Entanglement of single-atom quantum bits at a distance

Quantum information science involves the storage, manipulation and communication of information encoded in quantum systems, where the phenomena of superposition and entanglement can provide enhancements over what is possible classically. Large-scale quantum information processors require stable and addressable quantum memories, usually in the form of fixed quantum bits (qubits), and a means of transferring and entangling the quantum information between memories that may be separated by macroscopic or even geographic distances. Atomic systems are excellent quantum memories, because appropriate internal electronic states can coherently store qubits over very long timescales. Photons, on the other hand, are the natural platform for the distribution of quantum information between remote qubits, given their ability to traverse large distances with little perturbation. Recently, there has been considerable progress in coupling small samples of atomic gases through photonic channels, including the entanglement between light and atoms and the observation of entanglement signatures between remotely located atomic ensembles. In contrast to atomic ensembles, single-atom quantum memories allow the implementation of conditional quantum gates through photonic channels, a key requirement for quantum computing. Along these lines, individual atoms have been coupled to photons in cavities, and trapped atoms have been linked to emitted photons in free space. Here we demonstrate the entanglement of two fixed single-atom quantum memories separated by one metre. Two remotely located trapped atomic ions each emit a single photon, and the interference and detection of these photons signals the entanglement of the atomic qubits. We characterize the entangled pair by directly measuring qubit correlations with near-perfect detection efficiency. Although this entanglement method is probabilistic, it is still in principle useful for subsequent quantum operations and scalable quantum information applications.     

Mapping photonic entanglement into and out of a quantum memory

Developments in quantum information science rely critically on entanglement-a fundamental aspect of quantum mechanics that causes parts of a composite system to show correlations stronger than can be explained classically. In particular, scalable quantum networks require the capability to create, store and distribute entanglement among distant matter nodes by means of photonic channels. Atomic ensembles can play the role of such nodes. So far, in the photon-counting regime, heralded entanglement between atomic ensembles has been successfully demonstrated through probabilistic protocols. But an inherent drawback of this approach is the compromise between the amount of entanglement and its preparation probability, leading to intrinsically low count rates for high entanglement. Here we report a protocol where entanglement between two atomic ensembles is created by coherent mapping of an entangled state of light. By splitting a single photon and performing subsequent state transfer, we separate the generation of entanglement and its storage. After a programmable delay, the stored entanglement is mapped back into photonic modes with overall efficiency of 17%. Together with improvements in single-photon sources, our protocol will allow 'on-demand' entanglement of atomic ensembles, a powerful resource for quantum information science.     

任意多光子Dicke态的制备

量子Dicke态对于多粒子量子纠缠结构和性质的研究,以及量子网络的构建有着重要的意义.基于线性光学和交叉相位调制技术,利用三个基本量子门,给出了四光子Dicke态制备、任意系数W态制备以及任意系数和光子数的Dicke态制备方案.这些方案的确定性、任意性、高效性将为研究量子纠缠结构性质以及量子网络提供一定的便利.     

Interaction-based quantum metrology showing scaling beyond the Heisenberg limit

Quantum metrology aims to use entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the standard quantum limit of sensitivity, δχ?∝?N(-1/2). However, using N entangled particles and exotic states, such an interferometer can in principle achieve the Heisenberg limit, δχ?∝?N(-1). Recent theoretical work has argued that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ?∝?N(-k) with appropriate entangled states and δχ?∝?N(-(k-1/2)) even without entanglement. Here we demonstrate 'super-Heisenberg' scaling of δχ?∝?N(-3/2) in a nonlinear, non-destructive measurement of the magnetization of an atomic ensemble. We use fast optical nonlinearities to generate a pairwise photon-photon interaction (corresponding to k = 2) while preserving quantum-noise-limited performance. We observe super-Heisenberg scaling over two orders of magnitude in N, limited at large numbers by higher-order nonlinear effects, in good agreement with theory. For a measurement of limited duration, super-Heisenberg scaling allows the nonlinear measurement to overtake in sensitivity a comparable linear measurement with the same number of photons. In other situations, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship between scaling and sensitivity in nonlinear systems. Our work shows that interparticle interactions can improve sensitivity in a quantum-limited measurement, and experimentally demonstrates a new resource for quantum metrology.     

