On-Demand Superradiant Conversion of Atomic Spin Gratings into Single Photons with High Efficiency

We create quantized spin gratings by single-photon detection and convert them on demand into photons with retrieval efficiencies exceeding 40% (80%) for single (a few) quanta. We show that the collective conversion process, proceeding via superradiant emission into a moderate-finesse optical resonator, requires phase matching. The storage time of $3\mu \mathrm{s}$ in the cold-atom sample, as well as the peak retrieval efficiency, are likely limited by Doppler decoherence of the entangled state.

Figure 1

(a) Experimental setup for the creation, storage, and on-demand retrieval of quantized spin gratings in an atomic sample by single-photon detection. Beam propagation directions, linear polarizations, and optical-cavity orientation are indicated. (b) Idealized atomic energy level diagram.

Figure 2

Conversion of quantized spin grating into photons. The emission probability $P$ per 200 ns (detected photon number multiplied by $Q^{-1}=20$) is shown versus time $t$. When the write pump is applied for 600 ns, the sample scatters photons into the cavity (thick black line). Application of the read pump after various time delays results in collective emission (thin lines). The inset shows $P(t)$ at a mean emitted write photon number of $M_w=0.06$ and a retrieval efficiency of $(57\pm 15)\%$. The dashed line indicates the read background.

Figure 3

Tests of phase matching. The retrieval efficiency $R$ is plotted versus angle between the write and read pump beams. A Gaussian fit (solid line) to the central peak indicates a $1/e^2$ width of 0.9(1) mrad. In the inset, retrieval efficiency is plotted versus write pump frequency for two different read pump frequencies, so that the transverse cavity mode for which read emission is resonant differs by 15 MHz between the two curves. Each curve is taken with the cavity frequency and read pump frequency fixed.

Figure 4

Retrieval efficiency $R$ of hyperfine (solid dots, $M_w=1$) or magnetic (open circles, $M_w=120$) excitations. $M_w$ is the detected write photon number multiplied by the inverse detection efficiency $Q^{-1}=20$. (a) Gaussian fits (dashed curves) to $R$ vs storage time give time constants of $3.4(9)\mu \mathrm{s}$ and $1.7(2)\mu \mathrm{s}$. The inset shows average retrieval $\overline{R}=0.44(3)$ for one stored quantum, $M_w\ll 1$. (b) Retrieval improves with increasing read pump power (scattering rate).