1. Introduction

In standard telecommunications, erbium-doped amplifiers are placed along the network to regenerate the depleted signals, compensating for the attenuation of the optical fibers. The quantum repeater has been introduced in quantum communication [1–3] to solve the same problem of attenuation, since the amplification of quantum states is not possible without a critical decrease in the qubit fidelity due to the no-cloning theorem, and therefore enable long-distance quantum networks, offering new opportunities in quantum communication, computing, and sensing [4]. One of the main challenges of building such a quantum network is to efficiently deliver entanglement between the remote nodes [5]. Entanglement is the main resource in quantum communication, as it can be used, for example, to perform quantum key distribution or to transmit qubits between nodes using quantum teleportation [6]. Similarly, it is at the base of the operation of quantum repeaters, which allow long-distance entanglement distribution through successive entanglement swapping operations combined with quantum memories.

Any system addressing long-distance quantum communication has to overcome several hurdles to achieve even the first stepping stone, namely quantum correlations between a matter qubit and a photon. While several different protocols have been proposed [2,3,7,8], all involve an information carrier propagating through several kilometers of communication channels. The commercial telecommunication network would then provide a natural platform over which to implement early tests of quantum communication. However, only a few quantum systems can operate at telecom wavelengths, and accessing it with quantum frequency conversion increases system losses and may reduce signal-to-noise. A promising option involves combining a quantum memory with a non-degenerate source of photon pairs, where one photon is compatible with the memory, while the other is at a telecom wavelength. Another desirable feature for a functional quantum repeater is the use of multiplexed communication [9]. It requires the encoding, storage and transmission of quantum information over several degrees of freedom, such as time, frequency, and space, each holding as many modes as possible. While this technique is routinely used in commercial networks, adapting it to the quantum regime is a task only recently faced in entanglement distribution, especially with quantum memories [7,10–16].

Several architectures are currently being investigated for the realization of quantum repeaters, based on the interaction of photons with individual quantum systems, such as ions and atoms [17–21], or with atomic ensembles [22–28]. Solid-state equivalents to the former, such as quantum dots [29,30] or color centers in diamond [31–36], are also being investigated for their scalability potential. Distribution of entanglement between systems linked by tens of kilometers of optical fiber have been demonstrated in some of the previous systems. Light–matter entanglement between a telecom photon and a single ion was demonstrated after propagation in 50 km of optical fiber [37]. Entanglement between two adjacent atomic clouds was recently demonstrated [38] where the heralding signal travelled through tens of kilometers of deployed fiber. This was followed by the distribution of light–matter entanglement between two quantum memories physically separated by 12.5 km [39]. More recently, the heralded entanglement between two single atoms separated by 33 km of optical fiber [40] was also demonstrated.

Rare-earth-doped crystals can be considered a solid-state version of an atomic ensemble, with billions of ions trapped inside a crystalline matrix [41]. They have long been used as a powerful platform for light–matter interaction. Cooling them to a few kelvin can result in long coherence times of the level of hours [42], a record amongst all of the aforementioned systems. They also possess a great potential for massive multiplexing, as the temporal, spectral, and spatial degrees of freedom can be harnessed for quantum communication [43]. These properties make them promising systems for quantum repeater applications. In that direction, several important steps have been performed, including the storage of single photons [44–47], of entanglement [48–51], and the realization of entangled states between remote memories [52–55]. More recently, the distribution of non-classical correlations [56] and entanglement [57] across kilometers of optical fiber was also demonstrated. An important validation step toward the realization of quantum networks with this technology is to move from laboratory to field demonstrations using the installed fiber network. This requires the development of robust quantum hardware operating outside of the laboratory environment, and sharing classical information, such as synchronization signals and optical references, between the nodes.

In this manuscript we present a set of measurements over a quantum network testbed, with the generation of entanglement between a multimode quantum memory based on a rare-earth-doped crystal and a telecom photon which is transmitted through up to 50 km of deployed optical fibers in the metropolitan area of Barcelona. We show that non-classical correlations and light–matter entanglement are maintained after the transmission, with any degradation coming only from the reduced signal-to-noise ratio. Finally, we fully decouple the photon generation from the detection by realizing a transportable detection setup which, placed at another location, we use to demonstrate non-classical correlations between two locations separated by 16 km.

