"Quantum communication is the art of transferring a quantum state from one place to another". The capability of distributing quantum states allows, for instance, provably secure communication and, in the near future, will enable the interconnection of quantum computers to establish a quantum internet. A convenient way to send quantum states from one place to another is to encode them into photons and distribute them using optical bres. The distance over which this can be achieved is still limited to a few hundred of kilometers. However, it can be extended in principle to arbitrary long distances by means of quantum repeaters. The realization of such quantum repeaters will require the engineering and interfacing of heterogeneous elements such as entangled photon-pair sources, quantum memories and entanglement swapping operations. The main goal of this thesis is to develop and study the compatibility of the main elements required to build a frequency multiplexed quantum repeater. This architecture requires a frequency multimode entangled photon pair source which, for example, could be implemented exploiting the process that involves the interaction of a strong light pulse with a non-linear crystal. Such a process is versatile and allows easy tailoring of the photon-pair spectral properties in order to match the requirements of the frequency multiplexed quantum repeater architecture. First, as a precursor of such a photon pair source, we developed a novel heralded single photon source that involves spectrally resolved single photon detection and on-demand frequency shifting. These capabilities are also essential tools in a frequency multiplexed quantum repeater. Next, we demonstrated the compatibility of such a sources with frequency multimode photonic quantum memories by performing spectrally multiplexed storage of single photons. We also tested the capability of high- delity storage of photons encoding quantum information in their polarization degree of freedom. Finally, we showed that entanglement swapping operations, i.e. Bell-state measurements, can be performed using photon pair sources compatible with quantum memories, quantum repeater architectures, and real-world scenarios. While a lot of e ort remains to be done, in the work presented in this thesis we demonstrated that all the key elements required to build a frequency multiplexed quantum repeater can be built and eventually be interfaced. The main obstacles towards that goal and possible ways to overcome them are also discussed.
"Quantum communication is the art of transferring a quantum state from one place to another". The capability of distributing quantum states allows, for instance, provably secure communication and, in the near future, will enable the interconnection of quantum computers to establish a quantum internet. A convenient way to send quantum states from one place to another is to encode them into photons and distribute them using optical bres. The distance over which this can be achieved is still limited to a few hundred of kilometers. However, it can be extended in principle to arbitrary long distances by means of quantum repeaters. The realization of such quantum repeaters will require the engineering and interfacing of heterogeneous elements such as entangled photon-pair sources, quantum memories and entanglement swapping operations. The main goal of this thesis is to develop and study the compatibility of the main elements required to build a frequency multiplexed quantum repeater. This architecture requires a frequency multimode entangled photon pair source which, for example, could be implemented exploiting the process that involves the interaction of a strong light pulse with a non-linear crystal. Such a process is versatile and allows easy tailoring of the photon-pair spectral properties in order to match the requirements of the frequency multiplexed quantum repeater architecture. First, as a precursor of such a photon pair source, we developed a novel heralded single photon source that involves spectrally resolved single photon detection and on-demand frequency shifting. These capabilities are also essential tools in a frequency multiplexed quantum repeater. Next, we demonstrated the compatibility of such a sources with frequency multimode photonic quantum memories by performing spectrally multiplexed storage of single photons. We also tested the capability of high- delity storage of photons encoding quantum information in their polarization degree of freedom. Finally, we showed that entanglement swapping operations, i.e. Bell-state measurements, can be performed using photon pair sources compatible with quantum memories, quantum repeater architectures, and real-world scenarios. While a lot of e ort remains to be done, in the work presented in this thesis we demonstrated that all the key elements required to build a frequency multiplexed quantum repeater can be built and eventually be interfaced. The main obstacles towards that goal and possible ways to overcome them are also discussed.
