Quantum state preparation of a mechanical resonator using an   optomechanical geometric phase
  We demonstrate that a geometric phase, generated via a sequence of four optomechanical interactions, can be used to increase, or generate nonlinearities in the unitary evolution of a mechanical resonator. Interactions of this form lead to new mechanisms for preparing mechanical squeezed states, and preparation of non-classical states with significant Wigner negativity. 
K. E. Khosla and M. R. Vanner and W. P. Bowen, and G. J. Milburn
quant-ph