Steady State Entanglement in the Mechanical Vibrations of Two Dielectric Membranes

We consider two dielectric membranes suspended inside a Fabry-Perot cavity, which are cooled to a steady state via a drive by suitable classical lasers. We show that the vibrations of the membranes can be entangled in this steady state. They thus form two mechanical, macroscopic degrees of freedom that share steady state entanglement.