  We extend the theory of quantum light memory in atomic ensemble of Lambda
type atoms with considering lower levels coherence decay rate and one and
two-photon detunings from resonances in low intensity and adiabatic passage
limit. We obtain that with considering these parameters, that there will be a
considerable decay of probe pulse and stored information; also, we obtain that
the group velocity of probe (light) pulse and its amplitude does not tend to
zero by turning off the control field. We propose a method to keep the probe
pulse in small values in turn off time of control field and to reduce the loss
of the stored probe pulse. In addition, we obtain that in the Off-resonance
case there will be a considerable distortion of the output light pulse that
causes in loss of the stored information, then we present limitations for
detunings and therefore for bandwidths of practical lasers also limitations for
maximum storage time to have negligible distortion of stored information. We
finally present the numerical calculations and compare them with analytical
results.
