Coherent scattering-mediated correlations between levitated nanospheres

We explore entanglement generation between multiple optically levitated nanospheres interacting with a common optical cavity via the Coherent Scattering optomechanical interaction. derive many-particle Hamiltonian governing unitary evolution of system and show that it gives rise to quantum correlations among various partitions setup, following non-Markovian dynamics birth, death revivals. also consider effects coupling external environments under reasonable experimental conditions mechanical modes can survive even at room temperature. Its dependence upon number nanoparticles, their initial temperature strength is studied. A numerical toolbox simulate closed open Gaussian states informational measures developed.