The wave-particle duality of light has led to two different encodings for optical quantum information processing. Several approaches have emerged based either on particle-like discretevariable states, e.g. finite-dimensional quantum systems, or on wave-like continuous-variable states, e.g. infinite-dimensional systems. Here, we demonstrate the first generation of entanglement between optical qubits of these different types, located at distant places and connected by a lossy channel. Such hybrid entanglement, which is a key resource for a variety of recently proposed schemes, including quantum cryptography and computing, enables to convert information from one Hilbert space to the other via teleportation and therefore connect remote quantum processors based upon different encodings. Beyond its fundamental significance for the exploration of entanglement and its possible instantiations, our optical circuit opens the promises for heterogeneous network implementations, where discrete and continuous-variable operations and techniques can be efficiently combined.

We report the experimental observation of slow-light and coherent storage in a setting where light is tightly confined in the transverse directions. By interfacing a tapered optical nanofiber with a cold atomic ensemble, electromagnetically induced transparency is observed and light pulses at the single-photon level are stored in and retrieved from the atomic medium with an overall efficiency of (10 ± 0.5)%. Collapses and revivals can be additionally controlled by an applied magnetic field. Our results based on subdiffraction-limited optical mode interacting with atoms via the strong evanescent field demonstrate an alternative to free-space focusing and a novel capability for information storage in an all-fibered quantum network.PACS numbers: 03.67.Hk, 42.50.Gy, 42.50.Ex, 42.81.Qb Over the recent years, the physical implementation of quantum interfaces between light and matter has triggered a very active research, with unique applications to quantum optics and quantum information networks [1,2]. Within this context, a promising approach consists in coupling light with atomic ensembles [3,4]. Reversible quantum memories have been realized in a variety of ensemble-based systems, e.g. doped crystals and free-space collection of alkali atoms [5]. Significant advances have been made, including the demonstration of entanglement between remote memories and the development of first rudimentary capabilities for quantum repeater architectures [6][7][8][9]. However, free-space focusing as used in these seminal works is limiting the coupling one can obtain and the connectivity to fiber networks.Interfacing guided light with atoms has therefore been foreseen as a promising alternative, enabling longer interaction length, large optical depth and potential nonlinear interactions at low power level [2]. A first possible implementation consists in encasing a vapor into the hollow core of a photonic-crystal fiber, confining thus atoms and photons in the waveguide. Slow-light, alloptical switching and few-photon modulation have been demonstrated [10][11][12]. Recently, single-photon-level Raman memory has been realized with larger core fibers, with storage limited to the 10 ns time-scale [13]. Another approach can be based on an even tighter confinement of light in a nanoscale waveguide leading to a large evanescent field that can interact with atoms located in the vicinity. This situation can be ideally realized with optical nanofibers exhibiting subwavelength diameter [14]. Using a nanofiber in a hot Rubidium vapor, nonlinear interactions and low-power saturation have been reported [15][16][17], albeit with very short transit time of hot atoms in the evanescent field and large broadening.In this new avenue of research, the unique prospects of combining cold atoms with nanofibers have triggered vast theoretical and experimental efforts. Pioneering works investigated the interaction of a small number of atoms with the guided mode, including fluorescence coupling and surface interactions [18][19][20], and the dipole trapping of...