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Quantum teleportation is an essential capability for quantum networks, allowing the transmission of quantum bits (qubits) without a direct exchange of quantum information. Its implementation between distant parties requires teleportation of the quantum information to matter qubits that store it for long enough to allow users to perform further processing. Here we demonstrate long distance quantum teleportation from a photonic qubit at telecom wavelength to a matter qubit, stored as a collective excitation in a solid-state quantum memory. Our system encompasses an active feed-forward scheme, implementing a conditional phase shift on the qubit retrieved from the memory, as required by the protocol. Moreover, our approach is time-multiplexed, allowing for an increase in the teleportation rate, and is directly compatible with the deployed telecommunication networks, two key features for its scalability and practical implementation, that will play a pivotal role in the development of long-distance quantum communication.

We demonstrate long-distance quantum teleportation from a telecom photonic time-bin qubit to a solid-state quantum memory. The storage time of the quantum memory allows for active feedforward, therefore completing the protocol.

We demonstrate the storage of light-matter entanglement between a telecom photon and an integrated solid-state quantum memory. The quantum memory is a fibre-coupled waveguide written in a rare-earth doped crystal.

The interaction of single quantum emitters with an optical cavity enables the realization of efficient spin-photon interfaces, an essential resource for quantum networks. The dynamical control of the spontaneous emission rate of quantum emitters in cavities has important implications in quantum technologies, e.g. for shaping the emitted photons waveform, for generating quantum entanglement, or for driving coherently the optical transition while preventing photon emission. Here we demonstrate the dynamical control of the Purcell enhanced emission of a small ensemble of erbium ions doped into nanoparticles. By embedding the doped nanoparticles into a fully tunable high finesse fiber based optical microcavity, we show that we can tune the cavity on- and out of-resonance by controlling its length with sub-nanometer precision, on a time scale more than two orders of magnitude faster than the natural lifetime of the erbium ions. This allows us to shape in real time the Purcell enhanced emission of the ions and to achieve full control over the emitted photons' waveforms. This capability opens prospects for the realization of efficient nanoscale quantum interfaces between solid-state spins and single telecom photons with controllable waveform, and for the realization of quantum gates between rare-earth ion qubits coupled to an optical cavity., 12 pages, 7 figures, submitted

Ensemble-based quantum memories are key to developing multiplexed quantum repeaters, able to overcome the intrinsic rate limitation imposed by finite communication times over long distances. Rare-earth ion doped crystals are main candidates for highly multimode quantum memories, where time, frequency and spatial multiplexing can be exploited to store multiple modes. In this context the atomic frequency comb (AFC) quantum memory provides large temporal multimode capacity, which can readily be combined with multiplexing in frequency and space. In this article, we derive theoretical formulas for quantifying the temporal multimode capacity of AFC-based memories, for both optical memories with fixed storage time and spin-wave memories with longer storage times and on-demand read out. The temporal multimode capacity is expressed in key memory parameters, such as AFC bandwidth, fixed-delay storage time, memory efficiency, and control field Rabi frequency. Current experiments in europium- and praseodymium-doped Y2SiO5 are analyzed within this theoretical framework, which is also tested with newly acquired data, as prospects for higher temporal capacity in these materials are considered. In addition we consider the possibility of spectral and spatial multiplexing to further increase the mode capacity, with examples given for praseodymium doped Y2SiO5.

Entanglement between photons at telecommunication wavelengths and long-lived quantum memories is one of the fundamental requirements of long-distance quantum communication. Quantum memories featuring on-demand readout and multimode operation are additional precious assets that will benefit the communication rate. In this Letter, we report the first demonstration of entanglement between a telecom photon and a collective spin excitation in a multimode solid-state quantum memory. Photon pairs are generated through widely nondegenerate parametric down-conversion, featuring energy-time entanglement between the telecom-wavelength idler and a visible signal photon. The latter is stored in a Pr^{3+}:Y_{2}SiO_{5} crystal as a spin wave using the full atomic frequency comb scheme. We then recall the stored signal photon and analyze the entanglement using the Franson scheme. We measure conditional fidelities of 92(2)% for excited-state storage, enough to violate a Clauser-Horne-Shimony-Holt inequality, and 77(2)% for spin-wave storage. Taking advantage of the on-demand readout from the spin state, we extend the entanglement storage in the quantum memory for up to 47.7 μs, which could allow for the distribution of entanglement between quantum nodes separated by distances of up to 10 km.

