Two-color quantum memory in double-$\Lambda$ media

We propose a quantum memory for a single-photon wave packet in a superposition of two different colors, i.e., two different frequency components, using the electromagnetically induced transparency technique in a double-$\Lambda$ system. We examine a specific configuration in which the two frequency components are able to exchange energy through a four-wave mixing process as they propagate, so the state of the incident photon is recovered periodically at certain positions in the medium. We investigate the propagation dynamics as a function of the relative phase between the coupling beams and the input single-photon frequency components. Moreover, by considering time-dependent coupling beams, we numerically simulate the storage and retrieval of a two-frequency-component single-photon qubit.

Figure 1

Double-$\Lambda$ atomic scheme coupled with single-photon frequency components, ${\widehat{E}}_{p1}^{+}$ and ${\widehat{E}}_{p2}^{+}$, and classical field amplitudes, $E_{c1}$ and $E_{c2}$, satisfying the two-photon resonance condition. The fields are detuned from the one photon resonance with corresponding detunings ${\delta }_{p1}$ and ${\delta }_{p2}$, with ${\delta }_{p1}\ll {\delta }_{p2}$. All the atoms are initially in state $\left|1\right.〉$.

Figure 2

(a) Normalized intensities of the single photon frequency components $I_1$ (black) and $I_2$ (gray), and (b) the relative phase between them for $\mathrm{Re}\left(\alpha \right)=2\pi /L$, with $L=0.1$ (a.u.) being the length of the medium, and $\mathrm{Im}\left(\alpha \right)=0$. Solid lines: $I_1\left(0\right)=0.99$, ${\varphi }_{12}=0$, ${\phi }_{12}=\pi /4$; dashed lines: $I_1\left(0\right)=0.85$, ${\varphi }_{12}=0$, ${\phi }_{12}=\pi /4$; dotted lines: $I_1\left(0\right)=0.70$, ${\varphi }_{12}=0$, ${\phi }_{12}=\pi /4$.

Figure 3

(a) Normalized intensities of the single-photon frequency components $I_1$ (black) and $I_2$ (gray), and (b) the relative phase between them for $\mathrm{Re}\left(\alpha \right)=2\pi /L$, with $L=0.1$ (a.u.) being the length of the medium, and $\mathrm{Im}\left(\alpha \right)=0$. Solid lines: $I_1\left(0\right)=0.5$, ${\varphi }_{12}=0$, ${\phi }_{12}=\pi /3$; dashed lines: $I_1\left(0\right)=0.5$, ${\varphi }_{12}=\pi /2$, ${\phi }_{12}=\pi /3$; dotted lines: $I_1\left(0\right)=0.5$, ${\varphi }_{12}=0$, ${\phi }_{12}=0$.

Figure 4

Normalized intensities of the single pulse frequency components, $I_1$ (a) and $I_2$ (b), as a function of normalized position and time, and (c) the phase between the frequency components at the pulse peak as a function of normalized position. The parameters correspond to the case represented with dotted lines in Fig. 2.

Figure 5

Temporal profile of the coupling beams (a) and normalized intensities of the single pulse frequency components, $I_1$ (b) and $I_2$ (c), as a function of normalized position and time. The parameters correspond to the case represented with dotted lines in Fig. 3.