Mapping broadband single-photon wave packets into an atomic memory

We analyze a quantum optical memory based on the off-resonant Raman interaction of a single broadband photon, copropagating with a classical control pulse, with an atomic ensemble. The conditions under which the memory can perform optimally are found, by means of a universal mode decomposition. This enables the memory efficiency to be specified in terms of a single parameter, and the control field pulse shape to be determined via a simple nonlinear scaling. We apply the same decomposition to determine the optimal configurations for read-out.

Figure 1

(Color online) Left: the level structure of the $i\text{th}$ atom comprising a quantum memory for broadband photons, with bandwidth $\delta$. Right: a schematic of the read-in process for the quantum memory.

Figure 2

(Color online) The five largest singular values of the kernel $G_0$, plotted as a function of the coupling parameter $C$.

Figure 3

(Color online) Left: the intensity $⟨A^{†}(\tau ,z)A(\tau ,z)⟩$ of a Gaussian signal photon $\mid 1_{\xi }⟩$, with wave packet amplitude $\xi \left(\tau \right)\propto \exp \{-2\ln 2{[(\tau -{\tau }_0)∕\sigma ]}^2\}$, as it propagates through an atomic ensemble with $C=2$. Here $\sigma =T∕8$, ${\tau }_0=2T∕3$. Right: the optimized control field intensity is shown along side the initial signal field intensity (scaled for clarity).

Figure 4

(Color online) The photon retrieval probability $\mathcal{N}$, for forward read-out, plotted as a function of the read-in and read-out coupling parameters $C$ and $C^r$.