The development of the quantum computer challenges the security of classical communication. This is due to the security of classical encryption being based on the computational complexity of an algorithm, for example, the difficulty of factoring a number into its prime product. Quantum communication uses quantum mechanics to manipulate quantum states and exchange information between two locations. Quantum communication has proven to be unconditionally secure. However, the fact that the maximum transmission distance is largely limited by attenuation in the distribution link remains one of the biggest challenges for practical quantum communication. Quantum repeaters can greatly extend this communication transmission distance. To realize quantum repeaters, one requires quantum memories, entanglement swapping operations, and photon pair-sources. In addition, quantum repeaters greatly benefit - in terms of the achievable entanglement distribution rate - if they can incorporate some form of multiplexing. Multiplexing is possible in any of the available photonic modes, which for transmission in single-mode fibers amounts to polarization, spectral, and temporal modes. The polarization degree of freedom is undesirable because it only has two orthogonal modes. The choice of the spectral or temporal modes for multiplexing then depends on what is most compatible with other components in the setup, particularly the quantum memory, which is the most demanding component. Based on prior demonstrations in the lab of spectral multiplexing in rare-earth ion doped crystals, the purpose of my project has been to build a spectrally multi-mode photon pair-source. Our implementation of the spectrally multi-mode photon pair sources relies on a nonlinear optics process that involves the interaction of strong light and a non-linear crystal. To achieve the spectral selection of specific modes, the non-linear crystal is combined with a suitable cavity.
Quantum communication founds on the possibility to encode quantum states into photons and allows, for instance, the provable secure distribution of encryption keys. Despite a lot of progress during the past two decades, quantum communication still faces a distance barrier, which can be overcome by quantum repeaters whose currently most challenging ingredient is a memory for quantum states of light. In addition to robustness and ease of use, the requirements for such a quantum memory include high fidelity quantum state storage and the preservation of entanglement, sufficiently long storage time with on-demand recall, high efficiency, large bandwidth, and high multimode capacity. Six years ago, some of these properties had already been demonstrated using atomic vapor. However, practical solid-state memories were virtually unexplored in view of quantum state storage. The main goal of this thesis was to realize a solid-state quantum memory for light with emphasis on meeting requirements for long distance quantum communication. First, we identified a potential material candidate, a thulium doped lithium niobate waveguide, and conducted spectroscopic investigations to assess its suitability for quantum state storage using a photon-echo type approach. Next, we demonstrated that our storage device is suitable for high fidelity quantum state storage and for the storage of photonic entanglement, and that its large spectral multimode capacity allows for on-demand selective recall in conjunction with standard spectral filters and frequency shifters. In addition, by performing two-photon interference experiments and Bell-State measurements, we found that our memory preserves not only quantum information, but, more generally, the entire photonic wave function, which further confirms its suitability for quantum repeaters as well as for linear optics quantum computers. Finally, we showed that our integrated device also allows for general temporal and spectral manipulation of individual quantum optical pulses, which paves the way towards on-chip quantum optical processors. While more work remains to be done, in particular to improve memory efficiency and storage time, the large number of achievements, together with known ways to overcome the remaining obstacles, makes us confident that a quantum memory suitable for quantum repeaters will soon be built.
Quantum Key Distribution (QKD) has opened a new avenue for secure communication, by allowing one to distribute a random secret key between two users that are connected through a public channel without revealing information to unauthorized parties. If a message is encrypted with the one time pad (a well-known crytography algorithm) using secret keys created by QKD, then the ciphertext is information-theoretically secure and thus unbreakable for adversaries. Despite its unprecedented security, loss in the physical channel has prevented QKD from being used over distances beyond a few hundred kilometers. Fortunately, quantum repeaters have opened a path for long-distance QKD by providing a means to establish entanglement between distant users. The goal of this thesis has been to develop a source of entangled photon pairs that is suitable for quantum repeaters and then use it to test some of the fundamental building blocks of a quantum repeater : the heralded creation of entangled photons by means of entanglement swapping with properties that allow interfacing with optical quantum memories; the reversible mapping of quantum states from members of entangled photon pairs in and out of solid-state quantum memories; two-photon interference and a Bell state measurement with photons recalled from separate quantum memories. The demonstration of these key ingredients of a quantum repeater constitutes a significant step towards the establishment of entanglement over hundreds of kilometer distance, and hence long-distance QKD.
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.