2. Description of the Setup

Our design for a quantum network node is based on the combination of a rare-earth-doped quantum memory and a photon-pair source [9]. We employ a crystal of Y$_2$SiO$_5$ doped with praseodymium (Pr) ions, where we implement the atomic frequency comb (AFC) [11] scheme on the $^3$H$_4$(0) $\leftrightarrow$ $^1$D$_2$(0) transition. This storage protocol is based on the preparation of a periodic absorption profile in the inhomogeneous broadening of an atomic transition, and it has been implemented in bulk crystals [10,56,58–61], erbium-doped fibers [47], waveguides [49,62–68], thin films [69], and also warm atomic vapors [70]. Light absorbed by the comb is mapped to a delocalized excitation of the ions in the crystal, each component with a different phase term. Due to the frequency periodicity $\Delta$ of the comb, these components rephase at time $\tau = 1/\Delta$, causing a collective re-emission in the forward direction referred to as an echo. The AFC protocol allows multiplexing in the temporal domain, as many consecutive photons can be stored in the memory, and will be re-emitted in the same order [11].

The narrow bandwidth of the Pr quantum memory requires a purposely built source of entangled light. The source we employ is based on cavity-enhanced spontaneous parametric downconversion (SPDC) [63,71]. Pairs of photons are generated simultaneously, but the exact time of generation is distributed within the coherence time of the 426 nm pump laser used for SPDC, which is referred to as energy–time entanglement. The cavity shapes the spectrum of the photon pair to 1.8 MHz, compatible with the 4 MHz bandwidth of the quantum memory. Moreover, the source is widely non-degenerate, with one photon of the pair, the signal, at 606 nm and resonant with the $^3$H$_4$(0) $\leftrightarrow$ $^1$D$_2$(0) transition of Pr$^ {3+}$:Y$_2$SiO$_5$, and the other, the idler, at 1436 nm in the telecom E band. As the spectrum of the photon pair has several frequency modes [72], a Fabry–Perot filter cavity is used to select only one idler mode, with the quantum memory performing a similar filtering on the signal photons. The energy–time entangled state exists within each frequency mode and is thus maintained after filtering. We use a pump power of around 4.6 mW unless stated otherwise, which results in a pair generation probability of $6.4 \times 10^{-3}$ per temporal mode (400 ns) of the central frequency mode. After the source, the signal and idler photons are coupled in optical fibers. The signal photon is stored in the quantum memory for a duration $\tau$, mapping the entanglement of the photon pair onto a light–matter entangled state. After retrieval from the quantum memory, the light is fiber-coupled and passes through another Pr-doped crystal, the analysis crystal, where a transparency window was prepared to act as an ultra-narrow-band filter 4 MHz-wide [51,73].

With this system it is possible to generate quantum correlations and entanglement between a telecom photon and a delocalized excitation stored in a multimode solid-state quantum memory [51]. We have now tested this system in a practical scenario, where the telecom photons travel through increasing distances $d_{\textrm{idler}}$ of optical fiber (in spools and deployed), with the goal of detecting any deterioration in the non-classical correlations after the transmission. A detailed setup is presented in Fig. 1. Initially the idler photons remain in the laboratory, traveling through only a few meters of fiber at first and then through a 11.4 km fiber spool instead. Next, we sent the idler photons through a dark fiber of the local network, approximately 25 km long, that connected our laboratory in the building of The Institute for Photonic Sciences (ICFO) in the municipality of Castelldefels, with the Centre for Telecommunication and Technologies of Information (CTTI) in the municipality of L’Hospitalet de Llobregat. We then connected it to a second fiber parallel to the first one, such that the photons could be detected back at ICFO after a round-trip $d_{\textrm{idler}} \approx 50$ km and a total loss of $\sim$15 dB at 1436 nm. After transmission through the fiber channel, the idler photons were then coupled back to free space where a bandpass filter removed any noise coming from the metropolitan fiber links. The photons were then fiber-coupled again and sent to superconducting nanowire detectors (ID Quantique), featuring 85% efficiency and 10 counts/s of background. We used a mechanical chopper to protect the superconducting detectors from the classical telecom light, which was generated during the locking of the SPDC cavity at the same frequency as the idler photons [51,54]. A similar chopper was placed in the signal path to block the light used to lock the cavity from reaching the quantum memory setup. The choppers were all synchronized to a 30 Hz signal from a function generator, which imposes a duty cycle of 55% during the measuring time. The time required to prepare the AFC imposes an additional duty cycle to the measurement of 41% for the 10 $\mathrm {\mu }$s AFC, and 30% for the 25 $\mathrm {\mu }$s AFC.

