Storage and retrieval of Airy light wave packets in a coherent atomic system

We propose a scheme to realize the storage and retrieval of Airy light wave packets in a $\Lambda$-type three-level atomic gas via electromagnetically induced transparency. We first show that (1 + 1)-dimensional Airy light wave packets with very slow propagating velocity and extremely low generation power can be stored and retrieved by switching off and on a control field. We then demonstrate that ultraslow and ultraweak (3 + 1)-dimensional light wave packets, by combining a spatial Bessel or Airy beam with an Airy temporal profile, can also be generated, stored, and retrieved in a controllable way. Because the Airy light wave packets obtained can withstand both diffraction and dispersion in a linear propagation regime, their storage and retrieval are more desirable and promising for quantum information processing in comparison with other types of light wave packets.

Figure 1

(a) Energy-level diagram and excitation scheme of $\Lambda$-type three-level atoms interacting with a weak pulsed probe field $E_p$ and a strong continuous-wave control field $E_c$. Here ${\Delta }_2$ and ${\Delta }_3$ are the two- and one-photon detunings, respectively and ${\Gamma }_{13}$ $\left({\Gamma }_{23}\right)$ is the decay rate from $|3\rangle$ to $|1\rangle$ $(|3\rangle$ to $|2\rangle )$. The initially populated atoms are indicated by black dots. (b) Plot of $\mathrm{Im}\left(K\right)$ (upper) and $\mathrm{Re}\left(K\right)$ (lower) as functions of $\omega$ for ${\Omega }_c=1.0\times {10}^7$ ${\mathrm{s}}^{-1}$, respectively.

Figure 2

(a) Evolution of a typical (1 + 1)D Airy light wave packet $|{\Omega }_p|{\tau }_0$ as a function $t/{\tau }_0$ with $a=0.05$. (b) Evolution of a Gaussian light wave packet. In both panels, curves indicated by 1–7 with different colors are $|{\Omega }_p|{\tau }_0$ for $z/L_D=0.6j$ $\left(j=0,1,...,6\right)$. The corresponding evolution of the control field $|{\Omega }_c|{\tau }_0$ is also shown (i.e., the curves in the upper part of each panel).

Figure 3

Storage and retrieval of the (1 + 1)D Airy light wave packet by switching off and on the control field. (a) Plot of $|{\Omega }_p|{\tau }_0$ as a function of $t/{\tau }_0$. Curves indicated by 1–7 with different colors are for $z/L_D=0.6j$ $\left(j=0,1,...,6\right)$. (b) Evolution of the atomic coherence ${\sigma }_{21}$ as a function of $t/{\tau }_0$. Curves indicated by 1–7 with different colors are for $z/L_D=0.6j$ $\left(j=0,1,...,6\right)$. Also shown in (a) and (b) is the corresponding evolution of the control field $|{\Omega }_c|{\tau }_0$ (i.e., the curves in the upper part of each panel). The corresponding 3D plots of $|{\Omega }_p|{\tau }_0$ and $|{\sigma }_{21}|$ as functions of $t/{\tau }_0$ and $z/L_D$ are shown in (c) and (d), respectively.

Figure 4

Airy-Bessel light wave packet. (a) The Bessel beam in the $x-y$ plane for $z/L_D=1.2j$ $(j=0,1,2,3$ from left to right). (b) Intensity isosurfaces of the (3 + 1)D light wave packet at $z/L_D=0$ and $3.6$ in 3D space, respectively.

Figure 5

Airy-Airy-Airy light wave packet. (a) The 2D Airy beam in the $x-y$ plane for $z/L_D=1.2j$ $(j=0,1,2,3$ from left to right). (b) Intensity isosurfaces of the (3 + 1)D Airy light wave packet at $z/L_D=0$ and $3.6$, respectively.

Figure 6

Storage and retrieval of the (3 + 1)D Airy light wave packets. Results are shown for spatial distributions of the (3 + 1)D Airy light wave packets in the $x-y$ directions for $z/L_{\mathrm{diff}}=1.2$ at (a) $t/{\tau }_0=0$, (b) $t/{\tau }_0=5$, (c) $t/{\tau }_0=10$, (d) $t/{\tau }_0=15$, and (e) $t/{\tau }_0=20$ [corresponding to the dots labeled a, b, c, d, and e in (f)]. The upper (lower) part in each panel is for the Airy-Bessel (Airy-Airy-Airy) light wave packet. Panel (f) shows $|{\Omega }_p|{\tau }_0$ (solid line) and $|{\Omega }_c|{\tau }_0$ (dashed line) as functions of $t/{\tau }_0$ for $z/L_D=1.2$. The gray domain indicates the switching-off period of the control field.