  Optomechanical systems offer unique opportunities to explore macroscopic
quantum state and related fundamental problems in quantum mechanics. Here, we
propose a quantum optomechanical system involving exchange interaction between
spin angular momentum of light and a torsional oscillator. We demonstrate that
this system allows coherent control of the torsional quantum state of a
torsional oscillator on the single photon level, which facilitates efficient
cooling and squeezing of the torsional oscillator. Furthermore, the torsional
oscillator with a macroscopic length scale can be prepared in Schr\"odinger
cat-like state. Our work provides a platform to verify the validity of quantum
mechanics in macroscopic systems on the micrometer and even centimeter scale.
