Quantum interference between two single photons emitted by independently trapped atoms

When two indistinguishable single photons are fed into the two input ports of a beam splitter, the photons will coalesce and leave together from the same output port. This is a quantum interference effect, which occurs because two possible paths-in which the photons leave by different output ports-interfere destructively. This effect was first observed in parametric downconversion (in which a nonlinear crystal splits a single photon into two photons of lower energy), then from two separate downconversion crystals, as well as with single photons produced one after the other by the same quantum emitter. With the recent developments in quantum information research, much attention has been devoted to this interference effect as a resource for quantum data processing using linear optics techniques. To ensure the scalability of schemes based on these ideas, it is crucial that indistinguishable photons are emitted by a collection of synchronized, but otherwise independent sources. Here we demonstrate the quantum interference of two single photons emitted by two independently trapped single atoms, bridging the gap towards the simultaneous emission of many indistinguishable single photons by different emitters. Our data analysis shows that the observed coalescence is mainly limited by wavefront matching of the light emitted by the two atoms, and to a lesser extent by the motion of each atom in its own trap.     

Plasmon-assisted transmission of entangled photons

The state of a two-particle system is said to be entangled when its quantum-mechanical wavefunction cannot be factorized into two single-particle wavefunctions. This leads to one of the strongest counter-intuitive features of quantum mechanics, namely non-locality. Experimental realization of quantum entanglement is relatively easy for photons; a starting photon can spontaneously split into a pair of entangled photons inside a nonlinear crystal. Here we investigate the effects of nanostructured metal optical elements on the properties of entangled photons. To this end, we place optically thick metal films perforated with a periodic array of subwavelength holes in the paths of the two entangled photons. Such arrays convert photons into surface-plasmon waves--optically excited compressive charge density waves--which tunnel through the holes before reradiating as photons at the far side. We address the question of whether the entanglement survives such a conversion process. Our coincidence counting measurements show that it does, so demonstrating that the surface plasmons have a true quantum nature. Focusing one of the photon beams on its array reduces the quality of the entanglement. The propagation of the surface plasmons makes the array effectively act as a 'which way' detector.     

Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement

Bell's theorem states that certain statistical correlations predicted by quantum physics for measurements on two-particle systems cannot be understood within a realistic picture based on local properties of each individual particle-even if the two particles are separated by large distances. Einstein, Podolsky and Rosen first recognized the fundamental significance of these quantum correlations (termed 'entanglement' by Schrodinger) and the two-particle quantum predictions have found ever-increasing experimental support. A more striking conflict between quantum mechanical and local realistic predictions (for perfect correlations) has been discovered; but experimental verification has been difficult, as it requires entanglement between at least three particles. Here we report experimental confirmation of this conflict, using our recently developed method to observe three-photon entanglement, or 'Greenberger-Horne-Zeilinger' (GHZ) states. The results of three specific experiments, involving measurements of polarization correlations between three photons, lead to predictions for a fourth experiment; quantum physical predictions are mutually contradictory with expectations based on local realism. We find the results of the fourth experiment to be in agreement with the quantum prediction and in striking conflict with local realism.     

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.     

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.     

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.     

Observation of Hanbury Brown-Twiss anticorrelations for free electrons

Fluctuations in the counting rate of photons originating from uncorrelated point sources become, within the coherently illuminated area, slightly enhanced compared to a random sequence of classical particles. This phenomenon, known in astronomy as the Hanbury Brown-Twiss effect, is a consequence of quantum interference between two indistinguishable photons and Bose Einstein statistics. The latter require that the composite bosonic wavefunction is a symmetric superposition of the two possible paths. For fermions, the corresponding two-particle wavefunction is antisymmetric: this excludes overlapping wave trains, which are forbidden by the Pauli exclusion principle. Here we use an electron field emitter to coherently illuminate two detectors, and find anticorrelations in the arrival times of the free electrons. The particle beam has low degeneracy (about 10(-4) electrons per cell in phase space); as such, our experiment represents the fermionic twin of the Hanbury Brown-Twiss effect for photons.     

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.     

Preparation and measurement of three-qubit entanglement in a superconducting circuit

Traditionally, quantum entanglement has been central to foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can have results at odds with classical behaviour. These discrepancies grow exponentially with the number of entangled particles. With the ample experimental confirmation of quantum mechanical predictions, entanglement has evolved from a philosophical conundrum into a key resource for technologies such as quantum communication and computation. Although entanglement in superconducting circuits has been limited so far to two qubits, the extension of entanglement to three, eight and ten qubits has been achieved among spins, ions and photons, respectively. A key question for solid-state quantum information processing is whether an engineered system could display the multi-qubit entanglement necessary for quantum error correction, which starts with tripartite entanglement. Here, using a circuit quantum electrodynamics architecture, we demonstrate deterministic production of three-qubit Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88 per cent, measured with quantum state tomography. Several entanglement witnesses detect genuine three-qubit entanglement by violating biseparable bounds by 830?±?80 per cent. We demonstrate the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of this encoding with decoding and error-correcting steps in a feedback loop will be the next step for quantum computing with integrated circuits.     

Squeezing and entanglement in a Bose-Einstein condensate

Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound attainable by classical means. This results in the standard quantum limit, which is reached in today's best available sensors of various quantities such as time and position. Many of these sensors are interferometers in which the standard quantum limit can be overcome by using quantum-entangled states (in particular spin squeezed states) at the two input ports. Bose-Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles. Here we demonstrate spin squeezed states suitable for atomic interferometry by splitting a condensate into a few parts using a lattice potential. Site-resolved detection of the atoms allows the measurement of the atom number difference and relative phase, which are conjugate variables. The observed fluctuations imply entanglement between the particles, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.     