We demonstrate entanglement between two quantum nodes. The entanglement is generated by parametric down conversion, heralded by telecom photons and stored in multimode rare-earth based quantum memories. The memories share a delocalized excitation.

we demonstrate entanglement between two quantum nodes, where the entanglement is generated by non-degenerate photon pair sources and stored in rare-earth based quantum memories that share a delocalized excitation.

Future quantum networks will enable the distribution of entanglement between distant locations and allow applications in quantum communication, quantum sensing and distributed quantum computation

Combining the quantum optical properties of single-photon emitters with the strong near-field interactions available in nanophotonic and plasmonic systems is a powerful way of creating quantum manipulation and metrological functionalities. The ability to actively and dynamically modulate emitter-environment interactions is of particular interest in this regard. While thermal, mechanical and optical modulation have been demonstrated, electrical modulation has remained an outstanding challenge. Here we realize fast, all-electrical modulation of the near-field interactions between a nanolayer of erbium emitters and graphene, by in-situ tuning the Fermi energy of graphene. We demonstrate strong interactions with a >1000-fold increased decay rate for ~25% of the emitters, and electrically modulate these interactions with frequencies up to 300 kHz – orders of magnitude faster than the emitter’s radiative decay (~100 Hz). This constitutes an enabling platform for integrated quantum technologies, opening routes to quantum entanglement generation by collective plasmon emission or photon emission with controlled waveform., K.-J.T. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 804349. ICN2 was supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706). This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 712721 (NanOQTech). F.H.L.K. acknowledges financial support from the Government of Catalonia trough the SGR grant, and from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa” Programme for Centres of Excellence in R&D (SEV-2015-0522), and Explora Ciencia FIS2017-91599-EXP. F.H.L.K. also acknowledges support by Fundacio Cellex Barcelona, Generalitat de Catalunya through the CERCA program, and the Mineco grants Plan Nacional (FIS2016-81044-P) and the Agency for Management of University and Research Grants (AGAUR) 2017 SGR 1656. Furthermore, the research leading to these results has received funding from the European Union’s Horizon 2020 under Grant Agreements No. 785219 (Core2) and No. 881603 (Core3) Graphene Flagship, and No. 820378 (Quantum Flagship). This work was supported by the ERC TOPONANOP under Grant Agreement No. 726001.

As the reach of quantum technologies extends ever further in communication and information science, a reliable way of transferring quantum information between distant locations becomes ever more crucial. While photons are widely accepted as excellent carriers due to their speed and low decoherence, losses of transmission (in free space or fibre) and the impossibility of cloning quantum information still pose a great challenge. The quantum repeater architecture was suggested as a solution to both problems [1]. In a quantum repeater the information encoded in an input state is transferred to a new one through entanglement swapping, that is then sent on along the channel. In this work we present our advances towards the realisation of a quantum repeater. Our system of choice combines a solid-state quantum memory with a source of photon pairs. The memory is based on a Rare-Earth Doped crystal, where quantum information can be stored in Pr3+ ions as a collective excitation using the Atomic Frequency Comb technique. On demand retrieval of the information is realised by transferring the excitation to a long-lived spin state. Record values of storage times and retrieval efficiencies have been demonstrated in this system [2]. Entangled pairs of single photons are generated by parametric down conversion in a periodically poled crystal placed inside a bow-tie cavity. This allows us to generate narrow band photons pairs, where the signal is spectrally matched to the memory (606nm), while the idler is in the telecom band [3]. Such a configuration allows us to benefit from the high performance of the memory, that also allows for temporal [2] and frequency [4] multimodality, while at the same time overcoming the high optical losses of 606nm photons by pair generation of a telecom photon. The first stepping stone, progress towards which is presented in this work, is the successful demonstration of energy-time entanglement between the telecom idler photon and the signal photon, stored as spin-wave excitation. The entanglement of the original pair is maintained by the memory temporal multimodality. The entanglement analysis will be made through time-bin qubit analysers made of a fibre-based Mach-Zehnder interferometer, for the former, and a solid-state equivalent based on two AFC with different storage times, for the latter [5]. In this direction we have already doubled the efficiency of the AFC storage protocols, that will be beneficial to count rates and signal-to-noise ratio. With respect to [2], we also increased the spectral-matching between the source and the memory [4]. Our experiment will provide an increase in storage time of 3 orders of magnitude with respect to previous demonstrations, as well as introducing for the first time on-demand read-out in a highly multi-mode memory. Demonstration of the successful transfer of quantum information between the signal photon and the long-lived solid-state excitation will open the way to the demonstration of long-distance entanglement between individual nodes in a quantum network.

