1. Introduction

Realization of entanglement distribution over long distances is a core task for long-distance quantum communications [1,2] and large-scale quantum networks [3]. Direct entanglement distribution over a distance of 1000 km is difficult because of the transmission losses in the fiber channel. Quantum repeaters (QRs) represent a promising solution to overcome this loss problem [1,2]. A QR [4] includes a number of elementary links, each of which is composed of two nodes. An atom-photon entanglement source, i.e., a quantum interface (QI) that generates the entanglement between the photonic and spin-wave (atomic memory) qubits, can be used as a repeater node [5,6]. In each link, quantum memories are deposited at the nodes and the photons are sent to a central station for entanglement generation between two nodes. The quantum memories are then converted into photons for entanglement connections between adjacent links [1,2].

Various mechanisms for optical quantum memories based on atomic ensembles have been studied widely, including electromagnetically-induced transparency (EIT) [7–19], the gradient echo memory (GEM) [20–23], the atomic frequency comb (AFC) [20–34], Raman memory [35–39], and the Duan-Lukin-Cirac-Zoller (DLCZ) protocol [1,40–64] etc. Among these protocols, EIT, GEM, and the AFC are called “read-write” [65] (or “absorptive” [66]) memory schemes, whereas the DLCZ is called a “read-only” memory scheme [65]. Realization of QRs in practice requires quantum memories with high performance characteristics, including high retrieval efficiency, multi-mode storage capacity, and long lifetimes [67,68].

High-efficiency “absorptive” optical memories have been realized using high-optical-depth atomic ensembles [14,16–18,21,39] or by coupling atomic ensembles with a low-finesse optical cavity [19,22,69,70]. Use of the EIT scheme in a high-optical-depth cold atomic ensemble allowed the retrieval efficiencies for single photons and single-photon-level qubits to reach 85% [18] and 68% [17], respectively. The retrieval efficiency of optical storage based on the AFC scheme has been improved by using cavity-enhanced atom-photon coupling [22,69]. Efficient DLCZ quantum memories have been realized using low-finesse optical cavities [49–52,60], with retrieval efficiencies of up to ∼75% being achieved in these experiments. Long-life memories have been achieved by loading atoms into an optical lattice and using magnetically-insensitive spin waves to store the photons [48, 52,61]. To date, the longest memory lifetime for a qubit memory has reached the order of seconds based on use of an atomic ensemble [60]. When compared with single-mode memories, multiplexed quantum memories represent a promising way to achieve increased entanglement generation rates in each elementary link [25,71–74]. Specifically, if the QRs use QIs that are capable of storing N modes as nodes, the repeater rate will then be increased by a factor of N when compared with those that use single-mode QIs as nodes. In recent years, temporally [53,54,75–81], spatially [55,74,82–84], and spectrally [25,31,85] multiplexed memories for single photons, weak coherent light pulses, or optical quantum states have been demonstrated successfully using solid-state and gaseous-state ensembles of atoms.

Using multiple spatial-channel collections, multiplexed QIs that generate entanglement between a spin-wave qubit and a photonic qubit in six modes have been demonstrated based on a cold atomic ensemble [74]. On the basis of that work [74], a long-lived and spatially-multiplexed atom-photon entanglement interface has been demonstrated [61]. Pu et al. realized a multiplexed DLCZ-type quantum memory with 225 individually accessible memory cells using a macroscopic cold atomic ensemble [55]. Recently, massively-multiplexed DLCZ-type quantum memories have been demonstrated in cold atoms via spatially-resolved single-photon detection [86]. Spin-wave-photon quantum correlations in more than ten temporal modes have been demonstrated using rare-earth ion-doped crystals (solid-state atomic ensembles) via the DLCZ approach [53,75,87]. By applying a train of write pulses to a cold atomic ensemble, with each pulse being sent along different directions, our group previously demonstrated a 19-temporal-mode atom-photon entanglement [81]. A temporally-multiplexed DLCZ-type quantum memory was also realized by applying a reversible gradient magnetic field to a cold atomic ensemble to control the rephasing of the spin waves [88] by Riedmatten’s group. Furthermore, their group demonstrated suppression of additional noise generated in the temporal multimode memory using a low-finesse optical cavity [89]. Because the cavity resonates with the “write-out” photons but not with the “read-out” photons, the retrieval efficiency achieved in that experiment has not been enhanced. Recently, Cox et al. experimentally demonstrated coupling of a single optical cavity mode with multiplexed spin waves created by multiple Raman dressing beams at different times and then observed the interference of two spin waves [90].

