Solid-State Source of Nonclassical Photon Pairs with Embedded Multimode Quantum Memory

The generation and distribution of quantum correlations between photonic qubits is a key resource in quantum information science. For applications in quantum networks and quantum repeaters, it is required that these quantum correlations be stored in a quantum memory. In 2001, Duan, Lukin, Cirac, and Zoller (DLCZ) proposed a scheme combining a correlated photon-pair source and a quantum memory in atomic gases, which has enabled fast progress towards elementary quantum networks. In this Letter, we demonstrate a solid-state source of correlated photon pairs with embedded spin-wave quantum memory, using a rare-earth-ion-doped crystal. We show strong quantum correlations between the photons, high enough for performing quantum communication. Unlike the original DLCZ proposal, our scheme is inherently multimode thanks to a built-in rephasing mechanism, allowing us to demonstrate storage of 11 temporal modes. These results represent an important step towards the realization of complex quantum networks architectures using solid-state resources.

Figure 1

(a) The experimental setup. The memory crystal, a 5-mm-long, 0.05%-doped ${\mathrm{Pr}}^{3+}:\mathrm{YSO}$, is hosted in a Montana Instruments Cryostation. The write and read pulses are counterpropagating. Their polarization is rotated along the $D_2$ crystal axis in order to maximize the absorption. Narrow-band filters at 600 nm (width 10 nm) are placed on both Stokes and anti-Stokes modes. The Stokes photons are fiber coupled to the detector with about 75% transmission. The anti-Stokes photons are first temporally gated by two acoustic optical modulators (AOMs) and later spectrally filtered by a 1-MHz-wide spectral hole at the ${1/2}_g\text{−}3/2_e$ transition frequency burned in a second ${\mathrm{Pr}}^{3+}:\mathrm{YSO}$ crystal, 3 mm long, also at 3.5 K. The total transmission in the anti-Stokes arm, from the cryostat to the detector, is typically 24%. We use two silicon single-photon detectors (SPDs) for the detection of both photons. (b) Hyperfine splitting of the first sublevels (0) of the ground ${}^3{H}_4$ and the excited ${}^1{D}_2$ manifolds of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$. The AFC structure (blue comb) is prepared with the read mode. (c) Temporal pulse sequence. The write pulses are $1\mu \mathrm{s}$ long (FWHM), and have a negative frequency chirp with a hyperbolic tangent waveform of 800 kHz. The read pulses, sent $8\mu \mathrm{s}$ after the write pulses, have power of 24 mW, duration of 900 ns (FWHM), and frequency chirp of +800 kHz with a hyperbolic tangent waveform. $T_{\mathrm{S}}$ ($T_{\mathrm{AS}}$) is the time separation between a Stokes (anti-Stokes) photon and the write (read) pulse. $T$ is the width of the Stokes detection window. For one AFC preparation we send 500 write-read pairs every $313\mu \mathrm{s}$ for $P_w\le 128\mu \mathrm{W}$. For higher $P_w$ we decrease the number of trials to prevent deterioration of the AFC.

Figure 2

(a) Stokes count rate in a $2\text{−}\mu \mathrm{s}$ detection window, for $P_w=16\mu \mathrm{W}$. (b) Stokes counts as a function of the position of a 1-MHz-wide spectral hole burned in the filter crystal. The 0 frequency corresponds to the frequency of the write pulse. The dotted gray horizontal line is the noise given by the detector dark counts. (c) Probability to create Stokes photons as a function of the write pulse power. The solid curve is a linear fit of the experimental data points. (d) Anti-Stokes count rate. The dotted vertical bars indicate the temporal mode where the anti-Stokes photons correlated to the Stokes photons of panel (a) should lie to satisfy the condition ${\mathrm{T}}_{\mathrm{S}}+{\mathrm{T}}_{\mathrm{AS}}={\tau }_{\mathrm{AFC}}$. This histogram shows a peak at around $8.5\mu \mathrm{s}$ originated from the second echo of the write pulse leaked into the anti-Stokes mode. Note that this peak is not in the temporal mode of the correlated anti-Stokes photons. Nevertheless, from the Gaussian fit of the two peaks we infer a contribution to the anti-Stokes counts of around 4%.

