Single-photon-level optical storage in a solid-state spin-wave memory

A long-lived quantum memory is a firm requirement for implementing a quantum repeater scheme. Recent progress in solid-state rare-earth-ion-doped systems justifies their status as very strong candidates for such systems. Nonetheless an optical memory based on spin-wave storage at the single-photon level has not been shown in such a system to date, which is crucial for achieving the long storage times required for quantum repeaters. In this paper we show that it is possible to execute a complete atomic frequency comb (AFC) scheme, including spin-wave storage, with weak coherent pulses of $\overline{n}=2.5\pm 0.6$ photons per pulse. We discuss in detail the experimental steps required to obtain this result and demonstrate the coherence of a stored time-bin pulse. We show a noise level of $(7.1\pm 2.3)\times {10}^{-3}$ photons per mode during storage, and this relatively low noise level paves the way for future quantum optics experiments using spin waves in rare-earth-doped crystals.

Figure 1

(a) The atomic level scheme of the optical transition ${}^{7}F$${}_0{\to }^5$$D$${}_0$ in ${}^{151}$Eu${}^{3+}$:Y${}_2$SiO${}_5$. (b) A schematic of the experimental setup around the memory; the rest of the experiment has been suppressed for simplicity. The control and preparation beam is in single pass (wide labeled arrow). The input mode (thin dashed line) is in double pass, with the help of a Faraday rotator (FR) and a polarizing beam splitter (PBS). On return from the crystal the input mode passes through a Fabry-Perot (FP) cavity (bandwidth of 7.5 MHz). A classical detector (Sd) and 10 $\mu$W of horizontally polarized light (thin dotted line) are used to actively and intermittently stabilize the cavity to the frequency of the input mode. An acousto-optical modulator (AOM) in double pass acts as a detector gate.

Figure 2

Storage of a weak coherent pulse with (a) $\overline{n}=2.5\pm 0.6$ and (b) $\overline{n}=11.2\pm 0.6$. The input mode recorded with no comb, the position of the control fields (C1 and C2), and finally a magnified ($\times$30) signal of the AFC spin-wave echo (blue dashed curve), the associated noise without an input pulse (green dotted curve), and the detector dark counts (red curve) are shown. Note that the total measurement time differs between the data sets in panels (a) and (b). (c) The same echo data of panel (a) with the temporally separated off-resonant echo (OREO). (d) Signal-to-noise ratio (SNR) for different $\overline{n}$. Shown is also a fitted linear slope fixed to 1 at $\overline{n}=0$ by definition.

Figure 3

(a) The method used to measure the coherence of the AFC spin-wave echoes. The single-write operation of Figs. 2a and 2b (C1) is replaced by a double-write operation (W1, W2). If the temporal separation ($T$) of the input mode is equal to that of the double-write operation, the first echo of the second write operation and second echo of the first operation interfere. (b) The visibility curve for two pulses with $\overline{n}=176\pm 8$. (c) The signal of a constructive and destructive case. The thick dashed lines show the temporal window which was used to obtain the interference curve. The detector gate has cut some of the first echo and the OREO is not shown in this temporal slice.

Figure 4

Experimental data, showing some of the main characteristics of the OREO. These include the emission frequency (a), the effect of the application of the first control field (C1) (b), and the relation between the magnitude of the OREO and the FWHM of the control field (c). Finally, in panel (d), we show the change in structure of the OREO, depending on the shape of the control fields used. See text for more details.

Figure 5

Experimental results showing the signal-to-noise (SNR) ratio as a function of the FWHM of the control pulse (see text for details). The average number of photons in the input pulse was 4.5 $\pm$ 0.5.

Figure 6

Simulations using a two-level Bloch equation simulator. Panel (a) shows the calculated transfer efficiency of a single control field. Panel (b) shows the off-resonant excitation probability, $+$35.4 MHz away from the carrier frequency. The horizontal scale shows the FWHM of a Gaussian pulse defined with the time slot of 2 $\mu$s. The thick (green online) line shows the optimal experimental FWHM.