To date, high-efficiency and multiplexed quantum memories have been demonstrated in separate experiments. For example, in cavity-enhanced atom-photon entanglement sources [51,91], the intrinsic retrieval efficiency has reached ∼76%, but the memories used for the photonic qubits are not multiplexed. In the spatially multiplexed DLCZ-type quantum memory used for single photons [92], the number of stored modes is more than 600, and the intrinsic retrieval efficiency is ∼35%. In the experiments on temporally-multiplexed DLCZ-type quantum memories, the numbers of stored modes are greater than ten, and the intrinsic retrieval efficiencies are ∼4% for the devices using rare-earth ion-doped crystals [53,54] and ∼16% in cold atoms [64,81]. To date, there have been no experimental reports of an atom-photon entanglement source having a multiplexed storage capacity and high retrieval efficiency simultaneously.

In the experiment presented here, we demonstrate a cavity-enhanced and temporally-multiplexed atom-photon entanglement interface by combining temporally-multiplexed storage [61] and cavity-enhanced retrieval schemes [91] into a system. A train of 12 write pulses in time is applied to a cold atomic ensemble along different directions, and each of these pulses generates a correlated pair of a Stokes photon and an atomic collective excitation (a spin wave) with a small probability based on a DLCZ memory scheme [1]. The cold atomic ensemble is placed at the center of a polarization interferometer. The Stokes fields that are created in a write pulse and emitted into the two arms of the interferometer are then encoded onto photonic qubits. The relative phase between the two arms is stabilized passively. Two spin-wave modes, each of which corresponds to one of the Stokes qubit fields, are used for the spin-wave qubit. All the spin-wave qubits are stored in a “clock” coherence. The photonic and spin-wave qubits created by each write pulse are entangled. The multiplexed spin-wave qubits are mapped into an anti-Stokes photon by applying read beams that are controlled using a feedforward system. A ring cavity that resonates simultaneously with the write-out (Stokes) and anti-Stokes fields propagating along the two arms of the interferometer is used to enhance retrieval of the multiplexed spin waves. The cavity in combination with the interferometer forms a polarization-interferometer-based cavity that was used in our previous experiment [91] to generate a high-retrieval-efficiency (77%) nonmultiplexed atom-photon entanglement. In the experiment presented here, the intrinsic retrieval efficiency of the multiplexed atom-photon entanglement interface reaches 70.4 ± 1.9%. We demonstrate a ∼12.1-fold (11.6-fold) probability increase in the generation of entangled atom-photon (photon-photon) pairs when compared with a nonmultiplexed entanglement source. The measured Bell parameter for the multiplexed atom-photon entanglement is 2.21(2), and is combined with a memory lifetime of up to ∼125 µs.

2. Experimental setup

Figure 1(a) shows a schematic diagram of our experimental setup, in which a cold ⁸⁷Rb atomic ensemble with an optical density of 16 is used as the memory medium. To generate pairs composed of a Stokes photon and a spin wave in temporally multiplexed modes, we apply a train of write pulses, each of which is incident along a different direction onto the atoms. A scheme of this type was demonstrated in our previous publication [81]. The main improvement in this work is that a ring cavity is applied to improve the retrieval efficiency. As shown in Fig. 1(a), the ring cavity is formed using three high-reflection mirrors (HR_1,2,3) and an output coupler (OC) with reflectance of 80%. The cavity supports the TEM₀₀ mode, which is labeled as A₀₀ in Fig. 1(a). To encode the Stokes photons onto qubits, we inserted a polarization interferometer that is formed using beam displacers BD₁ and BD₂ in the cavity. This polarization-interferometer-based cavity is the same as that used in our previous experiment [91], where cavity-enhanced single-mode atom-photon entanglement was demonstrated. When the interferometer is inserted into the cavity, an arbitrarily-polarized field propagating in the A₀₀ mode along the clockwise (counterclockwise) direction will be split into H (horizontally) and V (vertically) polarized components by BD₂ (BD₁). The H-polarized (V-polarized) field is directed into arm A_L (A_R) of the interferometer. Two optical lenses, L₁ and L₂, are inserted in the interferometer and make the arms A_L and A_R pass crossways through the atomic ensemble. More details on our polarization-interferometer-based cavity can be found in the report on our previous experiment in the literature [91].

