GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s54> GLYPH<s48>GLYPH<s46>GLYPH<s56> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s50> GLYPH<s49>GLYPH<s46>GLYPH<s52> GLYPH<s49>GLYPH<s46>GLYPH<s54> GLYPH<s49>GLYPH<s46>GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s54> GLYPH<s48>GLYPH<s46>GLYPH<s56> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s50> GLYPH<s49>GLYPH<s46>GLYPH<s52> GLYPH<s49>GLYPH<s46>GLYPH<s54> GLYPH<s49>GLYPH<s46>GLYPH<s56> GLYPH<s118> GLYPH<s103> GLYPH<s40>GLYPH<s50>GLYPH<s108>GLYPH<s43>GLYPH<s49>GLYPH<s41> GLYPH<s49>GLYPH<s47>GLYPH<s50> GLYPH<s47>GLYPH<s108> GLYPH<s32>GLYPH<s68>GLYPH<s105>GLYPH<s114>GLYPH<s101>GLYPH<s99>GLYPH<s116>GLYPH<s32>GLYPH<s110>GLYPH<s117>GLYPH<s109>GLYPH<s101>GLYPH<s114>GLYPH<s105>GLYPH<s99>GLYPH<s97>GLYPH<s108>GLYPH<s32>GLYPH<s115>GLYPH<s105>GLYPH<s109>GLYPH<s117>GLYPH<s108>GLYPH<s97>GLYPH<s116>GLYPH<s105>GLYPH<s111>GLYPH<s110> GLYPH<s32>GLYPH<s65>GLYPH<s110>GLYPH<s97>GLYPH<s108>GLYPH<s121>GLYPH<s116>GLYPH<s105>GLYPH<s99>GLYPH<s97>GLYPH<s108>GLYPH<s32>GLYPH<s115>GLYPH<s111>GLYPH<s108>GLYPH<s117>GLYPH<s116>GLYPH<s105>GLYPH<s111>GLYPH<s110>GLYPH<s32>GLYPH<s117>GLYPH<s110>GLYPH<s100>GLYPH<s101>GLYPH<s114> GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s97>GLYPH<s100>GLYPH<s105>GLYPH<s97>GLYPH<s98>GLYPH<s97>GLYPH<s116>GLYPH<s105>GLYPH<s99>GLYPH<s32>GLYPH<s97>GLYPH<s112>GLYPH<s112>GLYPH<s114>GLYPH<s111>GLYPH<s120>GLYPH<s105>GLYPH<s109>GLYPH<s97>GLYPH<s116>GLYPH<s105>GLYPH<s111>GLYPH<s110> 3 FIG. 3: (Color online) Light intensity | E s | $^{2}$+ | E$_{d}$ | 2 as a func- tion of time and position z for γ n = 0 with different length L 0 . Figures (a)-(f) represents L 0 /l$_{abs}$ = 5   10   20   30   40  and 50  respectively. The position is in unit of l$_{abs}$ and the time is in unit of 1 / Γ. Strong light is shown in red bright color  while the back ground is in blue. FIG. 2: (Color online) Group velocity v g of the recreated forward (backward)-propagating light pulse in the γ n = 0 limit. The unit of v g is c Ω 2 c g 2 $_{N}$. The red straight line is from the approximate analytic calculation (24)(25) in Appendix  while the black dots are obtained by the direct numerical simulation of Eqs.(6)-(9) in Sec. III. The error margins of the data points are ± 0 . 006. group velocity v$_{g}$ of the forward (backward)-propagating light pulse is shown in Fig.2. One finds that: 1)  the ap- proximate solution with cutoff at finite ℓ yields a non-zero v$_{g}$   and 2)  v$_{g}$ ( ℓ ) reaches the maximum value at ℓ = 1  and then vanishes with √$_{2}$$_{ℓ}$$_{+ 1}$$_{/ℓ}$$_{.}$ Since the real sys- tem corresponds to the infinite-order limit  one “seems” to conclude that the recreated light forms a stationary pulse. pulse in cold atomic systems ( γ$_{n}$ = | n | a Γ) for which the approximate treatment is unavailable  we directly simu- late Eqs.(6)–(9). Naturally  a cutoff takes place at finite ℓ and accordingly 5+4 ℓ equations are involved in each sim- ulation. The result for real systems ( ℓ → ∞ ) is obtained from the extrapolation of simulations for finite ℓ . We first consider the zero-decay limit ( γ$_{n}$ = 0). The initial condition is taken such that: 1)  only the zeroth component S$_{0}$ ( z  t = 0) of the ground-spin coherence is nonzero while all other components S$_{2}$$_{n}$ ( z  0) are zero; S$_{0}$ assumes a Gaussian shape S$_{0}$ ( z  0) = e − ( z/L$_{0}$ ) 2 with L$_{0}$ the length of the wave packet; 2)  all components of the optical coherence are zero P$_{2}$$_{n}$$_{+1}$ ( z  0) = 0  and 3)  no probe light exists at the beginning E + p ( z  0) = E − p ( z  0) = 0. Further  the wave-packet length is set at L$_{0}$ = 5 l$_{abs}$   with l$_{abs}$ = Γ c g $^{2}$N the absorption length. To be in the slow- light regime  we chose the parameters to be Ω$_{c}$ = 0 . 69Γ  g $^{2}$N = 138Γ $^{2}$. The equations are directly solved by Lax- Friedrichs method with sufficiently small step. The sim- ulation is up to ℓ = 100  and the group velocity v$_{g}$ of the recreated forward (backward)-propagating light pulse is measured. The results are shown in Fig. 2. As the ap- proximate analysis  v$_{g}$ ( ℓ ) reaches its maximum at ℓ = 1 and then starts to decrease. Nevertheless  the decrease of v$_{g}$ becomes slower and slower after ℓ ≈ 14 and eventu- ally stays unchanged at v$_{g}$ = 0 . 47 ± 0 . 006. From Fig. 2  For cold atomic systems where temperature is low but nonzero  one has γ$_{0}$ = 0 and γ$_{n}$ = 0 for n = 0. In this case  we set γ$_{n}$ = | n | a Γ  with a the decay constant. This decay model can well describe the decays of the coef- ficients of the ground-spin/optical coherence in various cold atomic systems. For instance  in the laser-cooled cold atomic ensembles  the higher-order coefficients have a phase grating of e ink$_{c}$z across the atomic gases  and thus will decay due to atomic random motion. The de- cay rate can be estimated by the time needed for the atoms moving across one wavelength of the phase grat- ing γ$_{n}$ ∼ | v$_{s}$ λ | = n | k$_{c}$v$_{s}$ 2 π | [17]. In the Bose condensation  the higher-order coefficients can be regarded as a particle excitation with momentum | n | k$_{c}$ ℏ   At average  they move out of the atomic gases after a time of L $_{(}$| n | k$_{c}$ ℏ m ) − 1 [18]  and the decay rate can be approximated by γ$_{n}$ ∼ | n | k$_{c}$ ℏ mL . To check the validity of the approximate solution in Fig. 2 and further find the dynamics of the recreated light III. NUMERICAL SOLUTION