Spatial-temporal dynamics of stimulated Raman scattering: Effects of populations and two-photon detuning

A quantum theory of stimulated Raman scattering is established that takes into account the time-dependence of pump laser pulse, two-photon detuning and atomic populations, allowing the general transient and spatial propagation study of Raman memory. Heisenberg-Langevin and Maxwell equations for the collective atomic operators are solved analytically under adiabatic condition, where the electric field envelopes and the collective atomic operators vary slowly. The analytical solution of Stokes/anti-Stokes signal electric field operator is obtained. The spatial-temporal intensity of quantum signal field is studied numerically and analytically for different two-photon detunings and initial populations.