Integrated spectrally multiplexed light–matter interface at telecom band

Xueying Zhang; Bin Zhang; Shihai Wei; Hao Li; Jinyu Liao; Tao Zhou; Guangwei Deng; You Wang; Haizhi Song; Lixing You; Boyu Fan; Yunru Fan; Feng Chen; Guangcan Guo; Qiang Zhou

doi:10.1364/PRJ.537109

1. INTRODUCTION

The light–matter interface with absorptive quantum memory, allowing to prepare entanglement between light and matter by mapping one of two entangled photons into matter, is an essential element for the quantum repeater based long-distance quantum networks [1 –6]. Scaling down the implementation of the light–matter interface to chips can offer significant advantages in scalability, enhanced interaction between light and matter, and improved mechanical stability. Such integrated light–matter interfaces have been demonstrated with various on-chip systems such as rare-earth-doped materials [7 –10], color centers [11 –14], quantum dots [15,16], and optomechanical resonators [17,18]. Erbium-ion-doped chips, thanks to the optical transition of ${{}^{4}I}_{15 / 2} \leftrightarrow^{4} I_{13 / 2}$ at 1.5 μm, stand as a potential candidate to implement the broadband integrated light–matter interface at the telecom band [10,19,20]. Recently notable efforts have been devoted to constructing emissive quantum memory based quantum repeater networks with single ${Er}^{3 +}$ ions [21 –23]. Compared to the emissive quantum memories [16,24 –28], light–matter interfaces with absorptive quantum memories are naturally suited to realize the broadband and multiplexed storage of photonic quantum information [29,30]. Considering the need for high-rate entanglement distribution in quantum networks, one challenge is to develop the light–matter interface with multiplexing capacities. The multiplexed storage can be performed by using one or multiple degrees of freedom [31], e.g., temporal [32,33], spatial [34,35], and spectral [36,37]. The spectrally multiplexed light–matter interfaces attract great interest for their promise to increase the rate of entanglement creation across lossy quantum channels without significant spatial constraints [38]. Several experiments demonstrate the spectrally multiplexed storage of weak coherent states and herald single photons [36 –41]. To date, the preparation of light–matter entanglement with spectral multiplexing has yet to be demonstrated, especially in a telecom-compatible chip, which is key for developing large-scale quantum networks with high-rate quantum information processing.

Here we report an integrated light–matter interface based on an ${Er}^{3 +} : {LiNbO}_{3}$ ( ${Er}^{3 +} : LN$ ) waveguide. A five-spectral-channel atomic-frequency-comb (AFC) photonic quantum memory with a channel spacing of 15 GHz is prepared for the storage and faithful recall of telecom-band entangled photons. The bandwidth of each channel is 4 GHz with the storage time of greater than 150 ns, resulting in a large time-bandwidth product of more than 3000. The entangled state without alteration during the spectrally multiplexed quantum storage is verified by the input/output fidelity of over 92%. Our demonstration represents an important milestone towards large-scale quantum networks based on integrated quantum devices.

2. RESULTS

The schematic diagram of a quantum link with a quantum repeater is shown in Fig. 1. Figure 1(a) shows the schematic of entanglement swapping through a Bell-state measurement (BSM) between two neighboring elementary links. Each elementary link includes two sources of entangled photon pairs (EPPs), a BSM device, and two quantum memories (QMs). At each end of the elementary link, there is a light–matter interface that stores one member of the EPPs (signal photons) by using a QM. Another member of the EPPs (idler photons) is transmitted to the midpoint of the elementary link for the BSM operation. The result of BSM serves as a heralding signal to announce the establishment of entanglement between the two QMs, thus constituting an elementary link. Towards a higher rate of entanglement creation, a telecom-band integrated light–matter interface with spectral multiplexing is shown in Fig. 1(b). The signal photons from the EPPs are sent to the on-chip spectrally multiplexed quantum memory (on-chip SMQM) based on an ${Er}^{3 +} : {LiNbO}_{3}$ ( ${Er}^{3 +} : LN$ ) waveguide for simultaneous storage and recall, thus resulting in a spectrally multiplexed light–matter interface.