 

Fig. 1. Setup of the experiment. Entangled photon pairs are generated by cavity-enhanced spontaneous parametric downconversion, where a periodically poled lithium niobate (ppLN) crystal is pumped by a laser at 426 nm. The two photons of the pair, signal, and idler, are separated by a dichroic mirror (DM). The idler photons pass through a filter cavity (FCav) for single frequency mode operation and are then fiber-coupled. Signal photons are instead filtered with a bandpass filter (BPF) and an etalon filter before being fiber-coupled and then stored in the quantum memory. The detection signal from the idler detectors is encoded to light and back to an electrical signal using electrical-to-optical (ETO) transducers. The fiber-based idler interferometer was used only for entanglement verification. TDC, time-to-digital converter; PZ, piezo-based fiber stretcher; PC, polarization controller. The energy-level scheme of praseodymium with the relevant transition for the atomic frequency comb (AFC) identified is shown at the bottom on the right-hand side.

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Aside from the additional transmission losses of the idler channel, a physical separation between the signal and idler detections will necessitate a way of transmitting the detection signal from one position to the other with low jitter. While GPS and ethernet synchronization is possible [36], an alternative solution is the use of an electrical-to-optical transducer, turning the electrical signal from the detector to an optical one and then back to electrical at the final destination. We employed this method whenever we included additional distance for the idler photons by placing a 50 km fiber spool between the sender and the receiving transducer. In this manner, the TTL signal of the detector was delayed by $\sim 250\,\mathrm {\mu }$s before being recorded by a time-to-digital converter (TDC), therefore simulating distant detection.

3. Results

We first tested for any degradation in the quantum correlations between signal and idler by measuring the second-order cross-correlation function $g^{(2)}_{\textrm{i,AFC}} \left ( t \right ) = \frac {p_{\textrm{i,AFC}}}{p_{\textrm{i}}\, p_{\textrm{s}}}$, where $p_{\textrm{i,AFC}}$ is the probability of detecting an idler–signal coincidence at the time of re-emission of the AFC echo, and $p_{\textrm{i}}$ and $p_{\textrm{s}}$ are the probabilities of detecting a photon in idler or in the signal mode, respectively, all within the same time window $\Delta t$, which corresponds to the size of the photonic mode. Photon pairs generated by the SPDC source were split at a dichroic mirror, with signal photons stored for a predetermined time in the quantum memory while idler photons were sent through increasing lengths $d_{\textrm{idler}}$. For each one we tested the system by preparing an AFC with a storage time of $\tau = 10\,\mathrm {\mu }$s and $\tau = 25\,\mathrm {\mu }$s, with storage efficiencies of 22(1)% and 7(1)% and storing 25 and 62 temporal modes, respectively, considering a mode duration of 400 ns which contains $\sim 92{\% }$ of the photons. The decrease in storage efficiency is ultimately limited by the optical coherence time [74], but in this case we also experience a reduction due to imperfect AFC preparation.

It should be noted that whenever the idler photon was delayed an additional synchronization was necessary. When there is no significant distance between the signal and idler photon's detection, the pump laser of the SPDC is turned off after the detection of an idler photon to remove the accidental counts from the signal path at the time of AFC emission and to ensure a high signal-to-noise ratio [51,73]. At the same time, the TDC stops recording idler detection events, since none would have been emitted and any detection would originate from the background. However, a delay in the idler path longer than the AFC storage time forbids the use of this technique, as is the case for $d_{\textrm{idler}}$ of 11 km and 50 km, where the delays corresponding to the travel times were 60 $\mathrm {\mu }$s and 250 $\mathrm {\mu }$s, respectively. Therefore, we periodically switched the pump laser on and off for an equal time and with a period corresponding to twice the storage time of the quantum memory. This allowed the storage of the maximum number of temporal modes and their re-emission in a noise-free time window. This generates a periodic noise pattern in the cross-correlation histogram, with a triangular shape coming from the convolution of the two square periodic distributions of the generation of signal and idler photons. We then set the TDC to periodically record idlers for a time equal to the memory storage time, synchronized with the pump laser gating but with a constant offset. With a proper calibration of this offset we could match the recording window of the TDC with the idler generation one. This ensured a maximum signal-to-noise ratio, and as a result placing the AFC echo at the minimum of the triangular noise pattern in the histogram.

