Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening

We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening. The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.

Figure 1

(Color online) Schematic representation of the spectral atomic distribution. The initial distribution $G_0\left({\Delta }_0\right)$ with characteristic bandwidth ${\gamma }_0$ is represented as a black dotted line. Three spectral components of the initial distribution are considered [blue, black, and red vertical lines (shown left to right)] and each of them is broadened according to a distribution $G^{\prime }\left({\Delta }^{\prime }\right)$ [blue, black, and red dashed lines (left to right)] with bandwidth $\gamma$. The final broadened distribution, called $G\left(\Delta \right)$, is the convolution of the initial distribution $G_0\left({\Delta }_0\right)$ and of the broadened distribution $G^{\prime }\left({\Delta }^{\prime }\right)$ associated to a single initial absorption line $\left({\Delta }_0\right)$. The pulse shape with bandwidth $\Gamma$ is represented as a green dashed-dotted line.

Figure 2

(Color online) Efficiency of the light pulse reemission in forward (full blue line) and backward (dashed black line) direction as a function of the optical depth for a constant broadening. The efficiencies vary as ${\left(\alpha L\right)}^2{e}^{-\alpha L}$ for the forward protocol and as ${(1-e^{-\alpha L})}^2$ for the backward protocol.

Figure 3

(Color online) Efficiency of the light pulse reemission for forward (full blue line) and backward (dashed black line) protocol as a function of the broadened distribution bandwidth $\gamma$ (in units of the pulse bandwidth $\Gamma$) for effective widths of the initial distribution $\nu =2\Gamma$ (top) and $\nu =0.05\Gamma$ (bottom).

Figure 4

(Color online) Comparison of memory efficiencies for a spectral distribution of atoms and light pulse with identical shapes (forward: full blue line; backward: dashed black line) and with different shapes (forward: dashed-dotted red line; backward: dotted red line) as a function of the inhomogeneous bandwidth (in units of the pulse bandwidth). The effective width of the initial distribution $\nu$ is taken equal to $2\Gamma$.