Figure 1.Schematic diagram of quantum link with quantum repeater. (a) Entanglement swapping between two neighboring elementary links. Each elementary link includes two sources of entangled photon pairs (EPPs), two quantum memories (QMs), and the Bell-state measurement (BSM) device composed of a beam splitter (BS) and two single photon detectors (SPDs). At each end of the elementary link, one member of EPPs is transmitted to the middle point of an elementary link to perform BSM through a long fiber. The result of BSM becomes a heralding signal to herald the establishment of entangled quantum memories at the two end points of each elementary link via entanglement swapping. The other member of EPPs is transmitted to the QM for storage and recall until the entanglement is established for the neighboring elementary link. The recalled member is sent to perform BSM, producing another heralding signal to announce the entanglement between the two neighboring elementary links. The achievement of long-distance entanglement relies on a hierarchical entanglement swapping among these adjacent elementary links. (b) Spectrally multiplexed light–matter interface. A spectrally multiplexed source of EPPs is generated with signal photons at 1532 nm and idler photons at 1549 nm. The signal photons are sent to the on-chip spectrally multiplexed quantum memory (on-chip SMQM) for simultaneous storage and recall, which is based on a fiber-pigtailed laser-written ${Er}^{3 +} : {LiNbO}_{3}$ ( ${Er}^{3 +} : LN$ ) waveguide. The spectrally multiplexed idler photons and recalled signal photons are sent to a BSM for entanglement swapping.

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The schematic of our experimental setup is shown in Fig. 2. It consists of a source of EPPs [Fig. 2(a)], an on-chip SMQM [Fig. 2(b)], and two qubit analyzers that allow projection measurements with each member of EPPs [Figs. 2(c) and 2(d)]. We generate EPPs by using a series of periodically repeated double pulses at 1540.60 nm with a pulse interval of 1.25 ns to pump a fiber-pigtailed periodically poled lithium niobate (PPLN) waveguide module. Time-bin EPPs are created by the cascaded second-harmonic generation (SHG) and spontaneous parametric down conversion (SPDC) processes (see Appendix A for details of EPPs). After a filtration process using dense wavelength division multiplexers (DWDMs), the spectral widths of the idler photons and signal photons are both selected at 100 GHz. The wavelengths of the idler and signal photons are centered at 1549.37 nm and 1531.93 nm, respectively. The time-bin entangled two-photon state can be written by $| Ψ^{+} ⟩ = \frac{1}{\sqrt{2}} (| e, e ⟩ + | l, l ⟩),$ (1)where $| m, n ⟩$ denotes a quantum state where the idler photon has been created in the temporal mode $m$ and the signal photon has been created in the temporal mode $n (m, n \in [e, l])$ . $| e ⟩$ and $| l ⟩$ denote early and late temporal modes, respectively. The idler photons are directly sent to one of the qubit analyzers. The signal photons are transmitted to the on-chip SMQM for storage. Combining the optical frequency comb (OFC) with a sideband-chirping technique, we prepare an SMQM with five AFC sections in an ${Er}^{3 +} : LN$ waveguide. After a predetermined storage time, the signal photons are recalled from the on-chip SMQM and sent to another qubit analyzer. To independently analyze the EPPs from different channels, we use two tunable fiber Bragg gratings (FBGs) with bandwidths of 5.2 GHz and 6.2 GHz to select the signal photons recalled from different spectral channels and the corresponding idler photons, respectively. The time-bin entangled two-photon state is analyzed using two unbalanced Mach-Zehnder interferometers (UMZIs) with the time delay of 1.25 ns between two arms. The superconducting nanowire single photon detectors (SNSPDs) are used to detect the photons, and a time-to-digital converter (TDC) is used as a coincidence unit to record the coincidence counts of the detection events.

