  We propose a scheme for the generation of strong mechanical squeezing beyond
3dB in hybrid atom-optomechanical systems in the highly unresolved sideband
(HURSB) regime where the decay rate of cavity is much larger than the frequency
of the mechanical oscillator. The system is formed by two two-level atomic
ensembles and an optomechanical system with cavity driven by two lasers with
different amplitudes. In the HURSB regime, the squeezing of the movable mirror
can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is
put into the optomechanical system. However, if two atomic ensembles are put
into the optomechanical system, the strong mechanical squeezing beyond 3dB is
achieved even in the HURSB regime. Our scheme paves the way toward the
implementation of strong mechanical squeezing beyond 3dB in hybrid
atom-optomechanical systems in experiments.
