Cavity-assisted atomic Raman memories beyond the bad cavity limit: Effect of four-wave mixing

Quantum memories can be used not only for storage of quantum information but also for a substantial manipulation of ensembles of quantum states. Therefore, the speed of such manipulation and the ability to write and retrieve signals of relatively short duration become important. One approach towards enhancing the performance of a quantum memory is to combine an active medium with an optical cavity. Previous works investigating cavity-enhanced memories concentrated on noise processes in the bad cavity limit, that is, for signals that are much longer than the cavity field lifetime. In this work we investigate four-wave mixing noise that arises from the retrieval of relatively short signals from cavity-assisted memories, thus complementing recent works by other authors. We propose an approach that allows one to account for noise sources of different frequencies and different physical origin by using two-band spectral filtering of the noise sources in the Heisenberg-Langevin picture. We demonstrate that in these spectrally selective memories the sideband atomic noise sources contribute to the four-wave mixing noise on par with the sideband quantized field entering the cavity.

Figure 1

Raman atomic memory schematic. A control field (double arrows) induces two-quantum Raman transitions in both $\mathrm{\Lambda }$ schemes. A cavity field (solid arrow) and a sideband noise field (dashed arrow) are generated via two-quantum transitions in the memory and luminescence channels, respectively. A signal is stored in the Raman coherence between the lower levels of the scheme (gray arrow).

Figure 2

The spin amplitude for the normalized retrieved signal ${\mathcal{E}}_0\left(t\right)$ of duration $2\kappa T=4$, 8, 12, 16, 20 (in units of the cavity excitation lifetime). At some time moments $t_s$, the collective spin excitation is completely mapped onto the cavity field, and the inverse process of the cavity field reabsorption begins in order to shape properly the rear slope of the signal. The shorter the signal is, the larger the fraction of initial atomic excitation is reabsorbed by the memory cell, thus reducing the memory quantum efficiency.

Figure 3

The added noise variance $4{〈{\left(\mathrm{\Delta }{Q}_d\right)}^2〉}^{\left(\mathrm{add}\right)}$ (curve 1) and the contributions $1-\eta$ (curve 2) and $2|G_{d-}{|}^2$ (curve 3), associated with the different-from-unity retrieval quantum efficiency $\eta$ and with the four-wave mixing noise, respectively. As we have demonstrated, the four-wave mixing term stems from both the quantized field and the atomic noise sources. The added noise variance exhibits a significant increase for short signals, especially the contribution $1-\eta$, which is sensitive to a partial signal field reabsorption beyond the bad cavity limit, as illustrated in Fig. 2. In the bad cavity limit (actually for $2\kappa T>15,\cdots ,20$), the quantum efficiency is limited by the excitation of lower atomic sublevels by the control field and by the cavity field absorption.