 

Fig. 1. Overview of the experiment. (a) Experimental setup. HR₁, HR₂, HR₃: high-reflectivity mirrors; OC: output coupler; HW (QW): half-wave (quarter-wave) plate; WP: wave plate; BS₁, BS₂, BS₃: beam splitters; PC: phase compensator; OSFS: optical-spectrum-filter set; PD: photodiode; PBS: polarizing beam splitter; PZT: piezoelectric transducer; AOM: acoustic optical modulator; L₁, L₂: lenses; BD₁, BD₂: beam displacers; SMF_S, SMF_AS: single-mode fibers; D_S1, D_S2, D_AS1, D_AS2: single-photon detectors; FPGA: field programmable gate array; w₁, w₂, ⋯ w_j ⋯ w_m: write pulses (${\theta _{{w_l},{w_k}}} \ge 0.2{\textrm{0}^ \circ }$ ($l,k \in m$ and $l \ne k$)); r₁, r₂, ⋯ r_j ⋯ r_m: read pulses; B₀: bias magnetic field. The free spectral range of the cavity is approximately 66.7 MHz and the finesse is measured to be ∼16. The angle between A_L and A_R is ${\theta _{{A_L},{A_R}}} \approx {0.21^ \circ }$. Both Stokes and anti-Stokes photon qubits are required to resonate with the ring cavity. To meet this requirement, an H-polarized cavity-locking beam is injected from the OC into the cavity to stabilize the cavity length using a Pound-Drever-Hall locking scheme. The H-polarized Stokes and anti-Stokes photons are made to resonate with the cavity by varying the position of cavity mirror HR₃, which is attached to a manual translation stage. The V-polarized photons are adjusted to resonate by adjusting the WPs of the PC. (b) Relevant atomic levels. (c) Time sequence for the experimental trials. W, C, R: write, cleaning, and read laser pulses. SG (ASG): Timeline of the S (AS) detector gate; the sizes of the detection windows denoted by S₁, S₂ ⋯ S_j ⋯ S_m and AS are all ∼250 ns; L: locking beam gate; MOT: magneto-optical trap gate. The experimental period is 50 ms, of which 42 ms is used for cold atom preparation, and the remaining 8 ms is used for atom-photon entanglement generation. We stabilize the cavity length intermittently during the cold atom preparation phase. A two-dimensional MOT of 41.5 ms and a subsequent Sisyphus cooling stage of 0.5 ms cool the atomic cloud to 100 µK. A train of 12 write pulses lasts for ΔT = 8 µs. If a Stokes photon is detected in the window of S_j, then the corresponding jth reading light pulse is switched on after a storage time t to convert the spin wave into an anti-Stokes photon via the feedforward-controlled readout system, which mainly consists of an FPGA and an AOM. After the retrieval process, a cleaning pulse is applied to empty the atomic memory. If no Stokes photons are detected in any of the detection windows, the cleaning pulse is then applied directly to start the next write-read-clean trial period.