Single quantum emitters coupled to optical cavities in the Purcell regime can be used as high-efficiency spin-photon interfaces that are essential for building a quantum network. Furthermore, the dynamical control of the spontaneous emission rate of quantum emitters can have important implications in quantum technologies, e.g. for shaping the emitted photons waveform, or for driving coherently the optical transition while preventing photon emission. Here we demonstrate the dynamical Purcell-enhanced emission of a mesoscopic ensemble of erbium ions doped into nanocrystals coupled to a fully-tunable high-finesse fiber-based optical microcavity. Erbium has excellent optical and spin coherence properties at cryogenic temperatures and, in addition, has a transition in the telecom band that can facilitate integration into existing commercial telecom fibers. We show that we can tune the cavity on and out of resonance at a rate of above 8 KHz, which is two orders of magnitude faster that the natural lifetime of the erbium ions (55 Hz), and a factor of five faster than the Purcell enhanced emission (1.8 KHz). This allows us to shape in real time the Purcell enhanced emission of the ions and to achieve full control over the emitted photon’s waveforms. With moderate improvements in our detection efficiency and cavity finesse, this capability will allow for the generation of single telecom photons with controllable wave-shape from single erbium ions and for the realization of quantum processing between rare-earth ion qubits using dipolar interactions.

Future quantum repeater architectures, capable of efficiently distributing information encoded in quantum states of light over large distances, rely on quantum memories for light [1]. Quantum repeaters can benefit from a modal multiplexing implementation of the memory, essentially scaling up the repeater's throughput [2]. In this work we demonstrate a temporally multiplexed quantum repeater node in a laser-cooled cloud of 87-Rb atoms (as proposed in [3]). We employ the DLCZ protocol where pairs of photons and single collective spin excitations (so called spin-waves) are created [4]. The latter can then be efficiently transferred into a second single photon. For selective readout, we need to control the dephasing and rephasing of the spin-waves created in different temporal modes. We achieve this by a magnetic field gradient, which induces an inhomogeneous broadening of the involved atomic hyperfine levels [5]. By employing this steering technique, combined with cavity-enhanced noise suppression and feed forward readout, we demonstrate distinguishable retrieval of up to 10 temporal modes. For each mode, we prove non-classical correlations between the first and second photon. Furthermore, an enhancement in rates of correlated photon-photon pairs is observed as we increase the number of temporal modes stored in the memory. The reported device is a crucial key element of a quantum repeater architecture implementing multiplexed quantum memories. [1] H.-J. Briegel, W. Dur, J. Cirac and P. Zoller; Phys. Rev. Lett. 81 5932 (1998) [2] C. Simon, H. de Riedmatten, M. Afzelius,N. Sangouard, H. Zbinden and N. Gisin; Phys. Rev. Lett. 98 190503 (2007) [3] C. Simon, H. de Riedmatten and M. Afzelius; Phys. Rev. A 82 010304(R) (2010) [4] L. Duan, M. Lukin, J. Cirac and P. Zoller, P; Nature 414 413 (2001) [5] B.Albrecht, P. Farrera, G. Heinze, M. Cristiani and H. de Riedmatten; Phys. Rev. Lett. 115 160501 (2015)

We study the photon statistics of weak coherent pulses propagating through a cold Rydberg atomic ensemble in the regime of Rydberg electromagnetically induced transparency. We show experimentally that the value of the second-order autocorrelation function of the transmitted light strongly depends on the position within the pulse and heavily varies during the transients of the pulse. In particular, we show that the falling edge of the transmitted pulse displays much lower values than the rest of the pulse. We derive a theoretical model that quantitatively predicts our results and explains the physical behavior involved. Finally, we use this effect to generate single photons localized within a pulse from the atomic ensemble. We show that by selecting only the last part of the transmitted pulse, the single photons show an antibunching parameter as low as 0.12 and a generation efficiency per trial larger than possible with probabilistic generation schemes with atomic ensembles., Comment: 21 pages, 11 figures

Future quantum repeater architectures, capable of efficiently distributing information encoded in quantum states of light over large distances, will benefit from multiplexed photonic quantum memories. In this work we demonstrate a temporally multiplexed quantum repeater node in a laser-cooled cloud of ^{87}Rb atoms. We employ the Duan-Lukin-Cirac-Zoller protocol where pairs of photons and single collective spin excitations (so-called spin waves) are created in several temporal modes using a train of write pulses. To make the spin waves created in different temporal modes distinguishable and enable selective readout, we control the dephasing and rephasing of the spin waves by a magnetic field gradient, which induces a controlled reversible inhomogeneous broadening of the involved atomic hyperfine levels. We demonstrate that by embedding the atomic ensemble inside a low finesse optical cavity, the additional noise generated in multimode operation is strongly suppressed. By employing feed forward readout, we demonstrate distinguishable retrieval of up to 10 temporal modes. For each mode, we prove nonclassical correlations between the first and second photon. Furthermore, an enhancement in rates of correlated photon pairs is observed as we increase the number of temporal modes stored in the memory. The reported capability is a key element of a quantum repeater architecture based on multiplexed quantum memories.