Stimulated emission of polarization-entangled photons

Entangled photon pairs-discrete light quanta that exhibit non-classical correlations-play a crucial role in quantum information science (for example, in demonstrations of quantum non-locality, quantum teleportation and quantum cryptography). At the macroscopic optical-field level non-classical correlations can also be important, as in the case of squeezed light, entangled light beams and teleportation of continuous quantum variables. Here we use stimulated parametric down-conversion to study entangled states of light that bridge the gap between discrete and macroscopic optical quantum correlations. We demonstrate experimentally the onset of laser-like action for entangled photons, through the creation and amplification of the spin-1/2 and spin-1 singlet states consisting of two and four photons, respectively. This entanglement structure holds great promise in quantum information science where there is a strong demand for entangled states of increasing complexity.     

非对称偏振三维纠缠态的预警制备

在量子信息处理过程中,量子纠缠态扮演着极为重要的角色,其特殊的物理性质,使得量子信息具有经典信息所没有的许多新的特征,为信息传输和信息处理提供了新的物理资源.针对非对称偏振三维纠缠态的制备,基于交叉相位调制技术,以纠缠光子对和两个单光子比特作为初态,通过单光子与相干光的相互作用以及双光子干涉来实现.如果通过三个非计数单光子探测器来预警制备三维最大纠缠态,其概率为3/64.而如果采用特殊的分段式光子探测器,其概率可以提高到3/8,达到理论极限值.该方案在理论上是可行的,效率相对较高,而且预警式的制备为其后续在量子信息过程中的使用提供了很大的灵活性.     

Generation of ultraviolet entangled photons in a semiconductor

Entanglement is one of the key features of quantum information and communications technology. The method that has been used most frequently to generate highly entangled pairs of photons is parametric down-conversion. Short-wavelength entangled photons are desirable for generating further entanglement between three or four photons, but it is difficult to use parametric down-conversion to generate suitably energetic entangled photon pairs. One method that is expected to be applicable for the generation of such photons is resonant hyper-parametric scattering (RHPS): a pair of entangled photons is generated in a semiconductor via an electronically resonant third-order nonlinear optical process. Semiconductor-based sources of entangled photons would also be advantageous for practical quantum technologies, but attempts to generate entangled photons in semiconductors have not yet been successful. Here we report experimental evidence for the generation of ultraviolet entangled photon pairs by means of biexciton resonant RHPS in a single crystal of the semiconductor CuCl. We anticipate that our results will open the way to the generation of entangled photons by current injection, analogous to current-driven single photon sources.     

Entanglement of spin waves among four quantum memories

Quantum networks are composed of quantum nodes that interact coherently through quantum channels, and open a broad frontier of scientific opportunities. For example, a quantum network can serve as a 'web' for connecting quantum processors for computation and communication, or as a 'simulator' allowing investigations of quantum critical phenomena arising from interactions among the nodes mediated by the channels. The physical realization of quantum networks generically requires dynamical systems capable of generating and storing entangled states among multiple quantum memories, and efficiently transferring stored entanglement into quantum channels for distribution across the network. Although such capabilities have been demonstrated for diverse bipartite systems, entangled states have not been achieved for interconnects capable of 'mapping' multipartite entanglement stored in quantum memories to quantum channels. Here we demonstrate measurement-induced entanglement stored in four atomic memories; user-controlled, coherent transfer of the atomic entanglement to four photonic channels; and characterization of the full quadripartite entanglement using quantum uncertainty relations. Our work therefore constitutes an advance in the distribution of multipartite entanglement across quantum networks. We also show that our entanglement verification method is suitable for studying the entanglement order of condensed-matter systems in thermal equilibrium.     

De Broglie wavelength of a non-local four-photon state

Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit, or quantum lithography beyond the classical diffraction limit. It has been generally understood that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.     

Scalable multiparticle entanglement of trapped ions

The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the 'W state' plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, 'Greenberger-Horne-Zeilinger' entangled states with up to six ions have been created and analysed in Boulder.     

