Manipulating Light Pulses via Dynamically Controlled Photonic Band gap

When a resonance associated with electromagnetically induced transparency in an atomic ensemble is modulated by an off-resonant standing light wave, a band of frequencies can appear for which light propagation is forbidden. We show that dynamic control of such a band gap can be used to coherently convert a propagating light pulse into a stationary excitation with nonvanishing photonic component. This can be accomplished with high efficiency and negligible noise even at the level of few-photon quantum fields thereby facilitating possible applications in quantum nonlinear optics and quantum information.

Figure 1

Atomic level configuration for EIT-induced photonic band gap. (a) Stationary atoms scheme, (b) moving atoms scheme. The standing wave of Rabi frequency ${\Omega }_s$ is detuned by $\Delta$ from resonance with the $|c⟩\to |d⟩$ transition, giving rise to the spatially modulated light shift ${\Delta }_s(z,t)=|{\Omega }_s(z,t){|}^2/\Delta$.

Figure 2

(a) Dispersion relation $\omega (K)$ for waves propagating in EIT-induced band gap medium. Plotted is the detuning from two-photon resonance $\omega -{\omega }_{ab}$ in units of linewidth $\gamma$ vs the Bloch wave vector $K$ in units of $\gamma /v_g$. For $|\omega -{\omega }_{ab}|\gg \gamma$, we have $\omega =cK$, while near resonance $\omega =v_{g}K$. For $|\omega -{\omega }_{ab}|\le {\Delta }_s$, a band gap appears, as shown in the inset (full line: real part of $K-k_s$; dashed line: imaginary part). (b) Reflection coefficient vs frequency near EIT resonance for ${}^{\mathrm{87}}\mathrm{R}\mathrm{b}$ atoms with density $n\sim {10}^{12}{\mathrm{c}\mathrm{m}}^{-3}$, length of medium $L\sim 4\mathrm{c}\mathrm{m}$, ${\gamma }_{bc}\sim 1\mathrm{k}\mathrm{H}\mathrm{z}$, $\gamma \sim 5\mathrm{M}\mathrm{H}\mathrm{z}$, $c/v_g\sim {10}^5$, ${\Omega }_s\sim 2\gamma$, and $\Delta \sim 1\mathrm{G}\mathrm{H}\mathrm{z}$ (${\Delta }_s={\Omega }_s^2/\Delta \sim 100\mathrm{k}\mathrm{H}\mathrm{z}$), giving a peak reflectivity of $\sim 97\%$.

Figure 3

(a) Evolution of forward and backward propagating polaritons ${\Psi }_{+}(z,t)$ and ${\Psi }_{-}(z,t)$ as calculated from (7). (b) Corresponding electric fields and (c) total intensity (forward and backward components) averaged over the optical wavelength. Also shown is the time dependence of the control field ${\Omega }_c(t)$ (solid grey line) and of the standing wave field ${\Omega }_s(t)$ (dashed black line). Note that $v_g^{in}/v_g^0\sim 15$ here so that initial motion of the pulse is noticeable on these plots. Axes are in arbitrary units.