  In a hybrid micromaser system consisting of an optical cavity with a moving
mirror connected to a low temperature thermal bath, we demonstrate, both
analytically and numerically, that for certain interaction times between a
random atomic flux and the optomechanical cavity, vacuum phonon trapping states
are generated. Furthermore, under the approach of the master equation with
independent phonon and photon thermal baths, we show that the trapping of the
phonons and photons is achieved for the same interaction times. The results
also indicate that by increasing the cavity-oscillator coupling one may
generate a coherent phonon state aside from the trapping states. Within the
same hybrid system, but now connected to the squeezed phonon reservoir, a
phonon blockade effect can be engineered. Moreover, we identify an
interconnection between the trapping and blockade effects, particularly if one
approaches the vacuum trapping state, strong phonon blockade can be achieved
when the system is connected with a weakly squeezed phonon reservoir.