Figure 2.Schematics of the experimental setup. (a) Source of EPPs. A series of double pulses at 1540.60 nm is sent to pump a fiber-pigtailed periodically poled ${LiNbO}_{3}$ (PPLN) waveguide module. Through cascaded second-harmonic generation and spontaneous parametric down conversion processes, the time-bin EPPs are generated with idler photons at 1549.37 nm and signal photons at 1531.93 nm. The idler photons are directly sent to one of the qubit analyzers, and the signal photons are transmitted into the on-chip SMQM. (b) On-chip SMQM. Combining the optical frequency comb (OFC) and the sideband-chirping technology, five AFC sections are prepared in a fiber-pigtailed laser-written ${Er}^{3 +} : LN$ waveguide placed in a dilution refrigerator. The storage time is set to 152 ns. (c), (d) Qubit analyzers. The signal photons recalled from different frequency channels and the corresponding idler photons are filtered by fiber Bragg gratings (FBGs). The entangled states are analyzed using two unbalanced Mach-Zehnder interferometers (UMZIs). The superconducting nanowire single photon detectors (SNSPDs) and the time-to-digital converter (TDC) are used to detect the photons and record the coincidence counts of the detection events, respectively. CW laser: continuous-wave laser; PM: phase modulator; VOA: variable optical attenuator; OS: optical switch; PC: polarization controller; IM: intensity modulator; EDFA: erbium-doped fiber amplifier; DWDM: dense wavelength division multiplexer; CIR: circulator; ISO: isolator. (e) Time sequence. The sequence is continuously repeated during the experiment. A whole time period is 500 ms. The pump laser of AFCs preparation continues for 200 ms. After a waiting time of 20 ms, the continuous pump laser of EPPs is intensity modulated into a series of double pulses with a period of 16 ns, a pulse interval of 1.25 ns, and single pulse duration of 300 ps. We repeatedly send, store, and recall signal photons for a total of 280 ms.

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We start to prepare five AFC sections in the ${Er}^{3 +} : LN$ waveguide, whose central wavelengths locate at $λ_{1} = 1531.69 nm$ , $λ_{2} = 1531.82 nm$ , $λ_{3} = 1531.93 nm$ , $λ_{4} = 1532.05 nm$ , and $λ_{5} = 1532.12 nm$ , respectively labeled as channels of 1, 2, 3, 4, and 5. The bandwidth of each AFC section is 4 GHz with the channel spacing of 15 GHz. The teeth spacing of each AFC section is set to $\sim 6.58 MHz$ , corresponding to the storage time of 152 ns (see Appendix B for details of all measured AFC sections). To perform the simultaneous storage of photons with different spectral modes, we sent the correlated photon pairs with the bandwidth of 100 GHz in a single temporal mode to the on-chip SMQM for storage. Figure 3(a) shows the temporal coincidence histogram between the idler photons and signal photons recalled from different spectral channels. The full width at half maximum (FWHM) of a temporal mode is 300 ps. To assess the nonclassical property of the on-chip SMQM, we measure the second-order cross-correlation function $g_{s, i}^{(2)} = P_{s i} / (P_{s} \cdot P_{i})$ , where $P_{s i}$ is the probability to detect a two-fold coincidence between the idler photons and signal photons triggered by the system clock, and $P_{s}$ ( $P_{i}$ ) is the probability to detect signal (idler) photons. Figures 3(b) and 3(c) show the $g_{s, i}^{(2)}$ for different spectral channels before/after quantum storage. The preservation of a nonclassical property is demonstrated by that the value of $g_{s, i}^{(2)}$ for each correlated spectral mode after quantum storage is around 20, which is nearly the same as the value for correlated photon pairs before quantum storage. The values of $g_{s, i}^{(2)}$ for the uncorrelated spectral modes are around one, which demonstrates the negligible crosstalk between different spectral channels [42].

Figure 3.Storage of correlated photons pairs. (a) Storage and recall of heralded single photons. The storage time is set to 152 ns. The full width at half maximum (FWHM) of a temporal mode is 300 ps. (b) Values of $g_{s, i}^{(2)}$ for correlated photon pairs before quantum storage. (c) Values of $g_{s, i}^{(2)}$ between the idler photons and signal photons recalled from different channels. The measurement time is 200 s and the time-bin width is 100 ps. The error bars are evaluated from the counts assuming the Poissonian detection statistics.