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The relevant energy levels are shown in Fig. 1(b). To define the quantization axis, we apply a bias magnetic field (B₀= 4 G) to the atomic ensemble. The ground states $|g \rangle = |{5{S_{{1 / 2}}},F = 1} \rangle $ and $|s \rangle = |{5{S_{{1 / 2}}},F = 2} \rangle $ combine with one of the excited states $|{e{}_1} \rangle = |{5{P_{{1 / 2}}},F^{\prime} = 1} \rangle $ or $|{e{}_2} \rangle = |{5{P_{{1 / 2}}},F^{\prime} = 2} \rangle $ to form a Λ-type atomic system. The atoms are initially prepared into the state $|{g,{m_F} = 0} \rangle $ via optical pumping. The atom-photon entanglement generation process then follows. At the beginning of a trial, a train of m (ranging up to 12) write pulses is applied to the atoms through beam splitter BS₁ [Fig. 1(a)]. The m write pulses are applied around z-axis and along m different directions, corresponding to m wave-vectors ${\bf k}_w^j$ with j = 1 to m. The write pulses are then ${\sigma ^\textrm{ + }}$-polarized and red-detuned from the $|g \rangle \to |{{e_\textrm{1}}} \rangle$ transition by 110 MHz. Each of these write pulses induces the Raman transition $|{g,{m_{{F_g}}} = 0} \rangle \to |{s,{m_{{F_s}}} = 0} \rangle$ via $|{e_{1},{m_{{F_{e1}}}} = 1} \rangle$ [see Fig. 1(b)], which emits ${\sigma ^\textrm{ + }}$-polarized Stokes photons and simultaneously creates spin-wave (SW) excitations associated with the “clock” coherence $|{{m_{{F_g}}} = 0} \rangle \leftrightarrow |{{m_{{F_s}}} = 0} \rangle$. During the interaction of the atoms with the jth write pulse, if a Stokes photon is emitted into the cavity mode A_R (A_L) and propagates along the counterclockwise direction, it is then called $S_R^j$ ($S_L^j$). Along with emission of the photon $S_R^j$ ($S_L^j$), an atomic excitation in the SW mode $M_R^j$ ($M_L^j$) defined by the wave-vector ${\bf k}_{{M_R}}^j = {\bf k}_w^j{\bf - }{{\bf k}_{{S_R}}}$ (${\bf k}_{{M_L}}^j{\bf = k}_w^j{\bf - }{{\bf k}_{{S_L}}}$) will be created, where ${{\bf k}_{{S_R}}}$ (${{\bf k}_{{S_L}}}$) denotes the wave-vector of the Stokes photons $S_R^j$ ($S_L^j$) with j = 1 to m. The ${\sigma ^\textrm{ + }}$-polarized Stokes photons $S_R^j$ and $S_L^j$ are transformed into H-polarized fields by a λ/4-wave plate labeled as QW_S in Fig. 1(a). Furthermore, the H-polarized $S_R^j$ is transformed into a V-polarized field by a λ/2-wave-plate that is labeled as HW_S in Fig. 1(a). These fields are combined into the cavity mode A₀₀ by BD₁ and then form a Stokes qubit $S_{qbit}^j$. As shown in Fig. 1(b), the write pulse also induces the Raman transition $|{g,{m_{{F_g}}} = \textrm{0}} \rangle \to |{s,{m_{{F_s}}} = \textrm{2}} \rangle$ via $|{{e_1},{m_{{F_e}_1}} = \textrm{1}} \rangle$, which emits ${\sigma ^ - }$-polarized Stokes photons. When a ${\sigma ^ - }$-polarized Stokes photon is directed into the A_R (A_L) mode along the counterclockwise direction, it will be transformed into an H- (V-) polarized photon by the λ/4-wave-plate QW_S (QW_S together with HW_S) and is then excluded from the A₀₀ cavity mode by BD₁.

The atom-photon joint state created by the jth write pulse can be written as ${\rho ^j} = {|0 \rangle ^j}{}^j\left\langle 0 \right|+ {\chi _j}|\Phi \rangle _{ap}^j{}_{ap}^j\left\langle \Phi \right|$, where ${|0 \rangle ^j} = {|0 \rangle _{{S_j}}}{|0 \rangle _{{M_j}}}$ denotes the vacuum state, ${\chi _j} \ll 1$ is the excitation probability induced by the jth write pulse, and $|\Phi \rangle _{ap}^j$ is the entanglement state between the spin-wave qubit encoded onto the $M_R^j$ and $M_L^j$ modes and the Stokes qubit $S_{qbit}^j$. This state is written as:

