  The present paper illustrates the realization of an atom-optomechanical
system where an atomic ensemble is confined in a ring optomechanical cavity
consisting of a fixed mirror and two movable ones. An analysis of the dynamics
and the linearization of the equations allows to derive the multimode
covariance matrix. Under realistic experimental conditions, we numerically
simulate the steady-state bipartite and tripartite continuous variable
entanglement using the logarithmic negativity, and analyze the shared
entanglement in the multimode system. The introduction of the atomic medium
allows to obtain a larger plateau for the entanglement and make more resilient
to the temperature decohering effects.