Photons are very good candidates to carry quantum information due to their negligible interactions. However, photon-photon interactions are needed to process photonic quantum information. This is very useful for quantum repeater applications [1], in which the success probability of entanglement swapping can be highly increased if the Bell-state measurement is performed deterministically. In the case of photons, it requires mapping them in a non-linear medium at the single-photon level. This strong non-linearity has been demonstrated by using Rydberg atoms, which are atoms excited to states with a high principal quantum number. However, previous experiments with Rydberg atoms have been implemented with weak coherent input states of light [2, 3]. Hence, the mapping of true single photons to a medium with strong single-photon non-linearity is, so far, an outstanding goal. In this work, we have demonstrated the storage and retrieval of a paired single photon on a highly non-linear medium based on atoms excited to Rydberg levels. More recently, we have also enhanced the non-linearity of our ensemble to the single photon-level, as witnessed by the antibunching of a stored and retrieved incoming coherent field [3]. This will allow the storage of a single photon in a medium with single-photon non-linearity.

Light-matter entanglement is an important resource in quantum information science. It enables complementing the advantages of using photons as flying qubits in quantum communication schemes, with those of matter qubits, which are ideal for quantum storage and processing. A very convenient method to directly generate light-matter entanglement in atomic ensembles is the Duan-Lukin-Cirac-Zoller (DLCZ) protocol [1].

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 qubits 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., 8 pages and 10 figures

We report experiments demonstrating entanglement between a single photon and a multimode solid-state spin wave quantum memory with on demand read-out. We also demonstrate a frequency multiplexed integrated quantum storage device.

We demonstrate a medium with single-photon non-linearity based on cold Rydberg atoms, suitable for the mapping of a paired single photon. This opens the door to quantum interactions between single photons.

In a step towards hybrid quantum networks, a quantum state can be transferred between two fundamentally different systems—a cold atomic ensemble and a solid-state crystal—by a single photon. As work on quantum networks continues apace, attention is being focused on the tools and techniques for integrating different quantum platforms to harness the distinct benefits of each. Nicolas Maring et al. now report an important step in the development of such a hybrid network. They demonstrate how a quantum state initially stored in a cold atomic ensemble can be faithfully transferred to a solid-state storage medium—a rare-earth-doped crystal—from where it can subsequently be recovered. Interfacing fundamentally different quantum systems is key to building future hybrid quantum networks1. Such heterogeneous networks offer capabilities superior to those of their homogeneous counterparts, as they merge the individual advantages of disparate quantum nodes in a single network architecture2. However, few investigations of optical hybrid interconnections have been carried out, owing to fundamental and technological challenges such as wavelength and bandwidth matching of the interfacing photons. Here we report optical quantum interconnection of two disparate matter quantum systems with photon storage capabilities. We show that a quantum state can be transferred faithfully between a cold atomic ensemble3,4 and a rare-earth-doped crystal5,6,7,8 by means of a single photon at 1,552 nanometre telecommunication wavelength, using cascaded quantum frequency conversion. We demonstrate that quantum correlations between a photon and a single collective spin excitation in the cold atomic ensemble can be transferred to the solid-state system. We also show that single-photon time-bin qubits generated in the cold atomic ensemble can be converted, stored and retrieved from the crystal with a conditional qubit fidelity of more than 85 per cent. Our results open up the prospect of optically connecting quantum nodes with different capabilities and represent an important step towards the realization of large-scale hybrid quantum networks.