Figure 3

(a) Coincidence counts between Stokes and anti-Stokes photons as a function of the sum $T_{\mathrm{S}}+T_{\mathrm{AS}}$. The bin size is $\mathrm{\Delta }\tau =400\mathrm{ns}$. The shaded area indicates the time window used to calculate the $g_{\mathrm{S},\mathrm{AS}}^{(2)}(\mathrm{\Delta }\tau =1\mu \mathrm{s})$ value. We also observe a smaller peak at $11\mu \mathrm{s}$, due to the noise generated by the second AFC echo of the write pulse [see Fig. 2]. However, this peak is also present when Stokes and anti-Stokes photons are detected in different trials and, therefore, does not correspond to correlated photons. (b) Coincidence counts per hour between Stokes and anti-Stokes photons in the $1\text{−}\mu \mathrm{s}$-wide temporal mode around ${\mathrm{T}}_{\mathrm{S}}+{\mathrm{T}}_{\mathrm{AS}}={\tau }_{\mathrm{AFC}}=8\mu \mathrm{s}$ in the same storage trial (bar at 0) and in different storage trials separated by multiples of $313\mu \mathrm{s}$. The $g_{\mathrm{S},\mathrm{AS}}^{(2)}$ value is calculated as the ratio between the coincidences in the same storage trial and the average of the coincidences in different storage trials. The inset shows the peak in the $g_{\mathrm{S},\mathrm{AS}}^{(2)}$ with a bin size of $\mathrm{\Delta }\tau =400\mathrm{ns}$. The fit of the correlation peak to a Gaussian curve, done over a $2\text{−}\mu \mathrm{s}$ window around the peak, is also shown. (c) $g_{\mathrm{S},\mathrm{AS}}^{(2)}$ value (squares) and readout efficiency (diamonds) as a function of the Stokes creation probability, $P_{\mathrm{S}}$, calculated by the raw detection counts backpropagated at the crystal using known losses. The black horizontal line sets the classical threshold for the $g_{\mathrm{S},\mathrm{AS}}^{(2)}$ given by the Cauchy-Schwarz inequality.

Figure 4

Readout efficiency (a) and $g_{\mathrm{S},\mathrm{AS}}^{(2)}(\mathrm{\Delta }t=1\mu \mathrm{s})$ cross-correlation values (b) as a function of the storage time in the spin state ${\mathrm{t}}_s$. The red line is the fit of the experimental data to a Gaussian decay, which gives a $1/e$ decay time of $(8.3\pm 0.8)\mu \mathrm{s}$, corresponding to a spin-inhomogeneous linewidth of $45\pm 2\mathrm{kHz}$ ($44\pm 4\mathrm{kHz}$ for $g_{\mathrm{S},\mathrm{AS}}^{(2)}$). For this curve, we do not subtract the accidental counts. The blue horizontal line in (b) sets the classical threshold for the $g_{\mathrm{S},\mathrm{AS}}^{(2)}$ given by the Cauchy-Schwarz inequality. (c) $g_{\mathrm{S},\mathrm{AS}}^{(2)}(\mathrm{\Delta }t=1\mu \mathrm{s})$ cross-correlation (squares) and coincidence counts per hour (circles) between the Stokes and anti-Stokes photons as a function of Stokes window size, $T$. The total Stokes window size is $5.5\mu \mathrm{s}$. In the data processing stage we adjust the Stokes window size as multiples of the duration of the write pulse ($\mathrm{FWHM}=500\mathrm{ns}$). The values are averages of all possible windows for different window sizes, e.g., 11 for a 500-ns window, 9 for a 150-ns window, etc. In this measurement ${\mathrm{P}}_w=64\mu \mathrm{W}$. The read pulse is sent $15\mu \mathrm{s}$ after the write pulse. The decrease on $g_{\mathrm{S},\mathrm{AS}}^{(2)}$ with respect to the one in Fig. 3 is due to the longer spin-state storage time and less-efficient readout for a shorter write pulse (${\eta }_{\mathrm{RO}}=1\%$).