Optomechanical systems couple light stored in an optical resonant cavity to the motion of a mechanical motion of the cavity walls. Single optomechanical cells have been successfully fabricated in a wide variety of systems. Recent experiments have further demonstrated setups, such as photonic crystal structures, that in principle allow to confine several optical and vibrational modes on a single chip.

In the first part of my presentation I will demonstrate the emergence of a robust, long-living and highly non-classical mechanical state in a standard single cell optomechanical setup. I will show that under some parameters, the longtime steady state of the mechanical degrees of freedom has significantly negative Wigner density. Such a negative Wigner density can be mapped experimentally using standard homodyne tomography. I will then discuss the signature of non-classical states in a very easily accessible observable, the unequal-time photon-photon correlation function. I show two robust signatures of quantum optomechanical instabilities and theoretically explain their physical origin. I then present results concerning the collective classical nonlinear dynamics in arrays of coupled optomechanical cells. It is shown that such “optomechanical arrays” can display synchronization which can be described by a modified Kuramoto model. I demonstrate that such synchronization behavior can be observed via a simple optical readout. Finite-Element-Modeling is used to obtain realistic parameters of optomechanical array available under current technology and it is confirmed that the complex phase-locking and synchronization transitions are observable in such parameter range.

Finally I briefly discuss the future possibilities of using such arrays to fabricate an integrated optomechanical circuits in the classical regime and to study quantum many-body dynamics.