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Then, to prepare light–matter entanglement, the signal photons from time-bin EPPs are sent to the on-chip SMQM to store and recall. We characterize the quantum properties of the time-bin entangled two-photon state before and after quantum storage, listed in Table 1. As an entanglement witness, we perform the tests of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [43,44] by carrying out the Franson interference. The tests after quantum storage for channel 1 are shown in Fig. 4. The phases for the UMZIs on the idler channel and signal channel sides are marked as $α$ and $β$ , respectively. These output ports of UMZIs are named as $A_{1}$ , $A_{2}$ , $B_{1}$ , and $B_{2}$ . We fix the phase $α$ at 0 and $π / 2$ , and then continuously scan the phase $β$ . Figures 4(a) and 4(b) show the phase $β$ dependence of the three-fold coincidence counts $C_{A_{i} B_{j}} (α = 0, β)$ involving the port combinations of $A_{i} & B_{j}$ triggered by the system clock ( $i$ , $j = 1$ , 2). $C_{A_{i} B_{j}} (α, β)$ corresponds to the projections of idler photons and signal photons onto their “energy basis”. According to the theory of Franson interference [45], $C_{A_{i} B_{j}} (α, β)$ is proportional to $1 + {(- 1)}^{i + j} V \cos (α + β)$ , where $V$ is the raw visibilities of the Franson interference fringes. The raw visibilities are $V = 88.79 % \pm 1.43 %$ , $89.56 % \pm 1.15 %$ , $86.54 % \pm 1.18 %$ , and $91.76 % \pm 1.42 %$ involving the four port combinations of $A_{1} & B_{1}$ , $A_{1} & B_{2}$ , $A_{2} & B_{1}$ , and $A_{2} & B_{2}$ . The correlation coefficient $E (α, β)$ is defined as $E (α, β) = \frac{C_{A_{1} B_{1}} (α, β) - C_{A_{1} B_{2}} (α, β) - C_{A_{2} B_{1}} (α, β) + C_{A_{2} B_{2}} (α, β)}{C_{A_{1} B_{1}} (α, β) + C_{A_{1} B_{2}} (α, β) + C_{A_{2} B_{1}} (α, β) + C_{A_{2} B_{2}} (α, β)} .$ (2)

Figure 4(c) shows the phase $β$ dependence of the correlation coefficient $E (α, β)$ with the phase $α$ set at 0 and $π / 2$ , respectively. The CHSH Bell inequality can be written as $S = | E (α, β) - E (α^{'}, β) + E (α, β^{'}) + E (α^{'}, β^{'}) | ⩽ 2 .$ (3)

The obtained $S$ parameter is $S = 2.549 \pm 0.020$ after quantum storage for channel 1 ( $S = 2.518 \pm 0.003$ before quantum storage) with the phases $α$ , $α^{'}$ , $β$ , $β^{'}$ set at 0, $π / 2$ , $π / 4$ , $- π / 4$ . It means that it is a violation of the CHSH Bell inequality by 27 standard deviations. As shown in Table 1, the $S$ parameters remain consistent before and after quantum storage for each spectral channel. And the qualities of the entanglement are high enough to enable a violation of a CHSH Bell inequality, making our on-chip SMQM suitable for applications in quantum networks. For each spectral channel, the measured coincidence detection rates of entangled photons after quantum storage are $2.00 \pm 0.09 Hz$ , $1.96 \pm 0.09 Hz$ , $2.68 \pm 0.10 Hz$ , $2.76 \pm 0.11 Hz$ , and $2.10 \pm 0.09 Hz$ involving the port combinations of $A_{1} & B_{1}$ .Table 1.

