The book is a study of nonlinear interaction between light and matter.Cooling a mechanical nano-structure towards its quantum ground state is in the heart of both fundamental science and technology nowadays.Also stationnary properties of quantum states as squeezed and entangled states.To give a satisfactory explanation to this problem,it focus on the non linear phononics study at the single-phonon level in optomechanical systems.Softening geometrical nonlinearity allows a classical control of the nanoresonator.Geometrical nonlinearity as the quantum decoherence, adds some of amount of phonons on the lowest result, and then limits the quantum ground state achievement.The relevant fact of these results is that nonlinear effects not only contribute to the advance of the fundamental science but also appear as pillar elements for an improvement of quantum applications