Time Entanglement between a Photon and a Spin Wave in a Multimode Solid-State Quantum Memory

The generation and distribution of entanglement are key resources in quantum repeater schemes. Temporally multiplexed systems offer time-bin encoding of quantum information which provides robustness against decoherence in fibers, crucial in long distance communication. Here, we demonstrate the direct generation of entanglement in time between a photon and a collective spin excitation in a rare earth ion doped ensemble. We analyze the entanglement by mapping the atomic excitation onto a photonic qubit and by using time-bin qubit analyzers implemented with another doped crystal using the atomic frequency comb technique. Our results provide a solid-state source of entangled photons with embedded quantum memory. Moreover, the quality of the entanglement is high enough to enable a violation of a Bell inequality by more than two standard deviations.

Figure 1

(a) Experimental setup. The write and read pulses are polarized parallel to the $D_2$ memory crystal (MC) axis to maximize the interaction. Both Stokes and anti-Stokes photons pass through the interferometric filter crystal (IFC), but in different spatial modes, where dedicated laser beams prepare the required spectral features (transparency window or AFC). Spectral filters at 600 nm (width 20 nm) are placed on both arms before the photons are fiber coupled to the single photon detectors (silicon SPD). (b) Hyperfine splitting of the first sublevels (0) of the ground ${{}^3\mathrm{H}}_4$ and the excited ${}^1{D}_2$ manifolds of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$. (c) Temporal pulse sequence for the AFC-DLCZ protocol. $T_S$ ($T_{\mathrm{AS}}$) is the time separation between a Stokes (anti-Stokes) photon detection and the write (read) pulse. The insets show the effect of the AFCs in the IFC on the Stokes (orange) and anti-Stokes (red) photons. (d) Sketch of the Stokes–anti-Stokes coincidence histogram vs $T_S+T_{\mathrm{AS}}$ when the IFC is prepared with an AFC in each photon arm, with equal transmission and echo probability.

Figure 2

Typical $g_{S,\mathrm{AS}}^{(2)}$ histogram as a function of the $T_S+T_{\mathrm{AS}}$ time, with a time-bin size of 600 ns. The write pulse power $P_w$ is $90\mu \mathrm{W}$, corresponding to a Stokes creation probability $P_S=0.4\%/\mu \mathrm{s}$.

Figure 3

(a) Examples of $g_{S,\mathrm{AS}}^{(2)}$ between Stokes and anti-Stokes photons when an AFC with ${\tau }_{\mathrm{IFC}}=2\mu \mathrm{s}$ is prepared in both the Stokes and the anti-Stokes mode in the IFC. The cases of constructive (darker bars) and destructive (lighter bars) interference are shown. For both measurements, the integration time is 10 h, approximately. (b) Interference fringes measured by tuning the frequency of the anti-Stokes filter AFC (i.e., by tuning ${\mathrm{\Phi }}_{\mathrm{AS}}$) in two different bases, selected by changing the frequency of the filter AFC for the Stokes photon. The circled points are the ones related to Fig. 3. The filled points are those used to calculate the $S$ parameter (integration time 6.5 h per point). The remaining data point are the result of 5.5 h of integration each.

Figure 4

Bell inequality $S$ parameter measured as a function of $T_S+T_{\mathrm{AS}}$. The red line denotes the threshold $S=2$ for violating the CHSH inequality.