The results are visible in Fig. 2, where we report the measurement of the $g^{(2)}_{\textrm{i,AFC}}$ for a detection window of $\Delta t = 400$ ns. The value of $p_{\textrm{i}}\, p_{\textrm{s}}$ can be estimated by considering the accidental coincidence counts in a region without correlations. The histograms of coincidences for 10 $\mathrm {\mu }$s storage and for increasing $d_{\textrm{idler}}$ are reported in Figs. 2(a)–2(c) where we highlighted the chosen region for accidentals, and the triangular pattern of accidental counts for higher distances. As visible from Fig. 2(d), which summarizes the results at all distances and for both storage times, all values of $g^{(2)}_{\textrm{i,AFC}}$ are well above the limit of 2 for classical correlations even after the longest fiber link, assuming thermal statistics for the signal and idler fields [73]. For a storage time of 10 $\mathrm {\mu }$s, the values of $g^{(2)}_{\textrm{i,AFC}}$ are 99(7), 96(8), and 41(5) for 10, 11, and 50 km, respectively, while for a storage time of 25 $\mathrm {\mu }$s, they are 74(5), 86(9), and 38(6), respectively. The decrease in the measured value of $g^{(2)}_{\textrm{i,AFC}}$ for the last case can be ascribed to the reduced signal-to-noise ratio of this configuration, due to the higher losses in the idler channel which lower the idler count rate and consequently the background counts have a larger relative contribution to the measured $R^i$. The rates are reported in Fig. 2(e) and the difference between the two sets is due to the longer preparation time required for an AFC of longer storage time, reducing the measurement duty cycle. The number of coincidences per 1000 idler detections, $C^{1000\, idlers}$, is also reported, where we note that background counts have not been subtracted. The number of coincidences decreases for the 25 $\mathrm {\mu }$s AFC compared with the 10 $\mathrm {\mu }$s AFC due to its lower storage efficiency.

 

Fig. 2. Measurement of cross-correlation. (a)–(c) Coincidence histograms between the retrieved signal photons, stored for 10 $\mathrm {\mu }$s, and the telecom idler photons, traveling over an increasing distance. The darker regions are the 400 ns windows selected for the analysis. In panel (a) it is possible to see the background noise from the SPDC pump disappearing as it is turned off around 2 $\mathrm {\mu }$s. The gray region is the one selected for the calculation of accidentals, with counts reported in black. In panels (b),(c) the triangular pattern of noise is visible. The regions used to calculate the accidentals are placed in the same position as the echo, but at subsequent periods of the noise pattern (i.e., every 20 $\mathrm {\mu }$s after the echo). The integration times for the three histograms were 6, 12, and 42 min, respectively. (d) Second-order cross-correlation for all storage times for increasing $d_{\textrm{idler}}$. (e) Table reporting the values of the idler detection rate $R^{i}$ and the coincidences per 1000 idler counts, $C^{1000\,\textrm {idlers}}$, for different storage times and distances. These values are not background-subtracted, and the rates are reported in counts per second.

