  We investigate the transient phenomenon or property of the propagation of an
optical probe field in a medium consisting of many $\Lambda$-type three-level
atoms coupled to this probe field and an classical driven field. We observe a
hidden symmetry and obtain an exact solution for this light propagation problem
by means of the spectral generating method. This solution enlightens us to
propose a practical protocol implementing the quantum memory robust for quantum
decoherence in a crystal. As an transient dynamic process this solution also
manifests an exotic result that a wave-packet of light will split into three
packets propagating at different group velocities. It is argued that
  "super-luminal group velocity" and "sub-luminal group velocity" can be
observed simultaneously in the same system. This interesting phenomenon is
expected to be demonstrated experimentally.