$|H \rangle _S^j$ ($|V \rangle _S^j$) denotes an H (V)-polarized Stokes photon, ${|{{1_{{M_L}}}} \rangle ^j}$ (${|{{1_{{M_R}}}} \rangle ^j}$) denotes an SW excitation in $M_R^j$ ($M_L^j$), and ${\varphi _S}$ is the relative phase between the two Stokes emissions along the A_L and A_R arms created in any of the temporal modes. In this experiment, the excitation probabilities for the various temporal modes are basically symmetrical, i.e., ${\chi _1} \approx \cdots {\chi _j} \cdots \approx {\chi _m} \approx \chi$. To retrieve the jth SW qubit, the jth read pulse with a wave-vector of ${\bf k}_r^j{\bf ={-} k}_w^j$ is applied to the atomic ensemble through BS₂, thus converting the SW $M_R^j$ ($M_L^j$) into an anti-Stokes photon $AS_R^j$ ($AS_L^j$) with a wave-vector ${{\bf k}_{A{S_R}}}{\bf = k}_w^j{\bf - }{{\bf k}_{{S_R}}}{\bf + k}_r^j{\bf ={-} }{{\bf k}_{{S_R}}}$ (${{\bf k}_{A{S_L}}}{\bf = k}_w^j{\bf - }{{\bf k}_{{S_L}}}{\bf + k}_r^j{\bf ={-} }{{\bf k}_{{S_L}}}$) [44]. The two anti-Stokes photons $AS_R^j$ and $AS_L^j$ with j = 1 to m propagate in the A_R (A_L) arms in the direction opposite to that of $S_R^j$ ($S_L^j$), where they are then combined after BD₂. The two-photon entangled state is written as follows:

3. Experimental results

To characterize the temporally multiplexed entanglement interface, we first measured its retrieval efficiency. The intrinsic retrieval efficiency of the temporally multiplexed entanglement interface is defined as ${\gamma ^{(m)}} = {{\sum\nolimits_{j = 1}^m {P_{S,AS}^j} } / {\left( {{\eta_{DAS}}\sum\nolimits_{j = 1}^m {P_S^j} } \right)}}$, where m is the number of multiplexed modes. $P_{S,AS}^j = P_{{D_{S1}},{D_{AS1}}}^j + P_{{D_{S2}},{D_{AS2}}}^j + P_{{D_{S1}},{D_{AS2}}}^j + P_{{D_{S2}},{D_{AS1}}}^j$ is the success probability of coincidence counting between the Stokes and anti-Stokes photons in the jth temporal mode (in detection window S_j), and $P_{{D_{S1}}({D_{S2}}),{D_{AS1}}({D_{AS2}})}^j$ is the coincidence probability between detectors D_S1 (D_S2) and D_AS1 (D_AS2) in the jth temporal mode. $P_S^j = P_{{D_{S1}}}^j + P_{{D_{S2}}}^j$ is the probability of detection of a Stokes photon in the jth temporal mode, and $P_{{D_{S1}}}^j$($P_{{D_{S2}}}^j$) is the detection probability for the Stokes detector D_S1 (D_S2). ${\eta _{DAS}} = {\eta _e} \times {\eta _{AS}}$ is the total detection efficiency for the anti-Stokes photon, where ${\eta _e} \approx \textrm{0}\textrm{.55}$ denotes its escape efficiency from the cavity and ${\eta _{AS}} \approx \textrm{0}\textrm{.25}$ denotes the detection efficiency of the anti-Stokes channel, which includes the coupling efficiency of SMF_AS (${\eta _{SMF}} \approx 0.72$), the transmission of the OSFS (${\eta _{OSFS}} \approx 0.56$), the transmission of the multi-mode fiber (${\eta _{MMF}} \approx 0.91$), and the detection efficiency of D_AS1 and D_AS2 (${\eta _D} \approx 0.68$). $P_{S,AS}^j$ and $P_S^j$ are measured when the polarization angles for the Stokes and anti-Stokes photons are set to be ${\theta _S} = {\theta _{AS}} = {0^ \circ }$.