Characterization of the Time-Bin Entangled Two-Photon State^a

		Channel 1	Channel 2	Channel 3	Channel 4	Channel 5
Measured $S$	In	$2.518 \pm 0.003$	$2.504 \pm 0.003$	$2.473 \pm 0.003$	$2.488 \pm 0.003$	$2.576 \pm 0.002$
Measured $S$	Out	$2.549 \pm 0.020$	$2.539 \pm 0.020$	$2.547 \pm 0.013$	$2.495 \pm 0.013$	$2.521 \pm 0.018$
Fidelity (%)	In	$91.33 \pm 0.32$	$90.81 \pm 0.24$	$89.45 \pm 0.33$	$89.63 \pm 0.48$	$89.34 \pm 0.44$
Fidelity (%)	Out	$86.57 \pm 1.31$	$84.91 \pm 1.17$	$85.37 \pm 1.74$	$85.10 \pm 1.68$	$84.25 \pm 0.91$
Input/output fidelity (%)		$95.23 \pm 2.08$	$94.14 \pm 1.23$	$94.03 \pm 1.81$	$96.27 \pm 1.85$	$92.00 \pm 0.93$
Purity (%)	In	$84.00 \pm 0.55$	$83.19 \pm 0.42$	$80.94 \pm 0.55$	$82.44 \pm 0.81$	$81.12 \pm 0.78$
Purity (%)	Out	$77.51 \pm 2.39$	$75.06 \pm 1.84$	$75.49 \pm 2.68$	$74.83 \pm 2.49$	$73.72 \pm 1.69$
Entanglement of formation (%)	In	$76.09 \pm 0.80$	$74.78 \pm 0.62$	$71.11 \pm 0.81$	$73.68 \pm 1.22$	$71.48 \pm 1.15$
Entanglement of formation (%)	Out	$65.94 \pm 2.94$	$65.36 \pm 2.19$	$64.02 \pm 3.32$	$63.29 \pm 3.74$	$59.59 \pm 2.71$

We measure these parameters for a time-bin entangled two-photon state before (in) and after (out) quantum storage for five channels. The measured $S$ values are obtained by the tests of the CHSH Bell inequality. Using reconstructed and ideal density matrices, the fidelity of the entangled state is calculated with the maximally entangled $| Ψ^{+} ⟩$ state. The input/output fidelity is calculated by $F_{in / out} = {(tr \sqrt{\sqrt{ρ_{out}} ρ_{in} \sqrt{ρ_{out}}})}^{2}$ ( $ρ_{in}$ and $ρ_{out}$ are the reconstructed density matrices of the entangled state before and after quantum storage, respectively). The purity is calculated by $P = tr (ρ^{2})$ , and the calculation of entanglement of formation can be found in Ref. [7]. The error bars are evaluated from the Poissonian detection statistics using the Monte Carlo simulation method.

Figure 4.Tests of the CHSH Bell inequality after quantum storage for channel 1. (a), (b) The phase $β$ dependence of the three-fold coincidence counts $C_{A_{i} B_{j}} (α = 0, β)$ involving the port combinations of $A_{1} & B_{1}$ (blue square), $A_{1} & B_{2}$ (red circle), $A_{2} & B_{1}$ (orange diamond), or $A_{2} & B_{2}$ (green triangle) triggered by the system clock ( $i$ , $j = 1$ , 2). The error bars represent one standard deviation deduced from Poissonian detection statistics. The time window of the three-fold coincidence counts is 600 ps, and each point was obtained by integrating for 250 s. The blue, red, orange, and green lines are the fitting curves with a 100-time Monte Carlo method. (c) The phase $β$ dependence of the correlation coefficient $E (α, β)$ with the phase $α$ set at 0 and $π / 2$ . The error bars are evaluated via propagation of statistical errors. The blue lines are the fitting curves with a 100-time Monte Carlo method.

