  Quantum control of engineered mechanical oscillators can be achieved by
coupling the oscillator to an auxiliary degree of freedom, provided that the
coherent rate of energy exchange exceeds the decoherence rate of each of the
two sub-systems. We achieve such quantum-coherent coupling between the
mechanical and optical modes of a micro-optomechanical system. Simultaneously,
the mechanical oscillator is cooled to an average occupancy of n = 1.7 \pm 0.1
motional quanta. Pulsed optical excitation reveals the exchange of energy
between the optical light field and the micromechanical oscillator in the time
domain at the level of less than one quantum on average. These results provide
a route towards the realization of efficient quantum interfaces between
mechanical oscillators and optical fields.
