Collective dynamics in optomechanical arrays

Summary form only given. The field of optomechanics [1] seeks to explore the interaction between light and mechanical motion. Optomechanical system are typically composed of a single mechanical and a single optical mode interacting via radiation pressure: Ĥint = -ħg0 â†â(b + b†), where â/b are the photon/phonon operators. In this talk, we will introduce arrays of optomechanical cells, and discuss our first theoretical results on the nonlinear dynamics of such a setup [2,3].First we have studied the classical nonlinear dynamics of optomechanical arrays. For blue-detuned laser drive, a Hopf bifurcation towards self-sustained mechanical oscillations takes place. For static disorder of the frequencies in the array, we have shown that there can be a transition towards phase-locking. The slow dynamics of the mechanical oscillation phase field is described by a specific modification of the Kuramoto equation known in synchronization physics: in the simplest case δ φ = -δΩ - Ksin(2δφ), for the phase difference δφ between two cells with frequency difference δΩ, corresponding to a particle sliding down in a tilted washboard potential.In a second step, we have turned towards the quantum dynamics of arrays without static disorder [3]. There, the effects of the fundamental quantum noise can lead to phase diffusion. Upon increasing the coupling between cells, we observe a transition between incoherent mechanical oscillations and a collective phase-coherent mechanical state. To study the driven-dissipative dynamics, we employ a mean-field approach based on the Lindblad master equation, as well as semiclassical Langevin equations. We will also discuss the prospects of observing this non-equilibrium dynamics in an experimental implementation based on currently available setups. Very promising candidates in this regard are optomechanical crystal setups, where defects in photonic crystal structures are used to generate co-localized optical and mechanical modes in a two-dimensional geometry [4].