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To further verify the ability to store quantum entanglement for the on-chip SMQM, we carry out quantum state tomography to reconstruct the density matrix of the time-bin entangled two-photon state. The density matrix is calculated by projecting the entangled state onto 16 measurement bases [46] (see Appendix C for more details). Figure 5 shows the real and imaginary parts of the entangled state’s reconstructed density matrix before and after the quantum storage for channel 1. A fidelity and purity of the entangled state before quantum storage with the maximally entangled $| Ψ^{+} ⟩$ state are calculated to $91.33 % \pm 0.32 %$ and $84.00 % \pm 0.55 %$ , respectively, while the fidelity and purity after quantum storage are $86.57 % \pm 1.31 %$ and $77.51 % \pm 2.39 %$ , respectively. The imperfection of the measured fidelities and purities may be caused by errors in the calibration of UMZI’s phase as well as the imperfection in a double-pulsed pump laser, including nonuniform pulse intensity, unstable phase difference between double pulses, and limited extinction ratio. The slight change before and after quantum storage originates from the increased noise photons after quantum storage affecting the calculation of the density matrix in projection measurements. The input/output fidelity is $F_{in / out} = 95.23 % \pm 2.08 %$ of the entangled state after quantum storage with respect to that before quantum storage for channel 1, and the input/output fidelities are over 92% for five channels (see Table 1). These results demonstrate that our on-chip SMQM is reliable for storing the time-bin entangled two-photon state. Another important parameter is the entanglement of formation, which can also be used to indicate entanglement if its value exceeds zero. The values of entanglement of formation are all above zero for five channels, which further demonstrates that the entanglement still remains through our storage device.

Figure 5.Measurement of density matrices for channel 1. (a), (b) The real and imaginary parts of density matrices before quantum storage. (c), (d) The real and imaginary parts of density matrices after quantum storage. Density matrices are calculated using a maximum likelihood estimation for the two photon states.

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3. DISCUSSION AND CONCLUSION

Our spectrally multiplexed light–matter interface establishes the possibility for a spectrally multiplexed quantum repeater that outperforms the temporal multiplexing scheme when the entanglement is distributed over greater distances [38]. Future joint measurements of multiple photons in a spectrally multiplexed quantum repeater require one to select the mapping between any input and a specific recalled mode during storage; thus it is necessary to supplement with frequency shifts to allow feed-forward mode mapping [38,40]. In our experiment, the internal storage efficiency is $\sim 0.5 %$ corresponding to the storage time of 152 ns with spectral multiplexing. The storage efficiency is severely limited by the absorption background of the AFC. Combining on-chip electrodes with an ${Er}^{3 +} : LN$ photonic crystal microcavity, the storage efficiency can be greatly improved by utilizing the electro-optic effect of lithium niobate. However, the linewidth of the photonic crystal microcavity will limit the bandwidth of AFC memory [47]. Furthermore, the storage efficiency could be improved by optimizing the optical pumping of the AFC with complex hyperbolic secant pulses. This will result in better confined teeth with a more squarish spectral profile, thus reducing the absorption background [48,49]. A longer storage time could be obtained by using a frequency-stabilized laser system with a narrower linewidth to prepare the AFC [50,51], and optimizing the dopant concentration of the ${Er}^{3 +}$ ions to extend the optical coherence time [52]. A long-lived spin wave storage can be realized by further applying a magnetic field of orders of magnitude higher to explore a possible $\land$ -like hyperfine energy-level system, thereby constructing on-demand recall of quantum memory towards practical quantum repeaters [53,54]. Furthermore, our integrated quantum memory devices are sufficient to store and manipulate the quantum light source generated by a micro-ring suitable for scalable fabrication, thus enabling to build a multifunctional integrated quantum network infrastructure [55].

To conclude, we realize a telecom-compatible light–matter entanglement storage with spectral multiplexing in a fiber-integrated ${Er}^{3 +} : LN$ waveguide. In the future, with the improvement of quantum memory performance, it could be further extended to the distribution of light–matter entanglement to long distance through entanglement swapping, thereby constructing large-scale quantum networks. Our result presents a key building block towards the realization of a high-rate quantum repeater with scalability and compatibility of fiber communication infrastructure.

Category: Quantum Optics

Received: Jul. 19, 2024

Accepted: Sep. 11, 2024

Published Online: Nov. 27, 2024

The Author Email: Feng Chen (drfchen@sdu.edu.cn), Qiang Zhou (zhouqiang@uestc.edu.cn)