Experimental entanglement distillation and 'hidden' non-locality

Entangled states are central to quantum information processing, including quantum teleportation, efficient quantum computation and quantum cryptography. In general, these applications work best with pure, maximally entangled quantum states. However, owing to dissipation and decoherence, practically available states are likely to be non-maximally entangled, partially mixed (that is, not pure), or both. To counter this problem, various schemes of entanglement distillation, state purification and concentration have been proposed. Here we demonstrate experimentally the distillation of maximally entangled states from non-maximally entangled inputs. Using partial polarizers, we perform a filtering process to maximize the entanglement of pure polarization-entangled photon pairs generated by spontaneous parametric down-conversion. We have also applied our methods to initial states that are partially mixed. After filtering, the distilled states demonstrate certain non-local correlations, as evidenced by their violation of a form of Bell's inequality. Because the initial states do not have this property, they can be said to possess 'hidden' non-locality.     

An open-system quantum simulator with trapped ions

The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating quantum systems from the environment and coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled coupling to an environment remains largely unexplored. Here we realize an experimental toolbox for simulating an open quantum system with up to five quantum bits (qubits). Using a quantum computing architecture with trapped ions, we combine multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate our ability to engineer the open-system dynamics through the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions, and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation.     

High-speed linear optics quantum computing using active feed-forward

As information carriers in quantum computing, photonic qubits have the advantage of undergoing negligible decoherence. However, the absence of any significant photon-photon interaction is problematic for the realization of non-trivial two-qubit gates. One solution is to introduce an effective nonlinearity by measurements resulting in probabilistic gate operations. In one-way quantum computation, the random quantum measurement error can be overcome by applying a feed-forward technique, such that the future measurement basis depends on earlier measurement results. This technique is crucial for achieving deterministic quantum computation once a cluster state (the highly entangled multiparticle state on which one-way quantum computation is based) is prepared. Here we realize a concatenated scheme of measurement and active feed-forward in a one-way quantum computing experiment. We demonstrate that, for a perfect cluster state and no photon loss, our quantum computation scheme would operate with good fidelity and that our feed-forward components function with very high speed and low error for detected photons. With present technology, the individual computational step (in our case the individual feed-forward cycle) can be operated in less than 150 ns using electro-optical modulators. This is an important result for the future development of one-way quantum computers, whose large-scale implementation will depend on advances in the production and detection of the required highly entangled cluster states.     

Entanglement of the orbital angular momentum states of photons.

Entangled quantum states are not separable, regardless of the spatial separation of their components. This is a manifestation of an aspect of quantum mechanics known as quantum non-locality. An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement. Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons. Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum. As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography.     

Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles

Quantum information science attempts to exploit capabilities from the quantum realm to accomplish tasks that are otherwise impossible in the classical domain. Although sufficient conditions have been formulated for the physical resources required to achieve quantum computation and communication, there is a growing understanding of the power of quantum measurement combined with the conditional evolution of quantum states for accomplishing diverse tasks in quantum information science. For example, a protocol has recently been developed for the realization of scalable long-distance quantum communication and the distribution of entanglement over quantum networks. Here we report the first enabling step in the realization of this protocol, namely the observation of quantum correlations for photon pairs generated in the collective emission from an atomic ensemble. The nonclassical character of the fields is demonstrated by the violation of an inequality involving their normalized correlation functions. Compared to previous investigations of non-classical correlations for photon pairs produced in atomic cascades and in parametric down-conversion, our experiment is distinct in that the correlated photons are separated by a programmable time interval (of about 400 nanoseconds in our initial experiments).     

Experimental determination of entanglement with a single measurement

Nearly all protocols requiring shared quantum information--such as quantum teleportation or key distribution--rely on entanglement between distant parties. However, entanglement is difficult to characterize experimentally. All existing techniques for doing so, including entanglement witnesses or Bell inequalities, disclose the entanglement of some quantum states but fail for other states; therefore, they cannot provide satisfactory results in general. Such methods are fundamentally different from entanglement measures that, by definition, quantify the amount of entanglement in any state. However, these measures suffer from the severe disadvantage that they typically are not directly accessible in laboratory experiments. Here we report a linear optics experiment in which we directly observe a pure-state entanglement measure, namely concurrence. Our measurement set-up includes two copies of a quantum state: these 'twin' states are prepared in the polarization and momentum degrees of freedom of two photons, and concurrence is measured with a single, local measurement on just one of the photons.     