Spatial quantum noise interferometry in expanding ultracold atom clouds

In a pioneering experiment, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations--together with their fermionic counterparts--find numerous applications, ranging from quantum optics to nuclear and elementary particle physics. Spatial HBT interferometry has been suggested as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms.     

Experimental extraction of an entangled photon pair from two identically decohered pairs

Entanglement is considered to be one of the most important resources in quantum information processing schemes, including teleportation, dense coding and entanglement-based quantum key distribution. Because entanglement cannot be generated by classical communication between distant parties, distribution of entangled particles between them is necessary. During the distribution process, entanglement between the particles is degraded by the decoherence and dissipation processes that result from unavoidable coupling with the environment. Entanglement distillation and concentration schemes are therefore needed to extract pairs with a higher degree of entanglement from these less-entangled pairs; this is accomplished using local operations and classical communication. Here we report an experimental demonstration of extraction of a polarization-entangled photon pair from two decohered photon pairs. Two polarization-entangled photon pairs are generated by spontaneous parametric down-conversion and then distributed through a channel that induces identical phase fluctuations to both pairs; this ensures that no entanglement is available as long as each pair is manipulated individually. Then, through collective local operations and classical communication we extract from the two decohered pairs a photon pair that is observed to be polarization-entangled.     

Comparison of the Hanbury Brown-Twiss effect for bosons and fermions

Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in light emitted by a chaotic source, highlighting the importance of two-photon correlations and stimulating the development of modern quantum optics. The quantum interpretation of bunching relies on the constructive interference between amplitudes involving two indistinguishable photons, and its additive character is intimately linked to the Bose nature of photons. Advances in atom cooling and detection have led to the observation and full characterization of the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions should reveal an antibunching effect (a tendency to avoid each other). Antibunching of fermions is associated with destructive two-particle interference, and is related to the Pauli principle forbidding more than one identical fermion to occupy the same quantum state. Here we report an experimental comparison of the fermionic and bosonic HBT effects in the same apparatus, using two different isotopes of helium: (3)He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible; therefore, the contrasting bunching and antibunching behaviour that we observe can be fully attributed to the different quantum statistics of each atomic species. Our results show how atom-atom correlation measurements can be used to reveal details in the spatial density or momentum correlations in an atomic ensemble. They also enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations.     

Observation of the dynamical Casimir effect in a superconducting circuit

One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. Although initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences--for instance, producing the Lamb shift of atomic spectra and modifying the magnetic moment of the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed whether it might be possible to more directly observe the virtual particles that compose the quantum vacuum. Forty years ago, it was suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. The phenomenon, later termed the dynamical Casimir effect, has not been demonstrated previously. Here we observe the dynamical Casimir effect in a superconducting circuit consisting of a coplanar transmission line with a tunable electrical length. The rate of change of the electrical length can be made very fast (a substantial fraction of the speed of light) by modulating the inductance of a superconducting quantum interference device at high frequencies (>10 gigahertz). In addition to observing the creation of real photons, we detect two-mode squeezing in the emitted radiation, which is a signature of the quantum character of the generation process.     

Detection of doubled shot noise in short normal-metal/superconductor junctions

Shot noise refers to the fluctuations in electrical current through a device arising from the discrete nature of the charge-carrying particles. Recent experiments have exploited the fact that the shot noise is proportional to the charge of the carriers to establish fractional quantization of quasiparticles in the fractional quantum Hall effect. By a similar argument, it is expected that when a superconducting reservoir emits Cooper pairs, (which have a charge twice that of an electron) into a short normal-metal wire, the shot noise should be double that obtained for a normal-metal reservoir. Although the charge of Cooper pairs has been well established by flux quantization and tunnel experiments, doubling of their shot noise has not yet been observed. Here we report a shot-noise experiment using a short diffusive normal-metal superconductor contact, in which we confirm the predicted noise behaviour for double charges. The measurements, taken over a large range of bias current, establish that phase coherence is not required to observe the effect.     

Super-resolving phase measurements with a multiphoton entangled state

Interference phenomena are ubiquitous in physics, often forming the basis of demanding measurements. Examples include Ramsey interferometry in atomic spectroscopy, X-ray diffraction in crystallography and optical interferometry in gravitational-wave studies. It has been known for some time that the quantum property of entanglement can be exploited to perform super-sensitive measurements, for example in optical interferometry or atomic spectroscopy. The idea has been demonstrated for an entangled state of two photons, but for larger numbers of particles it is difficult to create the necessary multiparticle entangled states. Here we demonstrate experimentally a technique for producing a maximally entangled three-photon state from initially non-entangled photons. The method can in principle be applied to generate states of arbitrary photon number, giving arbitrarily large improvement in measurement resolution. The method of state construction requires non-unitary operations, which we perform using post-selected linear-optics techniques similar to those used for linear-optics quantum computing.     

Optical microcavities

Optical microcavities confine light to small volumes by resonant recirculation. Devices based on optical microcavities are already indispensable for a wide range of applications and studies. For example, microcavities made of active III-V semiconductor materials control laser emission spectra to enable long-distance transmission of data over optical fibres; they also ensure narrow spot-size laser read/write beams in CD and DVD players. In quantum optical devices, microcavities can coax atoms or quantum dots to emit spontaneous photons in a desired direction or can provide an environment where dissipative mechanisms such as spontaneous emission are overcome so that quantum entanglement of radiation and matter is possible. Applications of these remarkable devices are as diverse as their geometrical and resonant properties.     

Efficient quantum computing using coherent photon conversion

Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting systems with extremely strong intrinsic nonlinearities. Furthermore, exploiting higher-order nonlinearities with multiple pump fields yields a mechanism for multiparty mediation of the complex, coherent dynamics.     

Experimental demonstration of a BDCZ quantum repeater node

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, Dür, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.