synthesized and interrogated.