Figure 2 shows the intrinsic retrieval efficiency ${\gamma ^{(m)}}$ as a function of the storage time t. At the zero delay, where t = 0, the intrinsic retrieval efficiency is $70.4 \pm \textrm{1}\textrm{.9\%}$, which is only ∼16% in our previous work [64,81]. We fit the measured retrieval efficiency using the function ${\gamma ^{(12)}}(t) = \frac{{{\gamma _0}}}{2}({e^{ - {{(t/{t_0})}^2}}} + {e^{ - t/{t_0}}})$ with an initial retrieval efficiency of ${\gamma _0} = 0.71$ and a 1/e storage lifetime of ${t_0} = 262$ µs. Note that in all measurements, the excitation probability for each single-mode Stokes photon was adjusted to be $\chi \approx 1\%$ to avoid multiple excitations.

 

Fig. 2. Intrinsic retrieval efficiency of the 12-temporal-mode multiplexed entanglement source as a function of the storage time t. The red line is given by the fitting function ${\gamma ^{(12)}}(t) = \frac{{{\gamma _0}}}{2}({e^{ - {{(t/{t_0})}^2}}} + {e^{ - t/{t_0}}})$ with ${\gamma _0} = 0.71$ and ${t_0} = 262\textrm{ }\mu s$.

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Next, we verify the entanglement property of the multiplexed atom-photon interface by measuring the Clauser-Horne-Shimony-Holt (CHSH) inequality. The ${S^{(m)}}$ parameter for the multiplexed entanglement with m modes is defined as ${S^{(m)}} = |{E^{(m)}}({\theta_S},{\theta_{AS}}) - {E^{(m)}}({\theta_S},{{\theta^{\prime}}_{AS}})+$ ${E^{(m)}}({{\theta^{\prime}}_S},{\theta_{AS}}) + {E^{(m)}}({{\theta^{\prime}}_S},{{\theta^{\prime}}_{AS}}) |$, where ${\theta _S}$ and ${\theta ^{\prime}_S}$ (${\theta _{AS}}$ and ${\theta ^{\prime}_{AS}}$) are the polarization angles for the Stokes (anti-Stokes) photon. The correlation function ${E^{(m)}}({\theta _S},{\theta _{AS}})$ is given by:

Here, $C_{{D_{S1}}{D_{AS1}}}^{(m)}({\theta _S},{\theta _{AS}})$, $C_{{D_{S2}}{D_{AS2}}}^{(m)}({\theta _S},{\theta _{AS}})$, $C_{{D_{S1}}{D_{AS2}}}^{(m)}({\theta _S},{\theta _{AS}})$, and $C_{{D_{S2}}{D_{AS1}}}^{(m)}({\theta _S},{\theta _{AS}})$ are the coincidence counts between detectors D_S1/D_S2 and D_AS1/D_AS2. By setting ${\theta _S} = {0^ \circ }$, ${\theta ^{\prime}_S} = {45^ \circ }$, ${\theta _{AS}} = {22.5^ \circ }$, and ${\theta ^{\prime}_{AS}} = {67.5^ \circ }$, we measured the Bell parameter ${S^{(12)}}$ as a function of the storage time t, as indicated by the black squares in Fig. 3. At the beginning of the storage time ($t = \textrm{0 }\mu s$), the measured S parameter is $2.21(2)$, which violates the CHSH inequality ${S^{(12)}} \le 2$ by 10.5 standard deviations. At the later storage time $t = 125\textrm{ }\mu s$, the measured S parameter is $2.0\textrm{1}(2)$, which still violates the CHSH inequality.

 

Fig. 3. Measured Bell parameter ${S^{(12)}}$ as a function of the storage time t. The error bars represent the standard deviations of the measured values.

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Next, we study the generation probability of the temporally multiplexed photon-atom entanglement interface. Detection of the Stokes photon heralds generation of the photon-atom entanglement. The generation probability of the multiplexed photon-atom entanglement with m modes is proportional to the detection probability of the Stokes photon $P_S^{(m)}$, which is measured as the sum of the detection probabilities $P_{{S_1}}^{(m)}$ and $P_{{S_2}}^{(m)}$ by detectors D_S1 and D_S2. Here, the polarization angle for the Stokes photon ${\theta _S} = {0^ \circ }$. For $\chi \ll \textrm{1}$, the detection probability of the Stokes photon for the multiplexed photon-atom entanglement can be expressed as $P_S^{(m)} = P_{{S_1}}^{(m)} + P_{{S_2}}^{(m)} = 1 - {(1 - P_S^j)^m} \approx mP_S^j$ [71,74], where $P_S^j$ is the detection probability of the Stokes photon for a nonmultiplexed entanglement source. Figure 4 shows the measured $P_S^{(m)}$ as a function of m for $\chi \approx 1\%$. The results show that $P_S^{(m)}$ increases linearly with increasing m, and that ${{P_S^{(12)}} / {P_S^{(1)}}} \approx 12.1 \pm 0.2$, which is in general agreement with the expected results. This result implies that our multiplexed entanglement source achieves a 12-fold increase in the generation probability of the atom-photon entanglement.