利用两能级原子与相干态腔场相互作用实现纠缠浓缩

根据大失谐条件下原子–腔场相互作用的特点,讨论了一个制备纠缠相干态的方法,提出了一个利用两能级原子与腔场相干态相互作用实现纠缠浓缩的方案。在这个方案中,2个具有相同振幅但有着π相位差的相干光|α〉和|-α〉构成的纠缠态光场被用来作为量子信道,通过利用两能级原子与腔场的相互作用以及两模正交态测量实现了这个纠缠浓缩的过程。结果表明:对于纠缠相干态,无论其初始的纠缠是多么微弱,利用这种方法总有一定的几率可以从部分纠缠态中提取出最大纠缠态。     

Controlling cavity reflectivity with a single quantum dot

Solid-state cavity quantum electrodynamics (QED) systems offer a robust and scalable platform for quantum optics experiments and the development of quantum information processing devices. In particular, systems based on photonic crystal nanocavities and semiconductor quantum dots have seen rapid progress. Recent experiments have allowed the observation of weak and strong coupling regimes of interaction between the photonic crystal cavity and a single quantum dot in photoluminescence. In the weak coupling regime, the quantum dot radiative lifetime is modified; in the strong coupling regime, the coupled quantum dot also modifies the cavity spectrum. Several proposals for scalable quantum information networks and quantum computation rely on direct probing of the cavity-quantum dot coupling, by means of resonant light scattering from strongly or weakly coupled quantum dots. Such experiments have recently been performed in atomic systems and superconducting circuit QED systems, but not in solid-state quantum dot-cavity QED systems. Here we present experimental evidence that this interaction can be probed in solid-state systems, and show that, as expected from theory, the quantum dot strongly modifies the cavity transmission and reflection spectra. We show that when the quantum dot is coupled to the cavity, photons that are resonant with its transition are prohibited from entering the cavity. We observe this effect as the quantum dot is tuned through the cavity and the coupling strength between them changes. At high intensity of the probe beam, we observe rapid saturation of the transmission dip. These measurements provide both a method for probing the cavity-quantum dot system and a step towards the realization of quantum devices based on coherent light scattering and large optical nonlinearities from quantum dots in photonic crystal cavities.     

Controlled exchange interaction between pairs of neutral atoms in an optical lattice

Ultracold atoms trapped by light offer robust quantum coherence and controllability, providing an attractive system for quantum information processing and for the simulation of complex problems in condensed matter physics. Many quantum information processing schemes require the manipulation and deterministic entanglement of individual qubits; this would typically be accomplished using controlled, state-dependent, coherent interactions among qubits. Recent experiments have made progress towards this goal by demonstrating entanglement among an ensemble of atoms confined in an optical lattice. Until now, however, there has been no demonstration of a key operation: controlled entanglement between atoms in isolated pairs. Here we use an optical lattice of double-well potentials to isolate and manipulate arrays of paired (87)Rb atoms, inducing controlled entangling interactions within each pair. Our experiment realizes proposals to use controlled exchange coupling in a system of neutral atoms. Although 87Rb atoms have nearly state-independent interactions, when we force two atoms into the same physical location, the wavefunction exchange symmetry of these identical bosons leads to state-dependent dynamics. We observe repeated interchange of spin between atoms occupying different vibrational levels, with a coherence time of more than ten milliseconds. This observation demonstrates the essential component of a neutral atom quantum SWAP gate (which interchanges the state of two qubits). Its 'half-implementation', the root SWAP gate, is entangling, and together with single-qubit rotations it forms a set of universal gates for quantum computation.     

3-qubit量子相位门的纠缠能力

研究了3-qubit量子纯态性质与其单体约化密度矩阵之间的关系,给出判断3-qubit最大纠缠纯态和直积态的一种简便判据,并利用此判据研究了一种简单的量子计算模型,推导出该模型下3-qubit量子相位门的纠缠能力.