Efficient spatially resolved multimode quantum memory

Light storage in atomic ensembles has been implemented successfully, but the retrieval efficiency can be low. We propose to improve this efficiency with appropriately phase-matched backward propagating retrieval. This method allows for easy spatial filtering of the retrieved light; in addition, multiple optical modes can be stored in the transverse momentum of the ensemble. We model walk-off effects with a full numerical simulation, and confirm the applicability of the scheme.

Figure 1

(Color online) (a) The level structure of the atoms in a typical ensemble memory. (b) A schematic of the storage process, in which an incident signal field is converted to a distributed excitation within the ensemble known as a spin wave.

Figure 2

(Color online) (a) A general phase-matching diagram for the combined storage and retrieval processes. (b) The phase-matching diagram for our proposed scheme.

Figure 3

(Color online) Comparison of numerical results for the optimal angle $\theta$ with the prediction in Eq. (1) (solid line). The filled circles correspond to tight control focusing, with $w_c=w_s$; the open diamonds correspond to loose focusing, with $w_c=2w_s$. We plot the results for a typical EIT protocol in (a): the signal pulse bandwidth is of order $\gamma$, the ensemble optical depth is $d=30$. In (b) we present equivalent results for a Raman protocol, with the larger optical depth of $d=300$. The signal bandwidth is of order $10\gamma$ and the detuning is $\Delta =150\gamma$.

Figure 4

(Color online) Memory efficiencies versus the phase mismatch $\delta \chi$. (a) and (b) contain the results for the EIT protocol, with tight and loose focusing, respectively. (c) and (d) report the results for the Raman protocol for tight and loose focusing. The solid lines represent the efficiencies achieved if the angles predicted by Eq. (1) are used. The filled circles are the best efficiencies achievable. The dotted lines delimit the optimal efficiency attainable using collinear backwards retrieval, calculated using the one-dimensional theory described in Appendix . The dashed straight lines denote the efficiencies achieved using collinear forwards retrieval.

Figure 5

(Color online) Efficiency versus optimal phase-matching angle. The solid lines correspond to tight control focusing $w_c=w_s$, the dotted lines to looser focusing, with $w_c=2w_s$. Each line has two “branches”: the upper branch is achieved for positive momentum mismatch, the lower for negative momentum mismatch. The results for the EIT protocol are plotted in (a); those for the Raman protocol in (b).

Figure 6

(Color online) (a) Memory efficiency versus deviation angle ${\theta }_d$ for an EIT protocol with a wide control beam $w_c=9w_s$. The dotted line corresponds to zero phase mismatch, the solid line to $\delta \chi =1$. (b) Angular multiplexing. Different signal fields may be stored with different angles $\theta$. Provided the difference $\delta \theta$ in angle between adjacent modes is large enough, the modes are “holographically isolated” and may be addressed, and resolved, independently. The largest angle $\Delta \theta$ for which the memory protocol is acceptably efficient sets a limit to the multimode capacity of such a multiplexed memory.