 

Fig. 4. Detection probability $P_S^{(m)}$ of the Stokes photon as a function of mode number m. The red line is a linear fitting of the measured data.

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To evaluate the generation probability of the polarization-entangled photon pair per trial, we measured the coincidence probability between the Stokes and anti-Stokes photons. The generation probability is measured as the coincidence count between the Stokes and anti-Stokes photons $P_{S,AS}^{(m)}$ at ${\theta _S} = {\theta _{AS}} = {0^ \circ }$. The coincidence count probability can be expressed as $P_{S,AS}^{(m)} = \sum\nolimits_{j = 1}^m {({({P_{{D_{S1}}}^j + P_{{D_{S2}}}^j} ){\gamma_j}{\eta_{DAS}}} )} $, where ${\gamma _j}$ is the retrieval efficiency of the jth mode of the spin-wave excitation. Figure 5 shows the measured $P_{S,AS}^{(m)}$ as a function of mode number m. When $m = 12$, ${{P_{S,AS}^{(1\textrm{2})}} / {P_{S,AS}^{(1)}}} \approx 1\textrm{1}.\textrm{6}$. We also measured the Bell parameters ${S^{(m)}}$ of the multiplexed entanglement source as a function of m. The measured ${S^{(m)}}$ was equal to 2.45(2) for $m = 1$ and decreased as m increased. This reduction is attributed to the additional noise from unwanted spin waves that are associated with undetected Stokes photons [73,81]. This issue can be overcome by using an asymmetric channel to collect the Stokes and anti-Stokes photons [64].

 

Fig. 5. Measured coincidence probability $P_{S,AS}^{(m)}$ (black squares) of the Stokes-anti-Stokes photons and the Bell parameter ${S^{(m)}}$ (blue dots) as a function of mode number m. The red line is a linear fitting of the measured $P_{S,AS}^{(m)}$.

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4. Conclusion

We demonstrate a high-retrieval-efficiency and temporally-multiplexed atom-photon entanglement interface. This multiplexed interface generates atom-photon entanglement in up to 12 pairs of spin-wave and photon modes and then increases the probability of the entanglement generation by a factor of ∼12, compared to the non-multiplexed interface. A ring cavity is used to enhance the retrieval fields from the spin-wave qubits, thus the intrinsic retrieval efficiency reaches 70.4 ± 1.9%. The multiplexed atom-photon interface uses a feedforward-controlled readout system. The multiplexed spin waves are converted into anti-Stokes photons propagating in a well-defined spatio-temporal mode. The measured Bell parameter for the multiplexed atom-photon entanglement is 2.21(2), and is combined with a memory lifetime of up to ∼125 µs. The additional noise generated during the multimode preparation process degrades the quality of the atom-photon entanglement interface, which may be suppressed by using an asymmetric channel to collect the Stokes and anti-Stokes photons [64] in the future. In our scheme, a magnetically-insensitive state is selected to store the quantum information; this approach has the potential to improve the lifetime of the memory qubit by more than three orders of magnitude if atoms are being loaded into an optical lattice [52]. Next, we intend to consider combining m temporal modes and n spatial modes into one memory system, thus allowing an atom-photon entanglement source with high retrieval efficiency and large-scale ($m \times n$) multiplexing capability to be realized.

In summary, the presented work is the first experimental demonstration of an atom-photon entanglement source having a multiplexed storage capacity and high retrieval efficiency simultaneously, which represents an important step towards the development of a multiplexed QR [71,72].