DOI:10.1364/PRJ.537109

CSTR:32188.14.PRJ.537109

Storage Time (ns)	Internal Storage Efficiency (%)
Storage Time (ns)	Channel 1	Channel 2	Channel 3	Channel 4	Channel 5
90	$1.05 \pm 0.01$	$0.98 \pm 0.01$	$1.02 \pm 0.01$	$1.04 \pm 0.01$	$1.10 \pm 0.01$
110	$0.90 \pm 0.01$	$0.83 \pm 0.01$	$0.90 \pm 0.01$	$0.89 \pm 0.01$	$1.02 \pm 0.01$
130	$0.77 \pm 0.01$	$0.73 \pm 0.01$	$0.64 \pm 0.01$	$0.74 \pm 0.01$	$0.78 \pm 0.01$
150	$0.59 \pm 0.01$	$0.56 \pm 0.01$	$0.59 \pm 0.01$	$0.61 \pm 0.01$	$0.68 \pm 0.01$
152	$0.56 \pm 0.01$	$0.55 \pm 0.01$	$0.56 \pm 0.01$	$0.60 \pm 0.01$	$0.66 \pm 0.01$
170	$0.67 \pm 0.01$	$0.61 \pm 0.01$	$0.60 \pm 0.01$	$0.64 \pm 0.01$	$0.81 \pm 0.01$
190	$0.55 \pm 0.01$	$0.51 \pm 0.01$	$0.51 \pm 0.01$	$0.59 \pm 0.01$	$0.68 \pm 0.01$
210	$0.42 \pm 0.01$	$0.40 \pm 0.01$	$0.35 \pm 0.01$	$0.48 \pm 0.01$	$0.58 \pm 0.01$
230	$0.40 \pm 0.01$	$0.35 \pm 0.01$	$0.28 \pm 0.01$	$0.41 \pm 0.01$	$0.43 \pm 0.01$

$v$	Photon 1	Photon 2	$\| D D ⟩$	$\| D R ⟩$	$\| R D ⟩$	$\| R R ⟩$	$n_{v}$
1	$\| e ⟩$	$\| e ⟩$	328	366	282	276	1252
2	$\| e ⟩$	$\| l ⟩$	39	37	31	38	145
3	$\| e ⟩$	$\| D ⟩$	390	–	369	–	759
4	$\| e ⟩$	$\| R ⟩$	–	416	–	359	775
5	$\| l ⟩$	$\| e ⟩$	50	43	51	59	203
6	$\| l ⟩$	$\| l ⟩$	355	403	350	388	1496
7	$\| l ⟩$	$\| D ⟩$	395	–	390	–	785
8	$\| l ⟩$	$\| R ⟩$	–	406	–	358	764
9	$\| D ⟩$	$\| e ⟩$	366	379	–	–	745
10	$\| D ⟩$	$\| l ⟩$	438	418	–	–	856
11	$\| D ⟩$	$\| D ⟩$	1485	–	–	–	1485
12	$\| D ⟩$	$\| R ⟩$	–	838	–	–	838
13	$\| R ⟩$	$\| e ⟩$	–	–	324	393	717
14	$\| R ⟩$	$\| l ⟩$	–	–	390	379	769
15	$\| R ⟩$	$\| D ⟩$	–	–	596	–	596
16	$\| R ⟩$	$\| R ⟩$	–	–	–	106	106

Before Storage	$\| e e ⟩$	$\| e l ⟩$	$\| l e ⟩$	$\| l l ⟩$
$\| e e ⟩$	0.455	0.005 − i0.013	−0.001 − i0.002	0.440 − i0.009
$\| e l ⟩$	0.005 + i0.013	0.025	0.001 − i0.009	−0.009 + i0.003
$\| l e ⟩$	−0.001 + i0.002	0.001 + i0.009	0.029	−0.021 + i0.020
$\| l l ⟩$	0.440 + i0.009	−0.009 − i0.003	−0.021 − i0.020	0.490
After Storage	$\| e e ⟩$	$\| e l ⟩$	$\| l e ⟩$	$\| l l ⟩$
$\| e e ⟩$	0.403	0.023 − i0.028	0.009 + i0.002	0.421 + i0.042
$\| e l ⟩$	0.023 + i0.028	0.047	0.004 + i0.048	0.013 + i0.018
$\| l e ⟩$	0.009 − i0.002	0.004 − i0.048	0.066	−0.019 + i0.023
$\| l l ⟩$	0.421 − i0.042	0.013 − i0.018	−0.019 − i0.023	0.483