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IEEE/LEOS Summer Topical Meetings

Low-noise frequency downconversion for long-distance distribution of entangled atomic qubits

Jungsang Kim, Ryan Clark, Daniel J. Gauthier

Published Jul 1, 2013• 1 citation
Publisher

Abstract

Distribution of quantum resources such as entanglement over distances beyond a few fiber attenuation lengths requires realization of quantum repeaters that utilize entanglement swapping to extend the distance between the entangled qubit pairs [1]. A quantum repeater is a small quantum computer capable of generating entangled qubit pairs with its neighboring repeaters and storing them in stable quantum memories. Once the entangled pairs are generated, it will perform Bell basis measurements, classical communication with appropriate repeaters, and single qubit gates necessary for entanglement swapping. For high fidelity operation, it might perform local operations and classical communications (LOCC) such as entanglement distillation [2] and/or quantum error correction [3,4]. Generation of remote entangled ion pairs mediated by photonic qubits has been demonstrated [5] but their reach is limited since the photons used in the experiment are in the UV part of the spectrum. Coherent conversion of the photons emitted by Yb ion at 369.5nm to a photon at 1310 nm would enable entanglement generation over long distances [6].

DOI
10.1109/phosst.2013.6614563

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Distribution of quantum resources such as entanglement over distances beyond a few fiber attenuation lengths requires realization of quantum repeaters that utilize entanglement swapping to extend the distance between the entangled qubit pairs [1]. A quantum repeater is a small quantum computer capable of generating entangled qubit pairs with its neighboring repeaters and storing them in stable quantum memories. Once the entangled pairs are generated, it will perform Bell basis measurements, classical communication with appropriate repeaters, and single qubit gates necessary for entanglement swapping. For high fidelity operation, it might perform local operations and classical communications (LOCC) such as entanglement distillation [2] and/or quantum error correction [3,4]. Generation of remote entangled ion pairs mediated by photonic qubits has been demonstrated [5] but their reach is limited since the photons used in the experiment are in the UV part of the spectrum. Coherent conversion of the photons emitted by Yb ion at 369.5nm to a photon at 1310 nm would enable entanglement generation over long distances [6].
Generating entangled states of quantum memories over a long distance is an essential component for scalable quantum communication and its application such as quantum key distribution. Generation of entangled ion pairs mediated by photonic qubits has been demonstrated with trapped ytterbium (Yb) ions [1] and is a promising approach. However the wavelength of a single photon emitted by most trapped ions is in the ultraviolet (UV) or short-wavelength visible range where the maximum distribution distance of the photons is severely limited due to high absorption coefficient in a single mode optical fiber. To overcome this limitation, we are currently developing a frequency down-conversion scheme [2,3] which can coherently transfer a qubit stored in a 370 nm photon emitted by a Yb ion to another photon at 1310 nm which coincides with the low loss window of a telecom fiber.
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.
Quantum key distribution systems represent a proven method to obtain fundamentally secure communication channels. However, the loss of entangled photons which create the encryption key limit the distance over which the systems are useful. Quantum repeaters have been used to increase the distance over which entangled photons can be transmitted. The most successful quantum repeaters entangle information between trapped ions and single photons and through the use of entanglement swapping protocols, relay the encryption keys over large distances. A requirement of these quantum repeaters is the ability to work in the telecom wavelengths (1310 nm or 1550 nm), where standard silica fibers exhibit low loss. With the majority of ions emitting in the ultraviolet and visible spectrum, and ytterbium in particular emitting at 369.5 nm, a conversion process is then needed that can translate the photons from 369.5 nm to the telecom band while preserving the entangled state. The experiment presented here details the first stage of a nonlinear frequency conversion setup that uses strong pump light to enable the conversion of 369.5 nm photons to 708 nm. The efficiency of the conversion process is analyzed to determine the optimum system parameters, with an initial single pass conversion efficiency of 0.20% achieved. Noise introduced during the nonlinear conversion process is examined to determine the effect it presents on the communication channel.
Quantum communication between two remote locations often involves remote parties sharing an entangled quantum state. At present, entanglement distribution is usually performed using photons transmitted through optical fibers. However, the absorption of light in the fiber limits the communication distances to less than 200 km, even for optimal photon telecom wavelengths. To increase this distance, the quantum repeater idea was proposed. In the quantum repeater architecture, one divides communication distance into segments of the order of the attenuation length of the photons and places quantum memory nodes at the intermediate locations. Since the photon loss between intermediate locations is low, it is possible then to establish entanglement between intermediate quantum memory nodes. Once entanglement between adjacent nodes is established, one can extend it over larger distances using entanglement swapping.\n\nThe long coherence time of a quantum memory is a crucial requirement for the quantum repeater protocol. It is obvious that the coherence time of a quantum memory should be much longer that the time it takes for light to travel between remote locations. For a communication distance l = 1000 km, the corresponding time is t = l/c = 3.3 ms. One can show that for a simple repeater protocol and realistic success probabilities of entanglement generation, the required coherence time should be on the order of many seconds, while for the more complicated protocols that involve multiplexing and several quantum memory cells per intermediate node, the required coherence time is on the order of milliseconds.\n\nIn this thesis, I describe a quantum memory based on an ensemble of rubidium atoms confined in a one-dimensional optical lattice. The use of the magnetically- insensitive clock transition and suppression of atomic motion allows us to increase coherence time of the quantum memory by two-orders of magnitude compared to previous work. I also propose a method for determining the Zeeman content of atomic samples. In addition, I demonstrate the observation of quantum evolution under continuous measurement. The long quantum memory lifetime demonstrated in this work opens the way for scalable processing of quantum information and long distance quantum communication.
We describe a quantum repeater protocol for long-distance quantum communication. In this scheme, entanglement is created between qubits at intermediate stations of the channel by using a weak dispersive light-matter interaction and distributing the outgoing bright coherent-light pulses among the stations. Noisy entangled pairs of electronic spin are then prepared with high success probability via homodyne detection and postselection. The local gates for entanglement purification and swapping are deterministic and measurement-free, based upon the same coherent-light resources and weak interactions as for the initial entanglement distribution. Finally, the entanglement is stored in a nuclear-spin-based quantum memory. With our system, qubit-communication rates approaching 100 Hz over 1280 km with fidelities near 99% are possible for reasonable local gate errors.
Long-distance entanglement distribution will require error correction/distillation in order to compensate for the loss of coherence in quantum memories and noise addition during entanglement swapping. In this paper, we argue why repeaters with error correction abilities should utilize more than one physical platform. Hybrid repeaters introduced in this work, utilize the best features of different platforms, such as high entanglement generation rates of one type and the low two-qubit gate errors and high coherence times offered by another type. At the same time, taking the resource-intensive nature of hybrid repeaters (financial or difficulty of deployment) into account, we propose a repeater chain where only some repeaters need to be hybrid, whereas the others can be simpler with no error correction abilities. We show through detailed simulations that these hybrid repeater architectures can outperform architectures that rely only on a single kind of quantum memory platform in terms of end-to-end fidelity and entanglement distribution rates/secret key rates. The advantage is greater in more resourceconstrained scenarios, making hybrid architectures relevant for current implementations.