Theory of noise suppression in $\mathrm{\Lambda }$-type quantum memories by means of a cavity

Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of $\mathrm{\Lambda }$-type atoms. However, at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here, we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory.

Figure 1

(a) A control field (green) mediates the storage of a signal field (red) in a free-space $\mathrm{\Lambda }$ memory. The control field can drive the spontaneous Raman emission of an anti-Stokes field (blue) that generates a spurious excitation in the memory. (b) Atomic transitions driven in the storage interaction, (c) the retrieval interaction. (d) Four-wave mixing noise refers to the retrieval of the spurious excitation generated by the anti-Stokes scattering.

Figure 2

(a) We model the dynamics of the cavity-enhanced $\mathrm{\Lambda }$ memory by considering the propagation of Stokes and anti-Stokes fields around a ring cavity through a storage medium comprising an ensemble of $\mathrm{\Lambda }$-type atoms. The boundary conditions imposed by the input-output coupler with amplitude reflectivity $r$ connects the intracavity fields to the incident and emitted fields. (b) The cavity resonances are tuned to suppress the density of scattering states (black peaks) at the anti-Stokes frequency with respect to the Stokes frequency. In our theoretical treatment, we allow arbitrary tuning of the Stokes and anti-Stokes fields with respect to the cavity resonances. By choosing the round-trip phases ${\varphi }_{\mathrm{s}}=0$ (Stokes on resonance) and ${\varphi }_{\mathrm{a}}=\pi$ (antiresonant anti-Stokes), we achieve the optimal suppression depicted in the plot. Tuned midway between the Stokes and anti-Stokes frequencies, the control field can be resonantly coupled into the cavity in an orthogonal polarization mode (gray peaks) [37].

Figure 3

The predicted efficiency ${\eta }_{\mathrm{tot}}$ and autocorrelation $g_{\mathrm{out},2}^{\left(2\right)}$ for the storage of single photons, heralded with efficiency $N_{\mathrm{in},1}=0.5$, in a cavity-enhanced Raman memory, as described in the text, with input-output coupler reflectivities $r=0.9$ [(a),(b)] and $r=0.95$ [(c),(d)], and a range of intracavity round-trip intensity losses (see legend).