High-Capacity Spatial Multimode Quantum Memories Based on Atomic Ensembles

We study spatial multimode quantum memories based on light storage in extended ensembles of $\Lambda$-type atoms. We show that such quantum light-matter interfaces allow for highly efficient storage of many spatial modes. In particular, forward operating memories possess excellent scaling with the important physical parameters: quadratic scaling with the Fresnel number and even cubic with the optical depth of the atomic ensemble. Thus, the simultaneous use of both the longitudinal and transverse shape of the stored spin wave modes constitutes a valuable and so far overlooked resource for multimode quantum memories.

Figure 1

(left) Atomic ensemble of cylindrical symmetry with Gaussian density distribution of length $L$ and width ${\sigma }_{\perp }$ (gray/red cloud in the middle). Full lines: Multimode operation is achieved by focusing beams to a transverse size $r_{\perp }<{\sigma }_{\perp }$. For high optical depth it is an advantage to use light beams which are only focused inside the sample for a distance $L{d}_{\mathrm{crit}}/d$ shorter than the length of the sample, so that one can store multiple modes along the axis (dashed and dotted lines, see text for details). (right) A schematic plot of the level scheme of the considered $\Lambda$-type atoms.

Figure 2

The number of modes with efficiency $\eta >0.5$ (squares and circles) and the capacity $C_m$ (diamonds and stars) for different values of the azimuthal quantum number $m$ for forward (blue, bottom and left axes) and backward (black, top and right axes) operating memory with $d_0=100$ and $F=1$.

Figure 3

The capacity $C_f$ for forward (red closed circles and stars) and $C_b$ backward (black open circles and stars) operating memories as functions of the Fresnel number $F$ for $d_0=40$ (circles) and $d_0=100$ (stars). The number of modes for the forward memory $N_{m,f}$ for $d_0=100$ with the threshold efficiency ${\eta }_{\min }=0.5$ (light gray stars) and ${\eta }_{\min }=0.6$ (light gray triangles). The dashed lines are quadratic $C_f\sim F^2$ and linear $C_b\sim F$ fits for the forward and backward direction of the readout, respectively.

Figure 4

The number of modes for the forward operating memory with efficiency $\eta \ge 0.65$ for two values of the Fresnel number $F=0.2$ (black triangles) and $F=0.5$ (green stars) and the capacity $C_b$ of the backward operating memory for $F=0.2$ (red circles) and $F=0.5$ (blue squares). The dashed lines are the corresponding fits for the forward $N_f\sim d_0^3$ and backward $C_b\sim d_0^{3/2}$ direction of the readout, respectively.