Pulse retrieval and soliton formation in a nonstandard scheme for dynamic electromagnetically induced transparency

We examine in detail an alternative method of retrieving the information written into an atomic ensemble of three-level atoms using electromagnetically induced transparency. We find that the behavior of the retrieved pulse is strongly influenced by the relative atom-light coupling strengths of the two relevant transitions. When the individual atom-light coupling strength for the retrieval beam is the stronger of the two transitions, regeneration of the stored pulse is possible. Otherwise, we show the retrieval process can lead to creation of solitonlike pulses.

Figure 1

Level structure of the atoms.

Figure 2

Envelope of pulses entering the medium at $z=0$ as a function of time. (a) ${\Omega }_p$ is the field driving the $\mid b⟩\leftrightarrow \mid a⟩$ transition and (b) ${\Omega }_c$ is the field driving the $\mid c⟩\leftrightarrow \mid a⟩$ transition. The parameters are $T_{\text{off}}=140{\gamma }^{-1},T_s=18.85{\gamma }^{-1},T_{\text{on}}=259{\gamma }^{-1},{\Omega }_p^0=0.0265\gamma$, and ${\Omega }_c^0=2.6526\gamma$. Amplitudes of pulses are displayed in units of $\gamma$. The input pulse to be stored is ${\Omega }_p$ before the start of storage. The retrieved pulse is ${\Omega }_c$ after the storage process.

Figure 3

Comparison of (a) amplitude and (b) phase of both the retrieved and input pulses. The solid line represents the retrieved pulse and the dashed line the input pulse (magnified by a factor of 10). The parameters are $N{\mid g_p\mid }^2=30177\gamma ,N{\mid g_c\mid }^2=29272c\gamma$, and $l=4\mathrm{cm}$. The input pulses are as shown in Fig. 2. The large amplitude on the retrieval pulse transition at earlier times is because the field on this transition was used as the writing beam initially. Similarly the large value on the input pulse transition at later times represents the retrieval beam.

Figure 4

Amplitude (a) and phase (b) of ${\rho }_{cb}$ during storage.

Figure 5

Spatial variation of the retrieval beam divides the medium into three regions as described in the text. At any time, the retrieved pulse is generated due to the dynamics that occur in region II where the retrieval beam is in the process of pumping population out of state $\mid b⟩$. In region I, all atoms are in state $\mid c⟩$. The beam has not yet penetrated to region III.

Figure 6

(a) ${\rho }_{cc}$ (dashed line) and ${\rho }_{aa}$ (solid line) as a function of $z$ during the retrieval process. A significant population resides in the excited state during the retrieval process. (b) $\mid {\rho }_{cb}(0.024,\tau )\mid$ as a function of $\tau {\gamma }^{-1}$. The spike in the graph shows the effect of optical pumping by the retrieval beam which overwrites the stored coherence.

Figure 7

Comparison of (a) amplitude and (b) phase of retrieved (solid line) and input (dashed line) pulses. The input pulse has been magnified by a factor of 10. The amplitude of the retrieval beam is now ${\Omega }_p^0=5.3052\gamma$, twice the value in Fig. 3. We see that the retrieved pulse is made earlier in time and narrower in time because of the increased pumping rate by the retrieval beam. All other parameters are identical to those in Fig. 3.

Figure 8

Comparison of (a) amplitude and (b) phase of retrieved (solid line) and input (dashed line) pulses. The input pulse has been magnified by a factor of 10. The abrupt cutoff of the retrieved pulse near $\tau {\gamma }^{-1}=600$ is due to the arrival of the retrieval beam at the exit of the cell $z=0.04$ which pumps all atoms into state $\mid c⟩$ and prevents any field existing on this transition. The parameters are $N{\mid g_p\mid }^2=N{\mid g_c\mid }^2=30177\gamma$ and $l=4\mathrm{cm}$. The input pulses are as given in Fig. 2.

Figure 9

Comparison of (a) amplitude and (b) phase of retrieved (solid line) and input (dashed line) pulses. The input pulse has been magnified by a factor of 10. The parameters are $N{\mid g_p\mid }^2=30177c\gamma <N{\mid g_c\mid }^2=31082c\gamma$ and $l=4\mathrm{cm}$. The input pulses are as given in Fig. 2.

Figure 10

Comparison of amplitudes of input pulse (dashed line) magnified by a factor of 10 and output pulse (solid line) for the three parameter regimes ${\mid g_p\mid }^2>{\mid g_c\mid }^2$ (a), ${\mid g_p\mid }^2={\mid g_c\mid }^2$ (b), and ${\mid g_p\mid }^2<{\mid g_c\mid }^2$ (c).

Figure 11

$\mid {\Omega }_p\mid$ (dashed line), $\mid {\Omega }_c\mid$ (dash-dotted line), and $\mid {\rho }_{cb}\mid \times 5$ (solid line) as a function of $z$ at times $\tau {\gamma }^{-1}=477.6$ (a), 489 (b), and 501.6 (c) for the ${\mid g_p\mid }^2={\mid g_c\mid }^2$ case. The field and atomic coherences propagate together unchanged across the cell.