Long-distance transfer of quantum information is an essential ability for many applications of quantum science. A natural choice to distribute quantum information is to encode it into photons and transfer it through optical fibers. However, due to the unavoidable transmission losses present in every communication channel, the distances for efficient quantum communication via direct-state transfer are limited to a few hundred kilometers. To overcome this limitation, the use of quantum repeaters has been suggested. A quantum repeater protocol aims to establish entanglement (i.e., quantum correlation) between remote nodes by first generating entanglement over shorter distance pieces, storing it in quantum memories, and finally extending it to the whole distance using entanglement swapping. The main goal of this thesis is to design quantum repeater architectures using single solid-state quantum emitters and to develop the two-qubit gates required for performing entanglement swapping. We first explain the basic ideas of quantum repeaters and introduce potential material candidates, single erbium (168Er) and europium (151Eu) ions doped yttrium orthosilicate photonic crystals. Next, we propose a quantum repeater scheme combing erbium and europium ions to generate and distribute entanglement over long distances. We study the entanglement generation rate of the protocol and compare it with the rate of a well-known ensemble-based quantum repeater. Then, using cavity assisted interactions, we propose three different schemes to perform high fidelity two-qubit gates between single quantum systems. We quantify their expected performance in detail by taking into account many realistic imperfections and compare their strengths and weaknesses. The ability to perform local two-qubits gates is especially crucial in terms of distributing entanglement. Finally, based on our gained knowledge through these projects, we propose our second quantum repeater architecture based on erbium (167Er) ions, which outperforms the first scheme. We study two possibilities for distributing entanglement and calculate the overall fidelity as well as the distribution rate of the protocol.
The ability to control the optical frequency of quantum state carriers (i.e. photons) is an important functionality for future quantum networks. It allows all matter quantum systems - nodes of the network - to be compatible with the telecommunication C-band, therefore enabling long distance fiber quantum communication between them. It also allows dissimilar nodes to be connected with each other, thus resulting in heterogeneous networks that can take advantage of the different capabilities offered by the diversity of its constituents. Quantum memories are one of the building blocks of a quantum network, enabling the storage of quantum states of light and the entanglement distribution over long distances. In our group, two different types of memories are investigated: a cold atomic ensemble and an ion-doped crystal. In this thesis I investigate the quantum frequency conversion of narrow-band photons, emitted or absorbed by optical quantum memories, with two different objectives: the first one is to connect quantum memories emitting or absorbing visible single photons with the telecommunication wavelengths, where fiber transmission loss is minimum. The second and main goal is to study the compatibility between disparate quantum nodes, emitting or absorbing photons at different wavelengths. More precisely the objective is to achieve a quantum connection between the two optical memories studied using quantum frequency conversion techniques. The main core of this work is the quantum frequency conversion interface that bridges the gap between the cold ensemble of Rubidium atoms, emitting photons at 780nm, and the Praseodymium ion doped crystal, absorbing photons at 606nm. This interface is composed of two different frequency conversion devices, where a cascaded conversions takes place: the first one converts 780nm photons to the telecommunication C-band, and the second one converts them back to visible, at 606nm. This comes with several challenges such as conversion efficiency, phase stability and parasitic noise reduction, which are important considerations to show the conservation of quantum behaviors through the conversion process. This work can be divided in three parts. In a first one, we built a quantum frequency conversion interface between 606nm and the C-band wavelength, capable of both up and down-conversion of single photon level light. We also characterized the noise processes involved in this specific conversion. In the down-conversion case we showed that memory compatible heralded single photons emitted from a photon pair source preserve their non-classical properties through the conversion process. In the up-conversion case, we showed the storage of converted telecom photons in the praseodymium doped crystal, and their retrieval with high signal to noise ratio. The second part of the work was devoted to the conversion of photons from an emissive Rubidium atomic quantum memory to the telecom C band. In this work we converted the heralding photons from the atomic ensemble and measured non-classical correlations between a stored excitation and a C-band photon, necessary for quantum repeater applications. In the last part of the thesis, we setup the full frequency conversion interface and showed that heralded photons emitted by the atomic ensemble are converted, stored in the solid state memory and retrieved with high signal to noise ratio. We demonstrated that a single collective excitation stored in the atomic ensemble is transfered to the crystal by mean of a single photon at telecom wavelength. We also showed time-bin qubit transfer between the two quantum memories. This work represents the first proof of principle of a photonic quantum connection between disparate quantum memory nodes. The results presented in this thesis pave the way towards the realization of modular and hybrid quantum networks.