ination, as illustrated below. Assuming that the charac- teristic interaction time T is long compared to the upper level relaxation–i.e., 1 Γ ≪ T , we can adiabatically elimi- nate ∂P$_{2}$$_{n}$$_{+1}$ ∂t in Eqs. (6) and (7) and obtain and weaker. The insets show that, for very large | k | , the dissipation always play the major role. In short, we argue that the phenomena in Sec. III can be qualitatively understood from the competition be- tween the effects of dispersion and of dissipation. For a ≈ 1, the dissipation dominates over the dispersion, and a stationary light pulse is generated. This applies to ther- mal atomic gases. For a ≪ 1, the dispersion wins as long as | k | > 0. If the length of the stored wave packet L$_{0}$ is sufficiently long–i.e., | k | ≈ 0, the recreated light forms a stationary pulse; otherwise, it splits into two counter- propagating light pulses. In the a = 0 limit and for a finite length wave packet, the generated light will always splits into two propagating light pulses for sufficiently long time, since the dispersion is always dominant over dissipation. Differentiating both sides of Eq. (15) with respect to t and substituting Eq. (16) yield Once more, the derivative terms can be eliminated by adiabatic treatment, and the equations become where we have introduced s mode and d mode Neglecting terms P$_{s,}$$_{2}$$_{n}$$_{+1}$ and P$_{d,}$$_{2}$$_{n}$$_{+1}$ for n ≥ ℓ , one has Making use of the Maxwell equations and the initial condition S$_{n}$ = 0 for n = 0, we obtain the propagating solution In summary, using direct simulation of the dynamic equations for Λ-type atomic systems, we find that both the decay rate γ and the length L$_{0}$ of the stored wave packet play an important role in determining the behav- ior of the new light generated by two counter-propagating control lights with equal strength. The numerical simu- lation of the γ = 0 limit defies the approximate analyt- ical solution. This means that the adiabatic-elimination treatment demonstrated in Appendix is invalid. For cold atomic systems, our calculations suggest that the recre- ated light forms a stationary pulse for large L$_{0}$ and/or γ while splits into two counter-propagating light pulses for small L$_{0}$ and/or γ . This scenario agrees well with the recent experiment. A qualitative understanding is given from the aspect of the dispersion relation. We ex- pect that our systematic calculation shall provide useful information for future experiments. We are very grateful to Ite A.Yu and Tao Xiong for helpful discussions. This work is supported by the NNSFC, the NNSFC of Anhui (under Grant No. 090416224), the CAS, and the National Fundamental Re- search Program (under Grant No. 2006CB921900). For γ$_{n}$ = 0, Eqs.(6) and (7) can analytically solved under additional approximation–i.e., the adiabatic elim- Where the group velocity of the splitting wave packet is c$_{0}$ = c/ √ (1 + ℓg $^{2}$N (2 ℓ +1)Ω 2 $_{c}$)(1 + ℓg $^{2}$N Ω 2 c ). In low the group- velocity limit, c$_{0}$ ≈ $_{c}$√$_{2}$$_{ℓ}$$_{+1Ω}$ 2 c ℓg $^{2}$N . [2] M. Fleischhauer, A. Amamoglu, J. P. Marangos, Rev. [1] S. E. Harris, Phys. Today 50 , 36(1997). ∗ Electronic address: bo.zhao@uibk.ac.at † Electronic address: yjdeng@ustc.edu.cn Appendix Acknowledgments V. DISCUSSION Γ P$_{2}$$_{n}$$_{+1}$ = igE$_{p,}$$_{2}$$_{n}$$_{+1}$ + i Ω$_{c}$( S$_{2}$$_{n}$ + S$_{2(}$$_{n}$$_{+1)}$ ) , (15) ∂S$_{2}$$_{n}$ ∂t = i Ω$_{c}$( $^{P$_{2}$$_{n}$}$− 1 + P$_{2}$$_{n}$$_{+1}$ ) . (16) Γ ∂P$_{2}$$_{n}$$_{+1}$ ∂t = ig ∂E$_{p,}$$_{2}$$_{n}$$_{+1}$ ∂t − Ω 2 $_{c}$( $^{P$_{2}$$_{n}$}$− 1 + 2 P$_{2}$$_{n}$$_{+1}$ + P$_{2}$$_{n}$$_{+3}$ ) . (17) P$_{s,}$$_{2}$$_{n}$$_{+1}$ = ( − 1) $^{n}$((2 n + 1) P$_{s,}$$_{1}$ − n ig Ω 2 c ∂E$_{s}$ ∂t ) , (18) P$_{d,}$$_{2}$$_{n}$$_{+1}$ = ( − 1) $^{n}$( P$_{d,}$$_{1}$ − n ig Ω 2 c ∂E$_{d}$ ∂t ) . (19) P$_{s,}$$_{2}$$_{n}$$_{+1}$ = P$_{2}$$_{n}$$_{+1}$ + $^{P}$− (2 n +1) , (20) P$_{d,}$$_{2}$$_{n}$$_{+1}$ = P$_{2}$$_{n}$$_{+1}$ − $^{P}$− (2 n +1) . (21) P$_{s,}$$_{1}$ = ℓ 2 ℓ + 1 ig Ω 2 c ∂E$_{s}$ ∂t , (22) P$_{d,}$$_{1}$ = ℓ ig Ω 2 c ∂E$_{d}$ ∂t . (23) E s ( z, t ) = − ( Ω c S 0 ( z − c 0 t, 0) g + Ω c S 0 ( z + c 0 t, 0) g ) , (24) E$_{d}$ ( z, t ) = − ρ 0 c 0 ( Ω c S 0 ( z − c 0 t, 0) g − Ω c S 0 ( z + c 0 t, 0) g ) . (25) 6