Entanglement between light and matter combines the advantage of long distance transmission of photonic qubits with the storage and processing capabilities of atomic qubits. To distribute photonic states efficiently over long distances several schemes to encode qubits have been investigated---time-bin encoding being particularly promising due to its robustness against decoherence in optical fibers. Here, we demonstrate the generation of entanglement between a photonic time-bin qubit and a single collective atomic spin excitation (spin wave) in a cold atomic ensemble, followed by the mapping of the atomic qubit onto another photonic qubit. A magnetic field that induces a periodic dephasing and rephasing of the atomic excitation ensures the temporal distinguishability of the two time bins and plays a central role in the entanglement generation. To analyze the generated quantum state, we use largely imbalanced Mach-Zehnder interferometers to perform projective measurements in different qubit bases and verify the entanglement by violating a Clauser-Horne-Shimony-Holt Bell inequality.

We report on quantum frequency conversion of memory-compatible narrow-bandwidth photons at 606 nm to the telecom C-band at 1552$\,$nm. The 200$\,$ns long photons, compatible with Praseodymium-based solid-state quantum memories are frequency converted using a single-step difference frequency generation process in a periodically poled Lithium Niobate waveguide. We characterize the noise processes involved in the conversion and by applying strong spectral filtering of the noise, we demonstrate high signal-to-noise ratio conversion at the single photon level (SNR$\,>\,$100 for a mean input photon number per pulse of 1). We finally observe that a memory compatible heralded single photon with a bandwidth of 1.8$\,$MHz, obtained from a spontaneous parametric down conversion pair source, still shows a strong non-classical behavior after conversion. We first demonstrate that correlations between heralding and converted heralded photons stay in the non-classical regime. Moreover, we measured the heralded autocorrelation function of the heralded photon using the converter device as a frequency-domain beam splitter, yielding a value of $0.19\pm0.07$. The presented work represents a step towards the connection of several quantum memory systems emitting narrow-band visible photons to the telecommunication wavelengths.

We report on the coupling of the emission from a single europium-doped nanocrystal to a fiber-based microcavity under cryogenic conditions. As a first step, we study the sample properties and observe a strong correlation between emission lifetime and brightness, as well as a lifetime reduction for nanocrystals embedded in a polymer film. This is explained by differences in the local density of states. We furthermore quantify the scattering loss of a nanocrystal inside the cavity and use this to deduce the crystal size. Finally, by resonantly coupling the cavity to a selected transition, we perform cavity-enhanced spectroscopy to measure the inhomogeneous linewidth, and detect the fluorescence from an ensemble of few ions in the regime of power broadening. We observe an increased fluorescence rate consistent with Purcell enhancement. The results represent an important step towards the efficient readout of single rare-earth ions with excellent optical and spin coherence properties, which is promising for applications in quantum communication and distributed quantum computation., Comment: 5 pages, 3 figures

Strong interaction between two single photons is a long standing and important goal in quantum photonics. This would enable a new regime of nonlinear optics and unlock several applications in quantum information science, including photonic quantum gates and deterministic Bell-state measurements. In the context of quantum networks, it would be important to achieve interactions between single photons from independent photon pairs storable in quantum memories. So far, most experiments showing nonlinearities at the single-photon level have used weak classical input light. Here we demonstrate the storage and retrieval of a paired single photon emitted by an ensemble quantum memory in a strongly nonlinear medium based on highly excited Rydberg atoms. We show that nonclassical correlations between the two photons persist after retrieval from the Rydberg ensemble. Our result is an important step towards deterministic photon–photon interactions, and may enable deterministic Bell-state measurements with multimode quantum memories., The state of a single photon can be stored as a Rydberg excitation using electromagnetically induced transparency, and this enables nonlinear interactions at the single-photon level. Here, the authors store a paired photon emitted by a quantum memory in an ensemble-based, highly nonlinear medium.

Spontaneous Raman processes in cold atoms have been widely used in the past decade for generating single photons. Here, we present a method to optimize their efficiencies for given atomic coherences and optical depths. We give a simple and complete recipe that can be used in present-day experiments, attaining near-optimal single photon emission while preserving the photon purity., 6+6 pages, 3 figures, 1 table

Photonic quantum memories are important devices in quantum information science, and are crucial for several applications including quantum repeaters and quantum networks. Rare-earth (RE) doped crystals are promising candidates as quantum memories for light as they offer coherence properties comparable to those of atomic systems, but free of the drawbacks deriving from atomic motion. The research on RE based quantum memories has been so far mostly focused on the mapping of photonic quantum bits to optical collective excitations, but this leads to short lived and mostly pre-determined storage. However, some RE ions, as Praseodymium and Europium, exhibit the suitable energy level scheme, with three long-lived hyperfine ground states, to enable the spin-wave storage by transferring the collective optical excitations into collective spin excitations. Proof of principle spin-wave quantum memories have been reported in rare-earth doped crystals, using weak coherent states as input [1,2]. Here, I will present our recent results on the realization of multimode spin-wave quantum memories in a Praseodymium doped crystal, using non-classical input light. [1] M. Gundogan, P. M. Ledingham, K. Kutluer, M. Mazzera and H. de Riedmatten , A solid state spin-wave quantum memory for time-bin qubits, Phys. Rev. Lett. 114, 230501 (2015) [2] P. Jobez, C. Laplane, N. Timoney, N. Gisin, A. Ferrier, P. Goldner, and M. Afzelius, Coherent Spin Control at the Quantum Level in an Ensemble-Based Optical Memory, Phys. Rev. Lett. 114, 230502 (2015)

