All-optical quantum storage based on spatial chirp of the control field

We suggest an all-optical quantum memory scheme which is based on the off-resonant Raman interaction of a signal quantum field and a strong control field in a three-level atomic medium in the case where the control field has a spatially varying frequency across the beam, called a spatial chirp. We show that the effect of such a spatial chirp is analogous to the effect of a controllable reversible inhomogeneous broadening of the atomic transition used in the gradient echo memory scheme. The proposed scheme does not require temporal modulation of the control field or the atomic levels and can be realized without additional electric or magnetic fields. This means that materials demonstrating neither linear Stark nor Zeeman effects can be used and/or materials which are placed in specific external fields remain undisturbed.

Figure 1

(a) Energy diagram of the off-resonant Raman interaction in a three-level $\Lambda$ system. The angular frequencies of the signal and control fields are ${\omega }_s$ and ${\omega }_c$, respectively; $\Delta$ is the one-photon detuning between the fields and the corresponding atomic transitions. The control field spectrum width is given by the spatial chirp $\Delta {\omega }_c$, which is $\beta L$ for the transverse excitation setup. (b, c) Transverse excitation setup in which the propagation directions of the signal and the control fields are perpendicular to each other: The signal, propagating along the $z$ axis of the cylindrical medium, experiences only the longitudinal inhomogeneity of the Raman interaction with the control field that is spatially chirped along the $z$ axis. During storage (b), the temporal profile of the signal field is mapped into a pattern of the spin wave (Raman coherence) distribution due to the Raman interaction of the signal with the longitudinally chirped control field. During retrieval (c), the stored spin-wave generates the output signal field and the spin-wave spatial pattern is mapped back into the output-signal temporal profile.

Figure 2

(a–d) Forward retrieval signal amplitude $|a_{\text{out}}\left(\tau \right)|$ (phase modulation is not shown in the figure but is taken into account in the fidelity ${\mathcal{F}}^{\prime })$ as a function of the retarded time in the transverse excitation regime for different values of the spatial chirp $\beta L$ across the control beam [(b) $2\pi \sqrt{2ln2}/\Delta t$, (c) $4\pi \sqrt{2ln2}/\Delta t$, (d) $8\pi \sqrt{2ln2}/\Delta t]$ for the (a) Gaussian temporal shape input signal field $a_{\text{in}}\left(\tau \right)$ with a FWHM duration $\Delta t=(\sqrt{2ln2}/15)T$, where $T$ is the duration of the writing process. (e, f) A double-peak Gaussian temporal shape input signal field (e) and its forward retrieval signal amplitude (f) for $\beta L=4\pi \sqrt{2ln2}/\Delta t$. The graphs are plotted for the parameter ${\left|g\right|}^{2}NL\Delta t=13.78$.