  We extend the theory to describe the quantum light memory in type atoms with
considering (lower levels coherency decay rate) and detuning for the probe and
the control fields. We obtain that with considering these parameters, group
velocity of the probe pulse does not tend to zero by turning off the control
field. We show that there are considerable decay for the probe pulse and the
stored information. Also, it is inferred that the light field does not tend to
zero when the control field is turned off. In addition, we obtain that in the
off-resonance case there is considerable distortion of the output light pulse
(with fast oscillations) that destroys the stored information. Then we present
the limitations on detuning (bandwidths) of the probe and the control fields to
achieve negligible distortion. We finally present the numerical calculations
and compare them with obtained analytical results.
