  We study in detail the interesting dynamical symmetry and its applications in
various atomic systems with electromagnetically induced transparency (EIT) in
this paper. By discovering the symmetrical Lie group of various atomic systems,
such as single-atomic-ensemble composed of complex $m$-level $(m>3)$ atoms, and
$two$-atomic-ensemble and even multi-atomic-ensemble system composed of of
$three$-level atoms etc., one can obtain the general definition of dark-state
polaritons (DSPs), and then the dark-states of these different systems. The
symmetrical properties of the multi-level system and multi-atomic-ensemble
system are shown to be dependent on some characteristic parameters of the EIT
system. Furthermore, a controllable scheme to generate quantum entanglement
between lights or atoms via quantized DSPs theory is discussed and the
robustness of this scheme is analyzed by confirming the validity of adiabatic
passage conditions in this paper.