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We then moved to the verification of the entanglement between the signal photon, stored in the multimode quantum memory, and the telecom idler. We employed the Franson scheme [75], where we placed an unbalanced Mach–Zehnder interferometer in the path of each photon to act as time-bin analyzers. This selects two time-bins for the detection of the entangled photon pair, post-selecting the joint state $\left ( \left | ee \right \rangle + e^{i\varphi } \left | ll \right \rangle \right )/\sqrt {2}$, where $\left | e \right \rangle$ and $\left | l \right \rangle$ are time bins associated with the short and long arms of the interferometers, respectively, and $\varphi$ depends on the relative phase between the two interferometers, such that $\varphi = \phi _i + \phi _s$. The phase $\phi _i$ or $\phi _s$ of each interferometer only depends on the relative phase between its arms. On the idler side we used a fiber-based interferometer [51] and a solid-state equivalent on the signal side [48,51]. This was realized by preparing an AFC in the analysis crystal with a storage time equal to the delay introduced by the long arm of telecom fiber interferometer. The short and long arms are represented by transmission of photons through the AFC and by absorption then reemission of photons, respectively. The phase of this interferometer can be controlled by varying the position of the spectral features of the AFC with respect to the input photon frequency. The phase of the fiber interferometer is instead controlled using a fiber stretcher installed in the long arm. We acquired signal–idler coincidences for various phases of the idler interferometer to obtain a two-photon interference fringe. We then shifted the phase setting of the signal interferometer by $\pi$/2 and acquired a second interference fringe to demonstrate the dependence of the interference on the phases of both interferometers. We repeated this process for a $\tau = 10\,\mathrm {\mu }$s storage time and for all $d_{\textrm{idler}}$, adopting the same synchronization between pump and idler recording and the electrical-to-optical signaling explained before. When the 50 km deployed fiber links were used, the visibility was calculated only by measuring the maximum and minimum values of the two interference fringes, due to the low count rate. A final value of visibility $V$ higher than 33% confirms the non-separability of the state of the idler and signal [76], while a visibility higher than 70.7% is enough to violate a Clauser–Horne–Shimony–Holt (CHSH) inequality [77]. For entanglement-based quantum key distribution (QKD), a visibility above $78{\% }$ is required to achieve positive rate [78] when finite-size effects are neglected. Our results are reported in Fig. 3, where the visibilities are the weighted arithmetic mean of each pair of fringes, giving $V_{\textrm{0 km}}$ = 83(3)%, $V_{\textrm{10 km}}$ = 81(3)%, and $V_{\textrm{50 km}}$ = 84(4)%. The values of visibility are all consistent with each other and well above both classical limits for all the distances considered. This is a different behavior from the cross-correlation, which decreased with increasing distance due to higher losses in the idler channel, therefore lowering the signal-to-noise due to the higher relative contribution of the dark counts to the idler rate. The visibility of the interference fringes varies with $g^{(2)}$ only as $V \propto \frac {g^{(2)} -1}{g^{(2)} + 1}$, which remains fairly constant across all of the distances we investigated. The visibility in our experiment is mostly affected by other parameters, such as the coherence time of the pump laser of the source, as well as the use of a particular AFC-based interferometer which is worse for the signal-to-noise but better for the coincidence rate [51]. These parameters do not change with increasing idler distance, and therefore the entanglement visibility remains constant. From the measured visibilities we can infer a post-selected two-qubit fidelity of the pair after storage and retrieval of the signal photon in the quantum memory with respect to a maximally entangled state as $F=(3V+1)/4$ [79]. For the various distances we obtained $F_{\textrm{0 km}} = 87(2){\% }, F_{\textrm{10 km}} = 86(2){\% }$, and $F_{\textrm{50 km}} = 88(3){\% }$.

 

Fig. 3. Measurement of light–matter entanglement. Interference fringes for (a) $d_{\textrm{idler}} =0$ km and (b) $d_{\textrm{idler}} =11$ km. Each fringe is acquired by changing the phase of the idler interferometer, $\phi _i$, with the fiber stretcher, and between the two fringes in each panel the phase of the signal interferometer is changed by $\pi /2$. (c) Visibility of interference for all $d_{\textrm{idler}}$. The integration times to obtain the three points were 440, 1254, and 1429 min, respectively. Inset: histograms of coincidences for $d_{\textrm{idler}} = 50$ km for the maximum and minimum of interference for one of the phase settings of the signal interferometer. The dark regions are those selected for the analysis. Similar histograms are obtained for each of the phase settings of panels (a),(b).

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All the measurements mentioned so far have been realized locally, with all the photons being ultimately detected in the same laboratory. We took a step further toward a field-deployed system by bringing the idler detection station to a separate location. We extended the fiber link to an office building of the i2CAT foundation in the city of Barcelona, 16 km away from ICFO and separated by 44 km of fiber. We used one of the two metropolitan fibers to send the idler photons from ICFO to Barcelona, while the other one was used for the transmission of the classical signal of the photon detection. Since the system of superconducting detectors could not be easily moved, we brought a more compact InGaAs detector. This detector had a much lower detection efficiency of approximately 10%, but a similar dark count rate. The full separation of the system required an additional synchronization, since one of the optical choppers was now placed at i2CAT, on a portable and blacked-out free-space setup, and it had to be synchronized with the one at ICFO. We therefore placed at the remote location the function generator outputting the master signal that all the choppers used as reference and we transmitted it back to ICFO using another available channel of the ETO transducer. This new fiber link introduced losses of approximately 13 dB. However, the less efficient detector drastically reduced the count rate of the experiment, making the entanglement verification measurement unpractical. We therefore focused on the measurement of $g^{(2)}_{\textrm{i,AFC}}$ for a storage time of $\tau = 10\,\mathrm {\mu }$s. The result is reported in Fig. 4(c), where the peak of coincidences from the AFC echo can be seen around $-422\,\mathrm {\mu }$s. The lower value of $g^{(2)}_{\textrm{i,AFC}} = 23(2)$ compared with the previous measurements is mostly due to the lower signal-to-noise coming from a lower detection efficiency, but nonetheless clearly confirms the non-classical correlations between the two photons, detected 16 km apart and with a delay of 210 $\mathrm {\mu }$s.

