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: Ĥ_int = -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 candidate- 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].