The reversible mapping of quantum states of light in cryogenically cooled rare earth doped crystals, represents one of the most promising routes towards the realization of efficient and high fidelity quantum memories. The miniaturization of these devices in robust and monolithic integrated-optics platforms would be beneficial both in terms of experimental scalability and of enhanced light-matter interaction, arising from the waveguide field confinement. Here, for the first time, we fabricate single mode channel waveguides for visible light at 606 nm in a Praseodymium-doped Yttrium Orthosilicate crystal, which is one of the most employed materials for light storage experiments, thanks to its excellent coherence properties. For the waveguide fabrication, we use the direct technique called femtosecond laser micromachining, in which a femtosecond laser beam is focused inside the crystal volume, and produces a permanent and very localized material modification. In particular, we fabricate the waveguide cladding by inscribing a pair of parallel damage tracks which confine light in the in-between region. With this approach, the waveguide core is not directly exposed to the laser irradiation and consequently its bulk properties result only marginally affected. Measurements of the optical coherence time in waveguide gave results comparable to those obtained in a bulk sample and this confirms that the fabrication procedure does not affect the coherence of the active ions. We performed the storage and the on-demand recall of bright coherent pulses in waveguide, using the atomic frequency comb (AFC) protocol extended to the ground state.

Quantum memories for light are important resources as quantum interfaces between light and matter in future quantum information networks. In particular, solid state optical memories based on rare earth ion doped (REID) crystals are of great interest due to their unique physical properties. They provide large number of atoms naturally trapped in a solid with narrow optical and spin transitions. They indeed have excellent optical and spin state coherence times at cryogenic temperatures. Among the various rare-earth doped materials, Pr3+ :Y 2 SiO 5 crystals have shown excellent properties for light storage and exhibit a level scheme suitable for long lived storage in spin states.

The ability to transfer entanglement over large distance is a main requirement for quantum networks. Another fundamental ingredient is the storage of such a quantum state in a quantum memory. To this end a useful resource is a photon pair for which one photon is resonant with the memory while its partner is at a low-loss telecommunication wavelength. We recently presented a photon pair source, compatible with a Pr:YSO solid state memory [1]. The photons have a narrow bandwidth for compatibility with the memory transition. Generating and transmitting qubits based on such photons is not straight forward, as usual implementations as e.g. polarisation qubits suffer distortion in fibres and time-bin qubits on the other hand require long interferometers for qubit analysis due to the long coherence time. Here we report on the implementation of frequency-bin entanglement [2, 3] which has neither of these drawbacks.

Strong interaction between two single photons [1], is a long standing and important goal in quantum photonics. This would enable a new regime of nonlinear optics and unlock several applications in quantum information science, including photon-photon gates and deterministic Bell-state measurements for quantum networking. In the context of quantum networks [2], a particularly important case is to achieve strong interaction between single photons from independent photon pairs that can be stored in quantum memories. So far, most of the efforts towards nonlinear effects at the single-photon level have been realized using weak classical input light.

Quantum correlations between long lived quantum memories and telecom photons that can propagate with low loss in optical fibers are an essential resource for the realization of large scale quantum information networks. Significant progress has been realized in this direction with atomic and solid state systems. Here, we demonstrate quantum correlations between a telecom photon and a multimode on-demand solid state quantum memory. This is achieved by mapping a correlated single photon onto a spin collective excitation in a Pr$^{3+}$:Y$_2$SiO$_5$ crystal for a controllable time. The stored single photons are generated by cavity enhanced spontaneous parametric down conversion (SPDC) and heralded by their partner photons at telecom wavelength. These results represent the first demonstration of a multimode on-demand solid state quantum memory for external quantum states of light. They provide an important resource for quantum repeaters and pave the way for the implementation of quantum information networks with distant solid-state quantum nodes., 6 pages, 4 figure, Appendix (6 pages and 10 figures), published version