 

Fig. 4. Measurement of non-classical correlations between remote locations. (a) Map of the metropolitan area of Barcelona, with the three locations highlighted: ICFO, where the memory and SPDC source are located; CTTI, where the two optical fiber segments are connected; i2CAT, where the idler photons are detected. Taken from Google Earth (Data SIO, NOAA, U.S. Navy, NGA, GEBCO. Image © 2023 TerraMetrics). (b) Schematic of the setup, highlighting the use of the ETO transducers to transmit the timestamps of the idler detections and the synchronization signal for the mechanical choppers. (c) Cross-correlation histogram built from the TDC at ICFO. The dark region corresponds to the counts used to calculate $g^{(2)}_{\textrm{i,AFC}}$. Data acquisition was completed in 861 minutes. For the measurements at 0 km in panel (a), the pump power was 3.8 mW instead of the typical 4.6 mW.

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4. Conclusion

In this work we have presented the detection of non-classical correlations and of light–matter entanglement between a visible photon stored as a delocalized excitation in a solid-state multimode quantum memory and a telecom photon traveling through increasing distances of optical fiber before being detected, both in the laboratory and in the installed fiber network. We measured non-classical cross-correlation values for storage times of 10 $\mathrm {\mu }$s and 25 $\mathrm {\mu }$s and up to a maximum fiber separation of 50 km between the detected photons, with a reduction due to a lower signal-to-noise. We also verified that light–matter entanglement was preserved after the transmission in the fiber, with two-qubit fidelities greater than 85% for all distances. Finally, we physically separated the generation and the detection of the telecom idler photon by placing its detector at a remote location, still measuring a non-classical value of cross-correlation. We modified our system to account for this full separation, introducing synchronization routines and employing a transducer that allowed precise timings to be transferred over optical fibers, taking the first steps toward the realization of fully independent quantum nodes. To the best of our knowledge, this is the first demonstration of light–matter entanglement distribution with telecom photons and a multimode quantum memory using deployed fibers.

To achieve the ambitious goal of building an elementary quantum repeater link over large distances would entail additional requirements, for which our system is well-suited. For most of the measurements presented in this paper, the memory was read-out and the signal photon detected much before the telecom photon reached its destination. On the one hand, this does not affect the quantum correlations as these are calculated based on idler–signal coincidence counts at a particular delay. On the other hand, for applications in quantum networks this post-selection should be avoided. To do so, the storage time of the quantum memory should be greater than the communication time between the two parties, roughly 5 $\mathrm {\mu }$s/km. Considering the longest storage time reported in this work, entanglement transmission without post-selection could be achieved across a separation of 5 km and storing 62 temporal modes. On-demand retrieval of the stored photon can be obtained by transferring the excitation to a ground-level hyperfine state [51,59,73], also allowing for ultra-long storage times [80–82] with the potential to reach the level of minutes for a Pr-doped crystal [83,84] due to the long coherence time of the hyperfine transitions. On-demand operation is particularly useful when several network links are present, avoiding the necessity of waiting for all of them to be entangled at the exact same time. The extra noise generated by the control pulses [51] can be limited using alternative schemes [85,86]. The rate of detection of coincidences can also be boosted by improving the efficiency of the memory, and this could be achieved by using an impedance-matched cavity [87–90]. Also, in an elementary quantum repeater link [9,54], the qubits have to be stored in the quantum memory at least until the heralding photons are detected after propagation in the long fiber and the classical heralding signals come back to the nodes. Therefore, we would not be able to turn the source on and off periodically as we did in this experiment, which would significantly reduce the count rate. This limitation can be overcome with a higher level of multiplexing. The Pr-memory used in this work already supported the storage of tens of temporal modes. The gigahertz-wide inhomogeneous broadening of Pr$^{3+}$:Y$_2$SiO$_5$ can be exploited for the storage of separate frequency modes [7,15,91,92], and the solid-state crystalline matrix can be designed to exploit spatial multiplexing [93,94], making rare-earth-doped crystals a promising system for high levels of multiplexing [43], and an equally promising candidate for the realization of the basic building block of a future quantum network.