  We discuss analytical approximations to the ground-state phase diagram and
the elementary excitations of the cooperative Jahn-Teller model describing
strongly correlated spin-boson system on a lattice in various quantum optical
systems. Based on the mean-field theory approach we show that the system
exhibits quantum magnetic structural phase transition which leads to magnetic
ordering of the spins and formation of the bosonic condensates. We determine
existing of one gapless Goldstone mode and two gapped amplitude modes inside
the symmetry-broken phase.
